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desheaflashcards.txt
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These flashcards were created to accompany DeShea & Toothaker's book "Introductory Statistics for the Health Sciences," 2015, Chapman & Hall/CRC Press.
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  1. Definition of science
    An area of study that objectively, systematically and impartially weighs empirical evidence for the purpose of discovering and verifying order within and between phenomena
  2. Definition of research
    Scientific structured problem solving
  3. Definition of qualitative research
    An approach to research involving in-depth description of a topic with the goal of obtaining a rich understanding of some phenomenon
  4. Definition of quantitative research
    An approach to research that relies on prior research to generate research questions and often to make predictions, with the results being analyzed mathematically
  5. Definition of data
    Information collected by researchers for later analysis to answer research questions
  6. Does having non-numeric data mean the research is qualitative?
    No, quantitative researchers may collect non-numeric data, such as gender, diagnosis, medications being prescribed, etc. Qualitative research is an entirely different approach to studying phenomena, with the goal of obtaining nuanced understanding of the topic
  7. Definition of mixed-methods research
    Research that involves two parts: a qualitative study and a quantitative study
  8. Definition of statistics
    Numerical summary measures computed on data
  9. Definition of a mean
    An arithmetic average
  10. Definition of literature review
    Process of identifying and reading articles and books about a topic on which subsequent research may be conducted
  11. Definition of theory
    An organized, research-supported explanation and prediction of phenomena
  12. Meaning of 'designing a study'
    Process of making decisions about the plans for a study, such as whether repeated measures or different groups of participants are needed
  13. Definition of population
    Larger group of people to whom we would like to generalize our results, or the larger group of entities that share a characteristic of interest to researchers
  14. Definition of unit of analysis
    The entity that is measured in a study. The unit of analysis often is the participant
  15. Definition of sample
    Subgroup of a population
  16. Characteristics of a population
    Large, usually unobtainable, sometimes hypothetical
  17. Why do we need samples?
    Because we can't get populations
  18. Definition of epidemiology
    The study of the distribution and spread of health conditions and diseases in human populations
  19. Definition of a variable
    A quantity or property that is free to vary or take on different values
  20. Definition of discrete variable
    A variable with discrete categories or values (example: gender)
  21. Definition of continuous variable
    A variable that theoretically could take on an infinite number of values between any two points (example: weight)
  22. Definition of bias
    A systematic influence on a study that makes the results inaccurate
  23. Definition of simple random sampling
    Process of obtaining a sample such that each participant is independently selected from the population
  24. Definition of sample size
    The number of people in a study (symbol is N)
  25. Definition of external validity
    Quality of our generalization from the sample back to the population
  26. Does simple random sampling require equal probability of selection?
    No. A random process involving independent selection of participants is required.
  27. Definition of convenience sample
    Groups of participants conveniently available to researchers
  28. Definition of judgment sample
    Same thing as a convenience sample
  29. Are magazine articles the same thing as journal articles?
    No, journal articles are published in scientific journals, such as the New England Journal of Medicine
  30. Definition of random assignment
    Process of placing participants into groups such that the placement of each participant is independent of the placement of any other participant
  31. Another term for random assignment
    Randomization
  32. Definition of manipulation or intervention
    The researchers' act of changing the experience of different groups of participants
  33. Definition of control
    Researchers' efforts to limit the effect of variables that may interfere with the ability to detect a relationship between other variables
  34. Definition of statistical replication
    Having a sample size greater than 1, or observing a phenomenon across multiple people or units of analysis
  35. Definition of experimental research
    Research which is characterized by random assignment of participants to groups, the researchers' manipulation of the participants' experiences, and statistical replication
  36. Definition of experiment
    Same as experimental research
  37. Definition of an independent variable
    A variable that is manipulated by the researcher. It comes first in time and is independent of the results
  38. Definition of levels
    The possible conditions or categories within an independent variable
  39. Definition of a dependent variable
    A variable that is measured as an outcome in experimental studies. It comes second in time
  40. Definition of an extraneous variable
    A variable that potentially interferes with the researchers' ability to detect the effect of the independent variable on the dependent variable
  41. Other terms for extraneous variable
    Confounding variable or lurking variable
  42. Definition of randomized controlled trials
    Studies in health sciences in which participants are randomized to groups and typically observed across time, with one group receiving a sham condition that mimics a real treatment but has no effect
  43. Definition of placebo
    A sham condition that is identical to the treatment condition except having no effect
  44. Definition of control group
    The group that receives a placebo or no intervention
  45. Definition of experimental group
    The group that receives an intervention
  46. Definition of treatment arm
    A term sometimes used to refer to an experimental condition in a study
  47. Definition of attention-control group
    A control group that receives some attention from the researcher but no intervention
  48. Definition of double-blinding
    A research method that keeps participants and the researchers who directly deal with them from knowing who is in which experimental condition
  49. Definition of randomized block design
    A study that contains at least one variable to which the participants cannot be randomly assigned, such as gender
  50. Definition of blocking variable
    A categorical variable with participants in naturally occurring or predefined groups. The variable is taken into account in the statistical analysis of the results
  51. Definition of blocking
    A method of incorporating a predictor variable (consisting of naturally occurring groups) into a study's design and statistically analyzing differences among levels of the predictor variable
  52. Definition of non-experimental research
    Research that lacks both random assignment to groups and manipulation of an independent variable
  53. Other terms for non-experimental research
    Observational research or descriptive research
  54. Definition of predictor variable
    A variable in descriptive/observational research that comes first in time and is thought to influence an outcome variable. It is analogous to the independent variable in an experiment, but researchers cannot randomly assign participants to conditions (example: gender)
  55. Definition of explanatory variable
    Another term used to describe a predictor variable
  56. Definition of a criterion variable
    In descriptive/observational research, it is the outcome variable that comes second in time. It is analogous to the dependent variable in an experiment
  57. Definition of response variable or outcome variable
    In non-experimental research, it is the same thing as the criterion variable
  58. Definition of case-control study
    A study in which people with a condition (the cases) are compared with otherwise-similar people who do not have the condition (the controls), then risk factors are assessed in an attempt to explain why some people have the condition and others don't
  59. Definition of cohort study
    A study in which people exposed or not exposed to a potential risk factor are compared by examining data across time, either retrospectively or prospectively
  60. Definition of cohort
    A group of people who share one or more characteristics and who are studied to assess eventual disease incidence or mortality
  61. Definition of quasi-experimental research
    Research characterized by manipulation of an independent variable, but in the absence of randomization
  62. Definition of an inference
    A conclusion drawn from information and reasoning
  63. Definition of internal validity
    Quality of inference about whether a causal relationship exists between variables
  64. Characteristics of experimental research
    Participants are randomly assigned to groups, an independent variable is manipulated, and there is statistical replication. This combination means we can make causal conclusions, thus we have good internal validity
  65. Characteristics of observational research
    Lack of randomization or manipulation, which means we can make only predictive conclusions, thus we have poor internal validity
  66. Characteristics of quasi-experimental research
    Lack of randomization, but presence of manipulation and statistical replication. The manipulative independent variable is one possible explanation for any observed differences, but internal validity is weak because of the lack of randomization
  67. Three ways of controlling extraneous variables associated with participants
    1) randomization 2) include the variable in the design as a factor to be studied 3) limit the study to make everyone the same on that variable (e.g., only females)
  68. What improves internal validity
    Randomization, because it controls extraneous variables that could interfere with the causal relationship between a manipulated independent variable and a dependent variable
  69. What improves external validity
    Random sampling from the population of interest
  70. Definition of descriptive statistics
    Statistics that summarize or describe information about a sample, such as the sample average blood pressure
  71. Another definition of statistic
    A numerical characteristic of a sample
  72. Definition of parameter
    A numerical characteristic of a population, such as the population average blood pressure
  73. What is an estimate of a parameter?
    A descriptive statistic estimates a parameter
  74. Definition of distribution
    A set of scores arranged on a number line
  75. Advantages of using the mean
    People understand it, and all scores in the sample go into its computation
  76. Disadvantage of using the mean
    One or more extreme scores can pull the mean in that direction
  77. Definition of the median
    Middle score in a distribution, or the score with the same number of scores below it and above it
  78. Advantage of using the median
    It is unaffected by extreme scores
  79. Definition of trimmed mean
    A mean computed on a data set from which some of the highest and lowest scores have been dropped. Also called a truncated mean
  80. Definition of the mode
    Most frequently occurring value or response (like the most commonly reported marital status in a sample)
  81. Disadvantages of using the mode
    There may be no mode if every value is equally occurring. There may be more than one mode. If numeric values are being analyzed, the mode may not be in the middle (e.g., if a lot of babies are at a family reunion, the most frequently occurring age may be 1, which doesn't describe the middle location of a distribution of the ages)
  82. Symbol for the sample mean
    M
  83. Definition of inferential statistics
    Statistics that are used for decision-making
  84. Symbol for the population mean
    Lower-case Greek letter mu
  85. Definition of variability
    The amount of spread or variation within a set of scores
  86. Definition of the range
    High score minus low score
  87. Why is the average distance from the mean a useless measure of variability?
    The distances below the mean balance out the distances above the mean, so the average distance from the mean is always zero
  88. Definition of sample variance
    The average squared distance from the mean
  89. Definition of sum of squares
    The process of squaring some numbers and adding them up
  90. How do we get the standard deviation based on the sample variance?
    Take the square root of the sample variance
  91. What does the sample variance estimate?
    Population variance
  92. Symbol for the population variance
    Lower-case Greek letter sigma, squared
  93. Symbol for the population standard deviation
    Lower-case Greek letter sigma
  94. Definition of unbiased variance
    A statistic computed by taking the sum of squared distances from the mean and dividing by N - 1
  95. How do we get the standard deviation based on the unbiased variance?
    Take the square root of the unbiased variance
  96. What do we get when you take the square root of a variance?
    A standard deviation
  97. What do we get when you square a standard deviation?
    A variance
  98. Name five measures of variability
    Range, sample variance, standard deviation based on sample variance, unbiased variance, standard deviation based on unbiased variance
  99. What numeric values can a standard deviation or variance have?
    Anything from zero and up
  100. Disadvantages of the sample variance and the unbiased variance
    They are both in squared units of measure. They are influenced by extreme scores. They are not intuitive
  101. What does it mean if a variance or standard deviation equals zero?
    All of the scores are the same. There is no variability
  102. Definition of skewness
    Degree of departure from symmetry
  103. A positively skewed distribution has only a few scores in which direction?
    The positive end of the distribution. The skew is named after the few extreme scores
  104. Meaning of skewness statistic = 0
    The distribution is symmetric. There is no skewness
  105. Meaning of a negative number for the skewness statistic
    The distribution has some negative skewness or skewness to the left (a few extreme scores on the lower end of the number line)
  106. Meaning of a positive number for the skewness statistic
    The distribution has some positive skewness or skewness to the right (a few extreme scores on the higher end of the number line)
  107. Why should we graph our data?
    To understand research results, to communicate quickly and accurately with others about research results, to summarize the data, to look for anomalies like outliers, gaps in the distribution, data entry errors, etc., and to see patterns that can't be seen with statistics
  108. Definition of frequencies
    Number of occurrences within categories
  109. A bar graph is used with what kind of data?
    Non-numeric or categorical data, like gender. Frequencies within categories are displayed
  110. A pie chart is used with what kind of data?
    Non-numeric or categorical data, like gender. Frequencies within categories and/or percentages are displayed
  111. Advantage of a pie chart
    It can show how much of the whole is contained in each category
  112. Disadvantage of a pie chart
    Can be hard to judge the relative sizes of the wedges
  113. A simple dot plot is used with what kind of data?
    Numeric data, such as systolic blood pressure. Each dot represents one score
  114. A multi-way dot plot is used with what kind of data?
    A multi-way dot plot usually has categories or non-numeric data, such as locations, combined with a frequency or percentage. The variable of location is non-numeric or categorical
  115. Advantage of a simple dot plot
    All scores are shown
  116. Advantage of a multi-way dot plot
    Frequencies can be placed in rank order, so locations or entities can be compared
  117. A scatterplot is used with what kind of data?
    Numeric or quantitative data for two variables, like height and weight
  118. What is the square root of pi?
    Just kidding! Hello from your first author, Lise DeShea!
  119. Advantage of a scatterplot
    Allows us to see whether two numeric variables appear to have a relationship with each other
  120. Definition of a point cloud
    Collection of dots on the scatterplot
  121. A histogram is used with what kind of data?
    Quantitative or numeric data, like ages
  122. Two differences between a histogram and a bar graph
    1) With a histogram the bars touch, but in a bar graph there are gaps between bars (so we have to bar hop). 2) A histogram uses numeric data, such as systolic blood pressure, and a bar graph uses non-numeric data, such as diagnosis
  123. Advantage of a histogram
    We can see gaps in the distribution of scores
  124. Disadvantage of a histogram
    Multiple scores may be combined in one bar, which could change our understanding of the data, depending on how scores are clumped together
  125. A time plot is used with what kind of data?
    Quantitative or numeric data, often used to connect observations or means for different occasions in time
  126. Another term for a time plot
    Line graph
  127. Advantage of a time plot
    Allows us to see whether there are trends across time
  128. Potential disadvantage of a time plot
    If means are being graphed for different points in time, we lose the ability to see how much variability is present at each occasion in time
  129. A boxplot is used with what kind of data?
    Quantitative or numeric data, like ages
  130. Advantage of a boxplot
    Ability to define outliers in a way that many researchers can agree upon
  131. Another term for a boxplot
    Box-and-whisker plot
  132. Definition of prevalence
    Proportion of people with a condition, usually expressed as a percentage or a rate
  133. What is represented by the length of the whiskers in a boxplot?
    The spread of scores in approximately the top 25% and bottom 25% of the distribution
  134. If one whisker is longer than the other whisker, does the longer whisker represent more scores?
    Generally, no. Approximately the same number of scores is represented by each whisker and each half of the box. The length represents the amount of spread in those scores
  135. Definition of an outlier
    An extreme score that meets certain criteria to be defined as notably different from the rest of the data. Belongs to either the top 25% or bottom 25% of the distribution
  136. Disadvantages of a boxplot
    The definition of an outlier differs in various statistical software programs. Boxplot does not show gaps in the distribution that are not associated with outliers
  137. How many of the scores in a data set are represented by the box in a boxplot?
    About half. The line that divides the box itself is the median, so the middle two quarters of the data set are represented by the box
  138. Definition of a percentile
    A score that has a certain percentage of the distribution below it
  139. What is the interquartile range?
    A term sometimes used to describe the distance between the ends of the box in a boxplot
  140. Disadvantage of graphs created by statistical software
    The software sometimes zooms in to enhance any apparent difference or trend, which can be misleading
  141. Definition of relative location
    A score's position on the number line, in comparison with the mean
  142. Verbal definition of a z score
    (something minus its mean) divided by its standard deviation
  143. A more general term for a z score
    It is one example of a standard score. The z comes from the word standardize
  144. Meaning of a positive z score
    The score is greater than the mean
  145. Meaning of a negative z score
    The score is less than the mean
  146. Meaning of z = 0
    The score equals the mean
  147. What does z = -0.5 mean?
    The score is one-half of a standard deviation below the mean
  148. What do z scores measure?
    The relative position or location of a score within a distribution, compared with the mean
  149. If every score in a sample were transformed into z scores, then the z scores were graphed, what would be the shape of the distribution?
    The distribution of z scores would look like the distribution of the original scores
  150. If every score in a sample were transformed into z scores, what would be the mean and variance of the set of z scores?
    "The mean of the z's would be zero, and the variance (and standard deviation) of the z's would be 1."
  151. Suppose we had a sample of systolic blood pressure readings. We compute each person's z score. If we graph the z scores, will we find a standard shape to the distribution?
    No. Computing z scores standardizes the distribution by making it have a mean of zero and a standard deviation of 1, but the shape is not standard. The shape is the same as the original distribution of scores
  152. What does a statistician's cat say?
    Mu
  153. How does the formula for a z score change if we want to compare a person's score with a population mean?
    The formula becomes: (something minus its population mean) divided by its population standard deviation
  154. What is a T score?
    A standard score that is computed so that the mean for the set of T scores equals 50 and the standard deviation equals 10
  155. Definition of norming
    Process of gathering scores and assessing the numerical results from a large reference group
  156. Definition of norms
    Usually the mean and standard deviation for the large reference group used in the norming process
  157. How do T scores for bone mineral density tests differ from most other T scores?
    The T scores for bone mineral density dests are scaled like z scores, with a mean = 0 and standard deviation = 1
  158. Definition of proportion
    A fraction expressed in decimals
  159. Definition of a normal distribution
    One distribution in a family of mathematically defined curves that are bell shaped and have a complex formula specifying the exact location and spread. Not all bell-shaped curves are normal distributions
  160. Definition of a theoretical reference distribution
    A distribution that is defined by a mathematical formula and describes the relative frequency of occurrence of all possible values for a variable. Normal distributions are considered one family of theoretical reference distributions
  161. How much of a normal distribution is contained between a score that is one standard deviation below the mean and another score that is one standard deviation above the mean?
    About 68%. To contain about 95% of scores in a normal distribution, we would draw vertical lines through the scores that are two standard deviations above the mean and two standard deviations below the mean
  162. Are samples normally distributed?
    No. We may hazard a guess that a variable like adult male height is normally distributed, but even a large sample will be lumpy, not a smooth curve
  163. Definition of the standard normal distribution
    The normal distribution that has a mean = 0 and a standard deviation = 1
  164. When can z scores be used in conjunction with a standard normal distribution?
    ONLY when the original scores are normally distributed. Computing z scores does not change the shape of the distribution.
  165. Characteristics of a normal distribution
    1) mean = median = mode. 2) symmetric (i.e., skewness = 0). 3) All of the scores are under the curve. 4) The total proportion (area) under the curve = 1 (that is, 100% of scores)
  166. What is a linear relationship?
    It is an association between variables that can be described with a straight line
  167. What does Pearson's correlation coefficient measure?
    The degree of linear relationship between two variables
  168. Other names for Pearson's r
    A zero-order correlation or product-moment correlation
  169. What does Pearson's r estimate?
    The population parameter rho, which represents the correlation between the two variables in the population
  170. Range of values for Pearson's r
    It can be as small as -1, and it can be as large as +1
  171. Meaning of r = 0
    There is no linear relationship between the two variables
  172. Comparing r = -.5 and r = +.5: Which is stronger?
    Neither -- they are equally strong
  173. What does bivariate mean?
    Related to two variables. Pearson's r measures bivariate correlation (two variables at a time)
  174. Meaning of r = -1
    There is a perfect negative linear relationship between the two variables
  175. Meaning of r = +1
    There is a perfect positive linear relationship between the two variables
  176. Does Pearson's r have units of measure?
    No, it is an index. It exists on a continuum from -1 (strongest negative linear relationship) to +1 (strongest positive linear relationship).
  177. Definition of covariance
    The shared corresponding variation between a pair of variables. When two variables co-vary, then the variation in one variable corresponds to variation in another variable
  178. How is the covariance statistic related to Pearson's r?
    It is the numerator of r. The denominator of r functions to standardize the covariance, taking away the units of measure
  179. Verbal definition of Pearson's r
    Average product of z scores for the two variables
  180. What is the coefficient of determination?
    It is r-squared, or Pearson's r times itself
  181. What is the purpose of the coefficient of determination?
    It is used to judge the strength of the correlation
  182. What is the meaning of a coefficient of determination = .49?
    It means almost half of the variance in Y is explained by X (or vice versa). We would say that 49% of the variance in Y is accounted for by its relationship with X
  183. If r = .9, can we say that one variable causes changes in the other variable?
    No. Correlation does not imply causation
  184. What kinds of relationships can be assessed with Pearson's r?
    Only linear relationships between two quantitative variables
  185. What effect can an outlier have on Pearson's r?
    An outlier can make Pearson's r seem stronger (closer to +1 or -1), or an outlier can dampen Pearson's r (make it closer to zero). An outlier even can reverse the sign of r (e.g., making it negative when most of the data showed a positive linear relationship)
  186. Effect of restriction of range on Pearson's r
    Same as outliers
  187. Effect of combined groups on Pearson's r
    Same as outliers and restriction of range
  188. Effect of linear transformations (e.g., switching from measuring height in inches to measuring it in cm) on Pearson's r
    None -- Pearson's r is unaffected by linear transformations on the data
  189. How do missing data affect Pearson's r?
    Any participant with missing data on one variable is excluded from the computation of Pearson's r, so the correlation will reflect only the participants with complete data on both variables
  190. How do we know which is the predictor variable and which is the criterion variable in Pearson's r?
    We don't. Pearson's r does not make the distinction between a predictor variable and a criterion variable
  191. Definition of probability
    Relative frequency of occurrence
  192. What is the numerator of a probability?
    The number of outcomes that specifically interest us at the moment
  193. What is the denominator of a probability?
    The total number of options available, or the pool from which we are choosing
  194. Range of a probability (numerically)
    Can be as small as zero, can be as big as 1
  195. What is a conditional probability?
    A relative frequency based on a reduced number of possible options. The condition that we place on the probability limits the number of people who can be counted in the denominator
  196. What is a gold standard in health care?
    It is the best, most widely accepted diagnostic tool
  197. What is sensitivity?
    A conditional probability of a positive diagnosis by a new test, given that the gold standard gave a positive diagnosis. Usually expressed as a percentage (i.e., the probability times 100)
  198. Meaning of the mnemonic SnNout
    Sensitivity: Negative test rules out a possible diagnosis
  199. Meaning of sensitivity = 100%
    The new test was positive for 100% of the tests that the gold standard said were positive
  200. Meaning of sensitivity = 25%
    The new test was positive for 25% of the tests that the gold standard said were positive (so the new test is missing a lot of positive cases)
  201. What is specificity?
    A conditional probability of a negative diagnosis by the new test, given that the gold standard gave a negative diagnosis. Usually expressed as a percentage (i.e., the probability times 100)
  202. Meaning of the mnemonic SpPin
    Specificity: Positive test rules in a possible diagnosis
  203. Meaning of specificity = 100%
    The new test was negative for 100% of the tests that the gold standard said were negative
  204. Meaning of specificity = 25%
    The new test was negative for 25% of the tests that the gold standard said were negative (so the new test's negative results are incorrect 75% of the time)
  205. What is positive predictive value?
    A conditional probability of a positive diagnosis by the gold standard, given that the new test gave a positive diagnosis. Expressed as the percentage of the new test's positive diagnoses that were confirmed by the gold standard
  206. Meaning of positive predictive value = 100%
    All of the new test's positive diagnoses were confirmed by the gold standard
  207. Meaning of positive predictive value = 25%
    One out of four positive diagnoses by the new test were confirmed by the gold standard (so the new test is giving false positive results three-fourths of the time)
  208. What is negative predictive value?
    A conditional probability of a negative diagnosis by the gold standard, given that the new test gave a negative diagnosis. Expressed as the percentage of the new test's negative diagnoses that were found to be truly negative according to the gold standard
  209. Meaning of a negative predictive value = 100%
    All of the new test's negative diagnoses were confirmed as negative by the gold standard
  210. Meaning of a negative predictive value = 25%
    One out of four negative diagnoses by the new test were found to be negative according to the gold standard (so three-fourths of the time that the new test is negative, the gold standard said the results should have been positive)
  211. What is a joint probability?
    An 'and' probability: two facts must be true at the same time in order to count the people in the numerator
  212. What is an 'or' probability?
    Only one of the two facts must be true in order to count the people in the numerator. We would count everyone for whom Fact A is true, everyone for whom Fact B is true, and everyone for whom both facts are true
  213. Two definitions of risk
    1) Probability of an undesired health outcome 2) "Uncertainty about and severity of the consequences (or outcomes) of an activity with respect to something that humans value" (Aven & Renn, 2009)
  214. Definition of disease surveillance
    Monitoring of disease incidence and trends for entire populations
  215. Definition of risk factor
    A variable that affects the chances of a disease
  216. Definition of relative risk
    A statistic that quantifies how people with a risk factor differ from people without the risk factor
  217. What is a hazard ratio?
    A complex statistic that is interpreted like a relative risk
  218. Definition of odds
    The probability of something happening divided by the probability of that same thing not happening
  219. Definition of sampling variability
    The tendency for a statistic to vary when computed on different samples from the same population
  220. How is sampling variability different from a sample variance?
    Sample variance is a measure of the spread of a sample's scores. Sampling variability is variation that we could expect in numeric values of a statistic that could be computed on repeated samples from the same population
  221. What is contained in a sample distribution?
    Scores
  222. What is contained in a population distribution?
    Scores
  223. Define sampling distribution
    A distribution of a statistic that could be formed by taking all possible samples of the same size from the same population, computing the same statistic on each sample, then arranging the numeric values of the statistic in a distribution
  224. What is contained in a sampling distribution?
    Values of some statistic
  225. Why we need sampling distributions
    To compute probabilities so we can test hypotheses and then make inferences from a sample to a population
  226. Theoretically, how would we get a sampling distribution of the mean?
    Decide on a sample size. Then repeatedly draw samples of that size from the same population. For each sample, compute the sample mean. Then arrange the pile of sample means along a number line
  227. Definition of point estimate
    A single number or point on the number line being used to estimate the parameter
  228. Definition of hypothesis
    A testable guess
  229. What does the Central Limit Theorem say?
    1) With a large enough N & independent observations, the sample mean's sampling distribution will have a normal shape, 2) the 'mean of the means' will equal the mean of the population from which we sampled, and 3) these means will have a variance equal to the population variance divided by N
  230. Why is the Central Limit Theorem a gift?
    It saves us from having to create a sampling distribution for one statistic: sample mean. We want to generalize from M to mu, so we need to know how likely it is to get a sample mean at least as extreme as ours, but we don't want to take all possible samples needed to create a sampling distribution of M
  231. What makes a point estimate (like the sample mean) unbiased?
    A statistic is unbiased if the mean of its sampling distribution equals the parameter estimated by the statistic
  232. Now that unbiased has been defined, what can we say about the unbiased variance?
    The unbiased variance has a sampling distribution made up of the unbiased variance statistics for all possible samples of the same size from the same population. The average of those statistics will be the population variance: the parameter estimated by the unbiased variance
  233. If the square root of the unbiased variance is a standard deviation, is that standard deviation unbiased?
    No, standard deviations are biased, but the square root of the unbiased variance generally is judged to be good enough in estimating the population standard deviation
  234. How do we compute the z test statistic?
    We take the sample mean and subtract the population mean, then this difference is divided by the square root of (sigma-squared divided by N)
  235. What is the standard error of the mean?
    It is the denominator of the z test statistic: the square root of (sigma-squared divided by N). It also can be written as the population standard deviation divided by the square root of N. It is the standard deviation of the sample mean's sampling distribution
  236. Which statistics have sampling distributions?
    All of them -- we could choose any statistic and imagine drawing all possible samples of the same size and computing that statistic on each sample
  237. Definition of interval estimate
    A pair of numbers that contain a range of values that is more likely to contain the true value of a parameter being estimated
  238. Definition of interval estimation
    An approach that quantifies the sampling variability by specifying a range of values in the estimation of a parameter
  239. Definition of confidence interval
    An interval estimate that could be expected to contain the true value of the parameter for a certain percentage of repeated samples from the same population
  240. Definition of margin of error
    A measure of spread that is used to define a confidence interval. It is generally computed by multiplying a critical value by a standard error of a statistic
  241. How do we get the two numbers that define a confidence interval?
    We take a point estimate and subtract the margin of error to get the lower limit. To get the upper limit, we add the margin of error to the point estimate
  242. Name three characteristics of a hypothesis that can make it testable
    Specific, objective and non-judgmental
  243. Definition of hypothesis testing
    Process of setting up two competing statements or hypotheses that describe two possible realities, then using probability to decide whether a study's results are typical or unusual for one of those realities
  244. What is a null hypothesis?
    A statement of what we don't really believe, but that we're setting up tentatively as a possible reality. The idea to be tested
  245. What is an alternative hypothesis?
    A statement of what we do believe. An idea opposite of the null hypothesis
  246. What are statistical hypotheses?
    DeShea & Toothaker's term for symbolic representations of the null and alternative hypotheses
  247. Symbol for the alternative hypothesis in DeShea & Toothaker's book
    H with a subscript 1
  248. Symbol for the null hypothesis in DeShea & Toothaker's book
    H with a subscript 0
  249. What is a non-directional alternative hypothesis?
    A statement of what we do believe, but not specifying or predicting an outcome in a particular direction (e.g., the rats will differ on average from health rats in their maze completion time)
  250. What is a directional alternative hypothesis?
    A statement of what we do believe, specifying or predicting an outcome in a particular direction (e.g., the rats will take longer on average to complete the maze)
  251. What is a significance level?
    A small probability chosen in advance by the researcher as a standard for how unlikely the results must be in order to declare that the results are evidence against the null hypothesis
  252. Symbol for the significance level
    Lower-case Greek letter alpha
  253. How do we know where to put alpha in a distribution?
    The alternative hypothesis tells us where we expect to find our results. If no direction is predicted, then for the z test statistic, alpha is split between the two tails of the distribution. If a direction is predicted, alpha goes in the predicted tail
  254. What are critical values?
    Values of the test statistic that cut off a total tail area equal to alpha
  255. Two-tailed critical value decision rule
    If the observed test statistic is equal to or more extreme than a critical value, reject the null hypothesis
  256. Two-tailed p value decision rule
    If p is less than or equal to alpha, reject the null hypothesis
  257. When to use 'prove' in statistics
    Never! Slap your own hand if you ever say 'prove' in conjunction with statistics! We can only say what is likely or unlikely
  258. Meaning of 'significant' in statistics
    Saying something is significant implies that a test statistic has been computed and a null hypothesis has been rejected
  259. Definition of p value
    Probability of observing a test statistic at least as extreme as the one computed on our sample data, given that the null hypothesis is true
  260. Reject and retain are actions taken on which hypothesis?
    Only the null. There is no action taken on the alternative hypothesis.
  261. Another way to say that we retain the null hypothesis
    Fail to reject the null hypothesis
  262. Can we say that we accept the null hypothesis?
    Please don't use the word accept in hypothesis testing! It implies that we are embracing the null hypothesis as Truth -- but in fact we never really believed the null hypothesis.
  263. What are decision rules?
    Requirements for taking the action to either reject or retain the null hypothesis
  264. One-tailed critical value decision rule
    If the observed test statistic is in the direction predicted by the alternative hypothesis AND the observed test statistic is equal to or more extreme than the critical value, reject the null hypothesis
  265. One-tailed p value decision rule
    If the results are in the predicted direction AND if the one-tailed p value is less than or equal to alpha, reject the null hypothesis
  266. How is a p value a conditional probability?
    It is conditional on the idea that the null hypothesis is true. The null hypothesis determines how we draw the distribution that is used in hypothesis testing -- as if the null were true
  267. Where to look to determine which tail to place alpha, if we have a directional hypothesis
    The alternative hypothesis. If it says mu < 50, then the directional arrow is pointing toward the lower tail, and that's where we put alpha
  268. How awesome are you for working through these flashcards?
    Just about as awesome as any student possibly could be -- keep up the good work!
  269. Definition of assumptions
    Statements about the data or population that allow us to know the distribution of the test statistic and to compute p values
  270. What does it mean for an assumption to be met?
    A condition that is described in the assumption has been achieved
  271. What does it mean for an assumption to be violated?
    A condition that is described in the assumption has been not achieved
  272. What are the assumptions of the z test statistic?
    Independence of scores, and a normally distributed population of scores is sampled
  273. What does it mean if a confidence interval that estimates the population mean does not contain the value of mu that is stated in the null hypothesis?
    It means we reject the null hypothesis and conclude it is unlikely that we have sampled from the population with that value of the population mean
  274. Definition of a Type I error
    Rejecting the null hypothesis given that it's actually true in the population
  275. Definition of a Type II error
    Retaining the null hypothesis given that it's actually false in the population
  276. What is the only kind of error that can be made if we reject the null hypothesis?
    Type I error
  277. What is the only kind of error that can be made if we retain the null hypothesis?
    Type II error
  278. What are the two correct decisions that can be made in hypothesis testing?
    1) Rejecting the null hypothesis given that it's actually false in the population, and 2) retaining the null hypothesis given that it's actually true in the population
  279. What is the probability of a Type I error?
    Alpha
  280. How is alpha a conditional probability?
    It is the probability of rejecting the null, given that the null is true in the population
  281. Why is the tail area for alpha in the drawing of the standard normal distribution representative of the probability of a Type I error?
    The distribution is drawn as if the null hypothesis is true. If the observed test statistic goes beyond the critical value that defines the border of alpha's area, then the decision would be to reject the null. But that tail probability exists within the distribution that reflects the idea that the null is true.
  282. What is the probability of correctly retaining the null hypothesis?
    1 minus alpha
  283. What is the probability of a Type II error?
    Beta
  284. What is power?
    The probability of rejecting the null, given that the null is false in the population. Rejecting a false null hypothesis would be a correct decision
  285. What is the correct decision that could be made when the null hypothesis is true in the population?
    If the null is true in the population, we would hope the sample data would lead us to the correct decision to retain the null.
  286. What is the correct decision that could be made when the null hypothesis is false in the population?
    If the null is false in the population, we would hope the sample data would lead us to the correct decision to reject the null.
  287. How can the probability of a Type II error be used to define power?
    Power can be defined as 1 minus the probability of a Type II error (i.e., 1 - beta)
  288. If alpha = .01, what is the probability of correctly retaining the null hypothesis?
    This correct retention of the null hypothesis would occur with a probability equal to 1 minus alpha = .99
  289. If beta = .15, what is power?
    Power = 1 - beta = .85, which would be the probability of correctly rejecting the null hypothesis
  290. Two definitions of effect size
    1) The magnitude of the impact of an independent variable on a dependent variable, or 2) the strength of an observed relationship between variables
  291. All else being equal, will a study need more power to detect a small effect size or more power to detect a large effect size?
    More power is needed to detect smaller effect sizes, just as a magnifying glass or microscope must be stronger to look at smaller objects
  292. All else being equal, will adding participants to a study tend to increase or decrease power?
    Adding participants should increase power
  293. All else being equal, which is associated with more power -- alpha = .05 or alpha = .01?
    Alpha = .05
  294. All else being equal, do we have more power or less power with a one-tailed test, compared with a two-tailed test?
    We have more power with a one-tailed test, unless we don't predict the correct direction. In that case, we have no power
  295. What does power = 0 mean?
    No probability of finding statistical significance, which can happen if the wrong direction is predicted for the results
  296. All else being equal, if we improve the control of extraneous variables, will we have generally more power or less power?
    More power -- with less extraneous variability, the test statistics will be more sensitive to detecting actual effects in the population
  297. What is the relationship between variability and the analogy of signal and noise?
    Variability is like static (noise) on a radio. If we reduce the static, we tend to be able to hear a signal better. The signal is like the effect of one variable on another variable
  298. Why do we need the one-sample t test?
    Sometimes we want to test a null hypothesis about a single population mean, but we don't always know a population standard deviation or variance. We must replace that parameter with a sample statistic, giving us a new test statistic (no longer a z test statistic)
  299. Verbal definition of a one-sample t test
    (Sample mean minus population mean) divided by the estimated standard error of the mean
  300. What is the estimated standard error of the mean in the denominator of the one-sample t test?
    Sample standard deviation divided by the square root of N
  301. How do the hypotheses for the one-sample t test differ from the hypotheses for the z test statistic?
    They don't differ. The same hypotheses can be tested with both statistics
  302. In practical terms, what are degrees of freedom, df?
    df are needed so that we know which t distribution to use to find critical values and p values. Each t distribution is defined by df. Different df lead to slightly different shapes of t distributions
  303. df for the one-sample t test
    N - 1
  304. Example of a null hypothesis for a one-sample t test
    Mu = 100, or our sample comes from a population where the mean equals 100
  305. When to use the one-sample t test
    When we're interested in testing a null hypothesis about a single known (or hypothesized) population mean, but we don't know the population variance or population standard deviation
  306. Critical value decision rule for a one-sample t test
    If the observed one-sample t test is equal to or more extreme than a critical value, reject the null hypothesis
  307. p value decision rule for a directional hypothesis for the one-sample t test
    If the results are in the predicted direction AND if the one-tailed p value is less than or equal to alpha, reject the null hypothesis
  308. p value decision rule for a non-directional hypothesis for the one-sample t test
    If the two-tailed p value is less than or equal to alpha, reject the null hypothesis
  309. When can we say that a one-sample t test is significant?
    When we have rejected the null hypothesis
  310. If we reject the null hypothesis for a one-sample t test, which hypothesis should we restate to describe the significant outcome?
    If we reject the null hypothesis for a one-sample t, we restate the alternative hypothesis and say there is a significant difference between the sample mean and population mean
  311. When can we reject the alternative hypothesis?
    NEVER! We either reject or retain the null hypothesis and take no action on the alternative hypothesis
  312. If a tree falls in a forest and no humans are there to hear it, did it happen?
    Yes, p < .05. :-)
  313. What are the assumptions for the one-sample t test?
    The scores are independent of each other and the scores in the population are normally distributed -- the same assumptions with the z test statistic
  314. For a single mean, how do we interpret a 95% CI computed using a critical value from a one-sample t test?
    If we computed 100 confidence intervals like ours, we could expect 95% of them to bracket the true population mean
  315. When computing a 95% CI around a sample mean, will our CI encompass the population mean?
    With any particular CI, it's impossible to know. We only can say that in the long run, 95% of the time we will get CIs that bracket the true mu
  316. If we have a null hypothesis that mu = 100 and we compute a 95% CI to estimate the population mean, how do we know whether there is a significant difference between the sample mean and population mean?
    If the 95% CI does not straddle the hypothesized value of mu (here, 100), then we can say the sample mean is significantly different from the population mean
  317. How do we interpret a 95% CI that brackets the value of mu in the null hypothesis (such as mu = 100)?
    If the 95% CI brackets the hypothesized mu = 100, then there is not a statistically significant difference between the sample mean and the population mean
  318. Why must we be cautious about interpreting histograms of means that show error bars for the confidence intervals?
    Usually the confidence intervals were computed using a one-sample t test for each group separately. But the difference between two means has a different computation for the confidence interval
  319. What is a limitation for using the z test statistic or the one-sample t test?
    In both cases we must know or hypothesize a value for a population mean. For the z test statistic we also must have a numeric value for the population variance or standard deviation. We rarely know these parameters
  320. What is a difference score?
    When two scores have a link to each other, such as a pretest score and posttest score for the same person, the difference score would be computed by subtracting one of the scores from the other
  321. What are three ways that scores can be paired?
    Pairs of scores are created when people are measured twice on the same variable, when naturally occurring pairs (like left-arm and right-arm blood pressure) are compared, or when a researcher creates pairs by matching people on extraneous variables
  322. What does it mean for participants to act as their own controls?
    When the same people are measured repeatedly on the same variable, each person is like his/her own little control group for comparison across time or conditions
  323. Describe the paired t test
    It is a one-sample t test computed on difference scores
  324. What is an order effect?
    An extraneous variable associated with the order in which conditions are presented to participants and the influence of that order on the outcome variable
  325. How can researchers combat order effects?
    The order of conditions can be randomized
  326. Why must difference scores be computed with the same direction of subtraction for all participants (such as pretest minus posttest)?
    So that all participants' difference scores are comparable
  327. List other names for the paired t test
    Dependent-samples t test, matched-pairs t test, Student's t test for paired samples, t test for related samples, etc.
  328. Does the paired t test require two samples?
    The paired t test can be computed when one sample is measured twice on the same variable, or it can be computed when two samples involve pairs of participants (such as doctor-patient pairs who are both measured on their satisfaction with their interaction)
  329. Explain our fun fact associated with paired means
    When dealing with pairs of scores, the difference scores will have a mean that equals the difference in each sample mean (such as the pretest mean minus the posttest mean)
  330. What is a mean difference?
    It is the difference in two means -- one mean minus the other mean
  331. If we have a null hypothesis that says two population means are equal, what would the null hypothesis say is the mean difference?
    If the two population means are equal, then the null hypothesis can say that the mean difference (one mu minus the other mu) is zero
  332. Give an example of a null hypothesis for a paired t test
    Two population means are equal, or our samples come from populations where the means are equal (with the understanding that there is a pairwise link between the means)
  333. What is the estimated standard error of the difference scores in the denominator of the paired t test?
    The standard deviation of the d's divided by the square root of the number of d's
  334. What are the assumptions of the paired t ets?
    Normality of the d's and independence of the d's
  335. What are the degrees of freedom for the paired t test?
    Number of d's minus 1 (or the number of pairs minus 1)
  336. If we have a non-directional alternative hypothesis for the paired t test and we reject the null hypothesis, what conclusion can we draw?
    Our samples come from populations where the paired means are different. There is a statistically significant difference in the paired means
  337. If we have a non-directional alternative hypothesis for the paired t test and we retain the null hypothesis using a paired t test, what conclusion can we draw?
    There is no statistically significant difference in the paired means
  338. What does the confidence interval associated with the paired t test estimate?
    It is an interval estimate of the difference in two paired population means (such as the difference in the population pretest mean and the population posttest mean)
  339. If a 95% confidence interval for the paired mean difference brackets zero, what can we conclude?
    There is no significant difference in the paired means. The paired means are statistically indistinguishable (their difference is essentially zero)
  340. When do we use an independent-samples t test?
    When we're interested in testing a null hypothesis about whether two independent means are equal: we have two independent groups, we're interested in means, and we have equal sample sizes with at least 15 people per group
  341. List other names for the independent-samples t test
    Student's t test, t test for unpaired samples, the independent t test, etc.
  342. What is an example of a null hypothesis for an independent-samples t test?
    Our samples come from populations where the means are equal
  343. If we have a directional alternative hypothesis for an independent-samples t test, why can the directional sign be confusing?
    The same idea can be expressed with the symbol "">"" or the symbol ""<."" If we think the first group will have a bigger mean, we can list it first and use >. Or we can list the bigger mean second and use <.
  344. What is the numerator of the independent-samples t test?
    The mean difference, or one sample mean minus the other sample mean
  345. What is in the denominator of the independent-samples t test?
    A big ugly estimated standard deviation
  346. Knowing the numerator and denominator of the independent-samples t test, how can we interpret an independent-samples t test = 3?
    The two means are three estimated standard deviations apart
  347. Give the df for the independent-samples t test
    Sample size for the first group plus sample size for the second group, minus 2
  348. If we reject the null hypothesis using an independent-samples t test, what conclusion can we draw?
    Our samples come from populations where the means are different. There is a statistically significant difference in the means
  349. If we retain the null hypothesis using an independent-samples t test, what conclusion can we draw?
    The two means are statistically indistinguishable
  350. If we have a directional alternative hypothesis for an independent-samples t test, how do we use the p value decision rule?
    First, we look at the sample means to see if we correctly predicted which sample mean would be bigger. If not, retain the null. If so, then we ask if the one-tailed p value is less than or equal to .05. If so, we reject the null hypothesis. Otherwise, we retain the null
  351. What are the assumptions of the independent-samples t test?
    That the scores are normally distributed in the populations that were sampled, that all scores are independent of each other, and that the two sampled populations of scores have equal variances
  352. Are we likely to violate the normality assumption of the independent-samples t test? If so, is that a problem?
    Yes, we are likely to violate it, but in many cases it is not a problem -- the theoretical t distribution will still match the sampling distribution of the independent-samples t test
  353. What does it mean for the theoretical t distribution to match the sampling distribution of the independent-samples t test?
    It means the p value for our observed independent-samples t test will be trustworthy for hypothesis testing
  354. Are we likely to violate the independence assumption of the independent-samples t test? If so, is that a problem?
    No, we are not likely to violate it, as long as we use careful research methods. If we do violate it, our study may be seriously compromised
  355. Are we likely to violate the equal variances assumption of the independent-samples t test? If so, is that a problem?
    Yes, we commonly do violate the equal variances assumption. The effect of violating it depends on sample sizes: If both samples have 15+ participants and are equal in size, then our p value will be trustworthy. Otherwise, we need to use a different test statistic
  356. Definition of robustness
    The ability of the sampling distribution of a test statistic to resist the effects of a violation of an assumption
  357. What does it mean if an assumption has been violated but the test statistic is robust to that violation?
    It means the statistic's sampling distribution will still look like the theoretical distribution that we want to use to compute p values
  358. Explain the cold analogy for the independent-samples t test
    Non-normality in the data is like a cold virus. Most of the time, the independent-samples t test can resist the effects of non-normality, and its sampling distribution still matches the theoretical t distribution
  359. Explain the analogy of the nuclear meltdown for the independent-samples t test
    Violating the independence assumption is like a nuclear meltdown. The independent-samples t test (and most other test statistics) cannot survive
  360. Explain the measles analogy for the independent-samples t test
    Robustness to the measles virus depends on whether we have had a measles shot. The measles virus is like having unequal variances in the populations being sampled. If the independent-samples t test has its shot (equal and large n's), then it is robust to the measles (unequal variances)
  361. When do we use the AWS t test?
    If we are interested in comparing two independent means and we have unequal n's, or samples with fewer than 15 people each, or we have both unequal and small n's
  362. If we sample from two populations and one of the populations is not normally distributed, will we know it?
    No, we rarely know whether we're violating the normality assumption, but in most cases it won't make a difference. If many outliers in one tail are expected, then there might be a problem
  363. What does it mean to say that the independent-samples t test is robust to most violations of normality?
    It means that the p value that we would have gotten from the statistic's sampling distribution (if it had been created) will roughly equal the p value that we actually get from the theoretical t distribution
  364. If we sample from two populations with unequal variances, will the independent-samples t test be robust?
    It depends. If the sample sizes are equal with at least 15 people per group, then the independent-samples t test will be robust to the unequal variances
  365. When would the independent-samples t test not be robust to unequal variances?
    When we have 1) unequal n's, 2) small n's, or 3) small-and-unequal n's
  366. If we want to use the independent-samples t test and some people who were in the control group later participated in the treatment group, will the independent-samples t test be robust?
    No, because the independence assumption is violated. If those participants were dropped from the study, in this case we might be able to rescue the research
  367. What is independent in the independent-samples t test?
    The groups are independent (and all participants are independent of each other)
  368. What are the assumptions of the AWS t test?
    Normality and independence
  369. Describe the robustness of the AWS t test
    The AWS test is generally robust to violations of normality, but it is NOT robust to violations of independence
  370. If we have a non-directional alternative hypothesis and we reject the null hypothesis using the AWS t test, what conclusion can we draw?
    Our samples come from populations where the means are different. There is a statistically significant difference in the means
  371. If we have a non-directional alternative hypothesis and we retain the null hypothesis using the AWS t test, what conclusion can we draw?
    The two means are statistically indistinguishable
  372. Give an example of a null hypothesis for the AWS test
    Two population means are equal, or our samples come from populations where the means are equal
  373. If we compute a 95% confidence interval to estimate the difference in two independent population means, what does it mean if the interval brackets zero?
    If the 95% CI brackets zero, then the difference in means is statistically indistinguishable from zero
  374. If we compute a 95% CI to estimate the difference in two population means, what does it mean if the CI does not straddle zero?
    It means the mean difference is statistically different from zero. Our samples most likely come from populations that have different means
  375. What is referenced by the term 'analysis of variance'?
    Analysis of variance is a family of statistics. These statistics have two estimates of variability, one in the numerator and one in the denominator
  376. What is a level?
    A level is one value of an independent variable. If the independent variable is the method of soothing babies, one level might be 'bottle-feeding'
  377. When do we use the one-way ANOVA F test?
    When we have two or more independent groups and we're interested in comparing their means
  378. What does one-way mean?
    It means there is one grouping variable (either an independent variable or predictor variable)
  379. Give an example of a null hypothesis for the one-way ANOVA F test
    Our samples come from populations with equal means
  380. Give an example of an alternative hypothesis for the one-way ANOVA F test
    There is some difference in the population means
  381. If we want to detect some difference in means for four independent groups, must all the means be different from each other?
    No, only one of them must differ from the others, which is why the alternative hypothesis for the one-way ANOVA says 'some difference in the population means'
  382. What are fixed effects?
    The levels of the independent variable can be replicated in another study, based on a specific definition of each level
  383. What does 'variability between groups' mean?
    In a one-way ANOVA F test, variability between groups refers to differences in the group averages, with at least one group differing from the others
  384. What does 'variability within groups' mean?
    People's scores will differ from each other for many reasons, even if they are in the same group. Variability within groups refers to this variation in the scores within the groups in a one-way ANOVA design
  385. Explain the logic of the one-way ANOVA F test
    1) Compute 2 estimates of variability: between and within. 2) Compute one-way ANOVA F = (between-variability)/(within-variability). 3) If the 2 estimates are about the same, F will be around 1. 4) As group means differ, F gets bigger. 5) At some point, F will exceed a critical value, indicating a significant difference somewhere in the means
  386. Numerator of the one-way ANOVA F
    Mean square between
  387. Formula for the mean square between for the one-way ANOVA F
    Between sum of squares divided by df-between
  388. What is the meaning of the between sum of squares for the one-way ANOVA F?
    It is a measure of variability of the sample means
  389. What is df-between for the one-way ANOVA F?
    Number of groups minus 1
  390. Denominator of the one-way ANOVA F
    Mean square within
  391. Formula for mean square within for the one-way ANOVA F
    Within sum of squares divided by df-within
  392. What is the meaning of the within sum of squares for the one-way ANOVA F?
    It is a measure of variability of scores within groups
  393. What is another phrase that means the same thing as mean square within?
    The error term, or mean square error
  394. What is df-within for the one-way ANOVA F?
    Total sample size minus the number of groups
  395. What is df-total for the one-way ANOVA F?
    Total sample size minus one, which equals the sum of df-between and df-within
  396. Critical value decision rule for the one-way ANOVA F
    If the observed one-way ANOVA F is equal to or more extreme than the critical value, reject the null hypothesis
  397. p value decision rule for the one-way ANOVA F
    If p is less than or equal to alpha, reject the null hypothesis
  398. If we reject the null hypothesis for the one-way ANOVA F, what can we conclude?
    Our samples come from a population where there is some difference among the population means
  399. Name each assumption of the one-way ANOVA F test and state whether the statistic is usually robust in the face of a violation of that assumption
    Normality: yes. Independence: no. Equal variances: no
  400. Does the one-way ANOVA F test have an inoculation against unequal variances?
    No. Even with large and equal n's, the one-way ANOVA F's p value can become untrustworthy
  401. Why isn't the one-way ANOVA F test's robustness problem in face of unequal variances a problem?
    Because most researchers really want to know more than whether there is some difference in the means -- they want to know which means differ. Multiple comparison procedures can answer these research questions
  402. What are multiple comparisons?
    The process of comparing all possible combinations of two means at a time (pairwise comparisons of means)
  403. What are the statistics that look at the combinations of two means at a time?
    Multiple comparison procedures
  404. How are multiple comparison procedures different from doing all possible independent-samples t tests in a one-way ANOVA design?
    Multiple comparison procedures have the goal of controlling the risk of making at least one Type I error for the entire set of pairwise comparisons
  405. What is the typical null hypothesis for almost any multiple comparison procedure?
    For each pair of means, the null hypothesis is that the population means are equal
  406. If we have four independent groups and we want to run a multiple comparison procedure to identify any statistically significant differences in means, how many null hypotheses will we test?
    If we have four independent groups, there are six possible pairs of means to compare, so we would have six null hypotheses to test
  407. What is a Bonferroni correction?
    An approach to controlling the probability of a Type I error for a set of comparisons. The most basic Bonferroni correction involves dividing alpha by the number of pairwise comparisons to be made, then applying that portion of alpha to each comparison's hypothesis test
  408. What is Tukey's Honestly Significant Difference (HSD)?
    A multiple comparison procedure that tests for differences in all pairs of means within a one-way ANOVA F design when n's are equal
  409. Why is the Ryan-Einot-Gabriel-Welsch Q statistic better than Tukey's HSD?
    It tends to have slightly more power, making it a more sensitive statistic for detecting differences in pairs of means when n's are equal
  410. When do we use Tukey's HSD or the REGWQ multiple comparison procedure?
    When we have a one-way ANOVA situation with equal sample sizes
  411. When do we use the Games-Howell multiple comparison procedure?
    When we have a one-way ANOVA situation with unequal sample sizes
  412. What does the term 'bivariate linear relationship' mean?
    It means two quantitative variables will be examined to determine whether their relationship can be described with a straight line
  413. When do we use Pearson's r for testing a hypothesis about a correlation?
    When we want to determine whether there is a statistically significant linear relationship between two continuous variables
  414. What does Pearson's r estimate?
    Rho, the population correlation between two variables
  415. Example of a null hypothesis for a test of correlation when no direction is predicted in the alternative hypothesis
    Rho = 0, or our sample comes from a population where there is no linear relationship between X and Y
  416. Example of an alternative hypothesis for Pearson's r when a positive correlation is predicted
    Rho > 0, or our sample comes from a population where there is a positive linear relationship between X and Y
  417. df for the correlation test
    N - 2, where N is the number of X-Y pairs of scores or the number of participants
  418. What are the assumptions of Pearson's r?
    The pairs of scores are independent of each other and the scores have a bivariate normal distribution in the population
  419. Is Pearson's r robust if the independence assumption is violated?
    No, having dependence between the participants' observations on either variable would make the study's results untrustworthy
  420. Is Pearson's r robust if the assumption of bivariate normality is violated?
    Usually yes, as long there is no extreme skewness in one or both variables
  421. What is the purpose of regression?
    Straight-line prediction. We use data from one sample to create a prediction equation. When someone new comes along who has a score on only one of the two variables, we can predict a value on the second variable
  422. What is the problem with recruiting participants for a treatment after observing a one-time reading that indicated high blood pressure?
    No matter whether the treatment is effective or not, chances are that the person's bp will be lower next time. This example demonstrates regression to the mean
  423. What does it mean to compare the rise and run in regression?
    The rise is the change in the Y score. The run is the corresponding change in the X score. The slope of the regression line is an expression of the change in Y (rise) relative to the change in X (run)
  424. What does a negative slope mean?
    As we read the graph from left to right, the line goes downhill, meaning that the change in Y is negative as the X variable increases
  425. What is a Y-intercept?
    The point on the Y axis where the regression line is crossing. That is, if X = 0, it is the predicted value of Y, based on the regression equation
  426. What two bits of information are needed to graph a regression line?
    The slope and Y-intercept
  427. Explain two ways that regression analysis different from correlation
    1) We can't make predictions with correlation, but we can with regression. 2) With correlation, it doesn't matter which variable is X and which variable is Y. In regression, one variable must be considered X (predictor variable) and the other variable is designated Y (criterion variable)
  428. How is simple regression similar to and different from multiple regression?
    They are similar because both involve a single outcome variable. But simple regression involves only one predictor, while multiple regression involves more than one predictor
  429. Explain the Predicted Y formula in words
    This is the regression line: Predicted Y equals the Y-intercept plus the product of two things: the slope and some value of the predictor variable
  430. What is a regression coefficient?
    This is a general term for both the slope and the Y-intercept, which are the two numeric elements that define any simple regression line
  431. Generally speaking, what is the ordinary least squares criterion?
    It is a standard for determining mathematically what is the best-fitting regression line
  432. What do we call the difference between an actual Y score and a predicted Y score, given a particular value of X?
    An error or residual = actual Y minus predicted Y (with both of these numbers being paired with the same given value of X)
  433. Explain the ordinary least squares criterion
    If we have an OLS regression line, we can find all of the errors for the scatterplot, square every error and add up the squared errors. The result is smaller than the same sum that could be computed for any other line drawn through that scatterplot
  434. Explain the ordinary least squares criterion in a less wordy way!
    OLS regression defines a regression line so that the sum of squared errors is minimized
  435. What does the slope b estimate?
    b estimates the population slope, beta
  436. If we expect two variables to have a positive linear relationship, what will our alternative hypothesis be for the slope?
    The null hypothesis will say beta > 0, or our sample comes from a population in which the slope for the regression line is positive
  437. How is the t test for the slope computed?
    The slope, b, is divided by the standard error of its sampling distribution
  438. We have computed a non-directional alternative hypothesis and a 95% confidence interval to estimate the population slope, and this interval does not bracket zero. What does that mean?
    There is a significant linear relationship between the two variables. We can look at whether the slope statistic is positive or negative to determine the direction of the linear relationship
  439. Why must we consider the range of the data in regression?
    Mathematical predictions can be made using any numbers, but our predictions can be trusted only within the range of numbers for which we have evidence (data)
  440. What is categorical data analysis?
    A family of statistics that analyze the frequencies for non-numeric variables (like type of obesity surgery and whether blood sugar is controlled a year later)
  441. What are rank tests?
    Statistics that involve computations performed on ranks instead of the original scores
  442. What is the relationship between a proportion and a percentage?
    If we multiply a proportion by 100, we get a percentage. If we divide a percentage by 100, we get a proportion"
  443. What is a sample proportion?
    The number of people who share an attribute divided by the total number of people in the sample
  444. What does it mean if a null hypothesis says a population proportion = .6?
    The null hypothesis is saying that our sample comes from a population where 6 out of 10 people share some attribute
  445. If the null hypothesis says the population proportion = .6 and a 95% confidence interval for the proportion does not bracket .6, what does that mean?
    It means we should reject the null hypothesis and conclude that our sample most likely comes from a population where the population proportion is not .6
  446. When do we use a chi square for goodness of fit?
    When we have one categorical variable (e.g., days of the week) and we are interested in frequency of occurrence of some event (e.g., heart attacks)
  447. What kind of null hypothesis is tested by the chi square test for goodness of fit?
    A null hypothesis that focuses on the proportions for all levels of a categorical variable. The null hypothesis may say that all of the proportions are equal (like the example of sudden cardiac deaths across days of the week), or it may specify the proportions (such as the population distribution of people in blood-type groups)
  448. What is another term for the chi square test for goodness of fit?
    One-way chi square test
  449. What are the expected frequencies in a chi square test for goodness of fit?
    The number of occurrences that we predict in each category based on theory or previous research
  450. What are the observed frequencies in a chi square test for goodness of fit?
    The number of occurrences that actually are found in the sample data for each level of the categorical variable being analyzed
  451. Describe the computation of the chi square test for goodness of fit
    Subtract the expected frequency from the observed frequency for each category. Square the differences. Divide each squared difference by its expected frequency. Add up the results
  452. df for the chi square for goodness of fit
    Number of categories minus 1
  453. p value decision rule for the one-way chi square
    If p is less than or equal to alpha, reject the null hypothesis
  454. What conclusion can be drawn if the chi square for goodness of fit is significant?
    The distribution of observations across categories are not equal. A difference in proportions lies somewhere among the categories
  455. How do you feel?
    Hey, if this question was good enough for a computer to ask Spock in a Star Trek movie, it's good enough for this set of flashcards!
  456. Name the three assumptions of the chi square test for goodness of fit
    Independence of observations, categories are mutually exclusive, and categories are exhaustive
  457. Why is it a problem if expected frequencies are too small in a chi square test for goodness of fit?
    The p value for the chi square test for goodness of fit may not be trustworthy
  458. Give an example of a null hypothesis for the chi square for independence
    There is no relationship between the two categorical variables, or Variable 1 is independent of Variable 2
  459. What are two other terms for the chi square test for independence?
    Two-way chi square, or chi square for contingency tables
  460. Assumptions of the chi square test for independence
    Same as the chi square test for goodness of fit: independence of observations, categories are mutually exclusive, and categories are exhaustive
  461. df for the chi square for independence
    (number of rows minus 1) times (number of columns minus 1)
  462. p value decision rule for the chi square for independence
    If p is less than or equal to alpha, reject the null hypothesis
  463. What conclusion can be drawn if the chi square for independence is significant?
    The two categorical variables are significantly related
  464. Why is relative risk usually associated with very large samples?
    Because epidemiologists studying disease risk want good estimates of actual risk in populations
  465. Why is relative risk usually associated with cohort studies?
    A cohort study is research that identifies people exposed or not exposed to a potential risk factor, then compares these people by observing them across time for the development of disease. Relative risk compares the disease risk for people who were exposed or not exposed to the potential risk factor
  466. Describe the two risks involved in the computation of a relative risk
    The numerator tells about the risk of disease given exposure to the risk factor, and the denominator tells about the risk of disease given the absence of exposure to the risk factor
  467. Describe the computation of a relative risk in terms of probabilities
    Relative risk is the probability of disease given exposure to the risk factor, divided by the probability of disease given no exposure to the risk factor
  468. What is the meaning of RR = 1?
    It means the probability of disease is the same for those exposed to the risk factor and those not exposed to the risk factor
  469. If a journal article reports that the 95% confidence interval for RR is [0.9, 1.1], what can we conclude?
    There is no significant difference in the risks for those exposed and not exposed because the interval contains 1
  470. Why is relative risk the wrong analysis for a case-control study?
    In case-control studies, researchers identify people with a condition (the cases), then they find people who are similar to the cases, except without the condition (i.e., they find controls). The researchers in case-control studies haven't watched exposed and unexposed groups over time
  471. How do we compute odds?
    By dividing the probability of something happening by the probability of that something not happening
  472. What goes into an odds ratio?
    Two odds: one odds computation is divided by another odds computation
  473. What is the meaning of OR = 1?
    The odds of getting the disease or condition are the same for those with and without exposure to the risk factor. There is no relationship between the risk factor and getting the disease or condition
  474. What is the meaning of OR = 7?
    The odds of the disease or condition for those with the risk factor are 7 times greater than the odds of the disease for those without the risk factor
  475. What is the meaning of the following 95% confidence interval for an odds ratio? [1.7, 3.2]
    People exposed to the risk factor have greater odds of getting the disease than those not exposed because the CI is greater than 1. The spread of people across categories of cases and controls is tilted toward cases for those who were exposed, compared with those not exposed to the risk factor
  476. What is the meaning of the term 'nonparametric statistics'?
    Nonparametric statistics test null hypotheses that do not contain parameters. In contrast, a parametric statistic will have a null hypothesis containing something like mu or rho
  477. How do nonparametric statistics' assumptions differ from the assumptions for parametric statistics?
    Nonparametric statistics generally free researchers from the assumption of normality
  478. Why would a researcher choose a rank test?
    If researchers expect to violate the normality assumption in a way that would make their parametric statistics untrustworthy, they may choose a nonparametric rank test instead
  479. Why not use rank tests all of the time?
    The hypotheses may not reflect the ideas that the researchers wish to test, a violated assumption may trigger a statistically significant result when the null is true, and rank tests may not have as much power as parametric tests in some cases

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