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 author "amcmullen"
 tags "Vocab"
 folders "Stats"
 description "statistics"
 fileName "stats2"
 Population
 a collection of entities we want to study

Sample
a subset of elements from a population

Random Sample
From a quantitative perspective, each element has an equal opportunity of being selected

External Validity
A study has external validity when the findings of the sample can be generalized to the population of interest. When selected accurately the sample represents the population from which it was drawn

Random Selection
 From a quantitative perspective, a process whereby each element of a population of interest has an equal opportunity of being selected
 (relates to external validity)

Random Sample
 A subset of the population whose information can be used to describe the entire population with a measured level of confidence
 (relates to external validity)

Internal Validity
When a study measures what it purports to measure

Random Assignment
 Assigning subjects (usually from a sample) randomly to conditions to avoid systematic groupings that may hinder clear interpretation of the results
 (relates to internal validity)

Variable
property of an entity of interest that can take on many values

Discrete Variable
variable that has no intermediate values between scale values

Continuous Variable
variable that has an infinite number of values between scale values

Measurement
assigning value to a property of an entity, assigning value to a variable

Measurement Data or Quantitative Data
 data that is obtained through some form of measurement
 values indicate amount (more/less) or degree of a variable
 values are continuous in their nature

Categorical, Frequency, or Qualitative Data
 data that is obtained via labeling or categorization
 values are discreet

Independent Variable
the variable manipulated by the experimenter, but conceptually not related to another variable

Dependent Variable
the variable not under the experimenter's control and depends on the independent variable

Descriptive Statistics
 a number that is describes a specific characteristic of a set of data
 mean
 median
 mode

Inferential Statistics
 statistics about a sample that is used to make inferences (educated guesses) about a population
 different populations
 making inferences about where the group is

Parameter
a measure referring to or deriving from the population

Statistic
a similar measure as a parameter that derives from a sample

Nominal Scale
 the value of a variable that has a nominal scale is just a label or a name
 (almost all values operate on a nominal scale)

Ordinal Scale
 Similar to the nominal scale but the order of the labels is important
 The differences between the labels do not have to be equal
 Includes nominal
 e.g.  class rank

Interval Scale
 In addition to having the same properties of a variable within an ordinal scale, the difference between units of measurement is similar
 Includes nominal and ordinal
 e.g.  temperature (Celsius and Farenheit)

Ratio Scale
 In addition to have the same properties of a variable with an interval scale, this type of variable also has a true 0 point
 Includes all the values of nominal, ordinal, and interval
 e.g. Kelvin temperature

Central Tendency
 Measures refer to a "middle" or "typical" value of the data we just collected, including:
 Mode
 Median
 Mean

Mode
 The value that occurs the most often in a distribution
 The value has a greater likelihood of being selected from a distribution of scores
 Appropriate for use with all scale variables
 Not as informative as other measures of central tendency since it merely uses one score from the whole distribution
 Not affected by extreme scores
 If the scores are too far apart, they are not averaged and the distribution is called bimodal

Median
 50th percentile  middle of distribution  half above and half below
 Median Value  middle number  add up middle scores and divide by 2
 Median Location  (N+1)/2
 Not as useful as other measures of central tendency since it merely represents a value that may not even exist in the distribution
 Not affected by extreme scores
 Appropriate for ordinal scale variables, and interval/ratio scales variables when the distribution is skewed

Mean
 The average value from a collection of scores
 Equal to the sum of the scores divided by the number of scores
 Appropriate for variables with interval/ratio scales
 Influenced by extreme scores and requires
 Easily manipulated algebraically
 Stable across multiple samples of a population, making it a good estimate of central tendency for the population
 Population
 Sample xbar =

Measures of Variability
 Focus on the dispersion of values around the mode, median, or the mean
 Include  range, average deviation, variance, standard deviation

Range
 Reflects the distance between the lower and highest value
 Highly influenced by extreme "outlier" scores that are not "representative" in the true population
 Interquartile range removes the top and bottom 25% of scores, eliminating extreme values from consideration
 Reduced data is a "trimmed sample"

Average Deviation
 The difference between each score and the mean of all scores in a sample can be summed and divided by the number of scores in that sample
 The sum of the deviations from the mean sum up to 0
 Not a useful measure of dispersion

The Mean Absolute Deviation (M.A.D.)
 Takes the absolute value between each score and the mean of all the scores
 The deviations no longer sum up to 0

Variance
 An alternative to the M.A.D. is the variance
 Population Variance = ^{2}
 Sample Variance = shat^{2}^{}
 Instead of taking the absolute value of the dispersion, square it
 The inflated values resulting from the squaring of the differences allow us to detect small dispersion that would not be as visible using the M.A.D.
 The squared (INFLATED) values do not correspond to those in the data set. The standard deviation (square root of the variance) does
 Highly influenced by extreme values

