Stats Chapter 1

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Stats Chapter 1
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Stats Chapter 1
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  1. Data
    • Consist of information coming from
    • observations, counts, measurements, or
    • responses. ex “People who eat three daily servings of whole grains have been
    • shown to reduce their risk of…stroke by 37%.”
  2. Statistics
    • The
    • science of collecting, organizing, analyzing, and interpreting data in order to
    • make decisions.
  3. Data Sets
    • Population
    • The collection of all outcomes, responses,
    • measurements, or counts that are of interest.
    • Sample
  4. A subset of the population.
  5. Sample
    A subset of the population.
  6. Population
    • The collection of all outcomes, responses,
    • measurements, or counts that are of interest.
  7. Parameter
    • A number
    • that describes a population characteristic.
    • Average age of all people in the United States
  8. Statistic
    • A number
    • that describes a sample
    • characteristic.
  9. Average age of people
    from a sample of three states
  10. Branches of Statistics
    Descriptive Statistics Inferential Statistics
  11. Descriptive Statistics
    • Involves
    • organizing, summarizing, and displaying data.
    • e.g. Tables, charts, averages
  12. Inferential Statistics
    Involves using sample data to draw conclusions about a population.
  13. Qualitative Data
    • Consists
    • of attributes, labels, or nonnumerical entries.
  14. Quantitative data
    Numerical measurements or counts
  15. Designing a Statistical Study
    • Identify
    • the variable(s) of interest (the focus) and the population of the study.
    • Develop a
    • detailed plan for collecting data. If you use a sample, make sure the sample is
    • representative of the population.
    • Collect
    • the data.
    • Describe
    • the data using descriptive statistics techniques.
    • Interpret
    • the data and make decisions about the population using inferential statistics.


    • Identify
    • any possible errors.
  16. Observational study
    • A
    • researcher observes and measures characteristics of interest of part of a
    • population.
    • Researchers
    • observed and recorded the mouthing behavior on nonfood objects of children up
    • to three years old. (Source: Pediatric
    • Magazine)
  17. Experiment
    • A
    • treatment is applied to part of a population and responses are observed.
  18. Simulation
    • Uses a
    • mathematical or physical model to reproduce the conditions of a situation or
    • process.
    • Often
    • involves the use of computers.
    • Automobile
    • manufacturers use simulations with dummies to study the effects of crashes on
    • humans.
  19. Control
    • for effects other than the one being
    • measured.
  20. Confounding variables
    • §Occurs
    • when an experimenter cannot tell the difference between the effects of
    • different factors on a variable.
    • §A coffee
    • shop owner remodels her shop at the same time a nearby mall has its grand
    • opening. If business at the coffee shop increases, it cannot be determined
    • whether it is because of the remodeling or the new mall.
  21. Placebo effect
    • §A subject
    • reacts favorably to a placebo when in fact he or she has been given no medical
    • treatment at all.
    • §Blinding is a technique where the subject does
    • not know whether he or she is receiving a treatment or a placebo.
    • §Double-blind experiment neither the subject nor the
    • experimenter knows if the subject is receiving a treatment or a placebo.
  22. Simple Random Sample
    • Every
    • possible sample of the same size has the same chance of being selected.
  23. Stratified Sample
    • Divide a
    • population into groups (strata) and select a random sample from each group.
  24. Cluster Sample
    • Divide
    • the population into groups (clusters) and select all of the members in one or
    • more, but not all, of the clusters.
  25. Systematic Sample
    • Choose a
    • starting value at random. Then choose every kth member of the population.
  26. nominal level of measurement
    • A
    • variable is at the nominal level of measurement if the
    • values of the variable name, label, or categorize. In addition, the naming scheme does not allow
    • for the values of the variable to be arranged in a ranked, or specific, order.
  27. ordinal level of measurement
    • A
    • variable is at the ordinal level of measurement if it
    • has the properties of the nominal level of measurement and the naming scheme
    • allows for the values of the variable to be arranged in a ranked, or specific,
    • order.
  28. interval level of measurement
    • A
    • variable is at the interval level of measurement if it
    • has the properties of the ordinal level of measurement and the differences in
    • the values of the variable have meaning.
    • A value of zero in the interval level of measurement does not mean the
    • absence of the quantity. Arithmetic
    • operations such as addition and subtraction can be performed on values of the
    • variable.
  29. ratio level of measurement
    • A
    • variable is at the ratio level of measurement if it
    • has the properties of the interval level of measurement and the ratios of the
    • values of the variable have meaning. A
    • value of zero in the ratio level of measurement means the absence of the
    • quantity. Arithmetic operations such as
    • multiplication and division can be performed on the values of the variable.
  30. Confounding
    • in a study occurs when the effects of two or more
    • explanatory variables are not separated.
    • Therefore, any relation that may exist between an explanatory variable
    • and the response variable may be due to some other variable or variables not
    • accounted for in the study.
  31. lurking variable
    • A lurking variable is an explanatory
    • variable that was not considered in a study, but that affect the value of the
    • response variable in the study. In
    • addition, lurking variables are typically related to any explanatory variables
    • considered in the study.
  32. Cross-sectional
    Studies
    • Observational studies that collect information about
    • individuals at a specific point in time, or over a very short period of time.
  33. Case-control Studies
    • These studies are retrospective,
    • meaning that they require individuals to look back in time or require the
    • researcher to look at existing records.
    • In case-control studies, individuals that have certain characteristics
    • are matched with those that do not.
  34. Cohort Studies
    • A cohort study first identifies a group of individuals
    • to participate in the study (cohort).
    • The cohort is then observed over a period of time. Over this time
    • period, characteristics about the individuals are recorded. Because the data is collected over time,
    • cohort studies are prospective.
  35. census
    • A census is a
    • list of all individuals in a population along with certain characteristics of
    • each individual.
  36. Random sampling
    • is the process of using chance to select individuals
    • from a population to be included in the sample.
  37. simple random sampling
    • A sample of size n from a
    • population of size N is obtained through simple random sampling if every possible
    • sample of size n has an equally
    • likely chance of occurring. The sample
    • is then called a simple random sample.
  38. The 110th Congress of the United States had 435 members
    in the House of Representatives. Explain how to conduct a simple random sample
    of 5 members to attend a Presidential luncheon.
    Then obtain the sample.
    Put the members in alphabetical order. Number the members from 1 - 435.
  39. stratified sample
    • A stratified sample is one
    • obtained by separating the population into homogeneous, non-overlapping groups
    • called strata, and then obtaining
    • a simple random sample from each stratum.
  40. A systematic sample
    • A systematic sample is
    • obtained by selecting every kth individual from the population. The first individual
    • selected is a random number between 1 and k.
  41. cluster sample
    • A cluster sample is
    • obtained by selecting all individuals within a randomly selected collection or
    • group of individuals.
  42. convenience sample
    • A convenience sample is one
    • in which the individuals in the sample are easily obtained.
    • Any studies that use this type of
    • sampling generally have results that are suspect. Results should be looked upon with extreme
    • skepticism.
  43. Bias
    • If the
    • results of the sample are not representative of the population, then the sample
    • has bias.
    • Three Sources of Bias
  44. 1.Sampling Bias
  45. 2.Nonresponse Bias
  46. 3.Response Bias
  47. Sampling bias
    • means that the technique used to obtain the individuals
    • to be in the sample tend to favor one part of the population over another.
  48. Undercoverage
    • Undercoverage is a
    • type of sampling bias. Undercoverage occurs when the proportion of one segment of the
    • population is lower in a sample than it is in the population.
  49. Nonresponse bias
    • Nonresponse bias exists when
    • individuals selected to be in the sample who do not respond to the survey have
    • different opinions from those who do.
  50. Response bias
    • exists when the answers on a survey do not reflect the
    • true feelings of the respondent.
    • Types of Response Bias
    • Interviewer error
    • Misrepresented answers
    • Words used in survey question
    • Order of the questions or words within the question
  51. Nonsampling errors
    • are errors that result from sampling bias, nonresponse bias,
    • response bias, or data-entry error. Such
    • errors could also be present in a complete census of the population.
  52. Sampling error
    • is error that results from using a sample to estimate
    • information about a population. This type of error occurs because a sample
    • gives incomplete information about a population.
  53. raw data
    • When data is collected from a survey or designed
    • experiment, they must be organized into a manageable form. Data that is not organized is referred to as raw data.
  54. frequency distribution
    • A frequency distribution lists
    • each category of data and the number of occurrences for each category of data.
  55. relative frequency
    • The relative frequency is the
    • proportion (or percent) of observations within a category and is found using
    • the formula:
    • A relative frequency distribution lists the
    • relative frequency of each category of data.
  56. bar graph
    • A bar graph is constructed by labeling each category of data on
    • either the horizontal or vertical axis and the frequency or relative frequency
    • of the category on the other axis.
  57. Pareto chart
    • A Pareto chart is a bar graph where
    • the bars are drawn in decreasing order of frequency or relative frequency
  58. Difference between discrete and continuos data
    • The first step in
    • summarizing quantitative data is to determine whether the data is discrete or
    • continuous. If the data is discrete and
    • there are relatively few different values of the variable, the categories of data
    • will be the observations (as in qualitative data). If the data is discrete, but
    • there are many different values of the variable, or if the data is continuous,
    • the categories of data (called classes)
    • must be created using intervals of numbers.
  59. histogram
    • A histogram is constructed by
    • drawing rectangles for each class of data whose height is the frequency or
    • relative frequency of the class. The
    • width of each rectangle should be the same and they should touch each other.
  60. stem-and-leaf plot
    • A stem-and-leaf
    • plot uses digits to the
    • left of the rightmost digit to form the stem. Each rightmost digit
    • forms a leaf.
    • For example, a data
    • value of 147 would have 14 as the stem and 7 as the leaf.
  61. dot plot
    • A dot
    • plot is drawn by placing
    • each observation horizontally in increasing order and placing a dot above the
    • observation each time it is observed.
  62. class midpoint
    • The class
    • midpoint is found by adding
    • consecutive lower class limits and dividing the result by 2.
  63. frequency polygon
    • A frequency
    • polygon is drawn by plotting
    • a point above each class midpoint on a horizontal axis at a height equal to the
    • frequency of the class. After the points
    • for each class are plotted, draw straight lines between consecutive points.
  64. cumulative frequency distribution
    • A cumulative
    • frequency distribution displays
    • the aggregate frequency of the category.
    • In other words, for discrete data, it displays the total number of
    • observations less than or equal to the category. For continuous data, it displays the total
    • number of observations less than or equal to the upper class limit of a class.
  65. cumulative relative frequency distribution
    • A cumulative
    • relative frequency distribution
    • displays the aggregate proportion (or percent) of observations less than or
    • equal to the category.
  66. ogive
    • An ogive (read as “oh jive”)
    • is a graph that represents the cumulative frequency or cumulative relative
    • frequency for the class. It is
    • constructed by plotting points whose x-coordinates are the upper class limits and whose y-coordinates are the
    • cumulative frequencies or cumulative relative frequencies. After the points for each class are plotted,
    • draw straight lines between consecutive points.
    • An additional line segment is drawn connecting the upper limit of the
    • class that would preceed the first class (if
    • it existed).
  67. time series data.
    • If the value of a
    • variable is measured at different points in time, the data is referred to as time
    • series data.

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