Ch 12: Descriptive Statistics

Descriptive Statistics

A set of techniques for summarizing and displaying data

Distribution

The way the scores on a variable are distributed across levels of that variable

Distributions are described using measures of ___ and ___

central tendency, variability

Distributions are represented by ___ and ___

frequency tables, histograms

Frequency tables

A table for displaying the distribution of a variable

First collumn of a frequency table: ___
Second column: ___

First: values of the variable
Second: frequency of each score

Levels in first collumn ususally go from ___ at the top to ___ at the bottom

highest, lowest

Levels in first collumn ususally ___/___ with the ___/___ scores in the data

begin/end, highest/lowest

Grouped frequency tables

Used when there are many different scores across a wide range of values

Frequency tables can be used for ___ variables, in which case the levels are ___ labels

categorical, category

Histograms

A graph for displaying the distribution of a variable

On a histogram, the x axis represents the ___ of the ___

Values, variable

On a histogram, the y axis represents the ___ of each ___

Frequency, score

peak

highest point of a distribution

tail

the ends of a distribution

Unimodal

distribution with a single distinct peak

Bimodal

distribution with two distinct peaks

Symmetrical

distribution in which the left and the right sides are near mirror images of each other

Negatively skewed

distribution with a relatively long negative tail

Positively skewed

distribution with a relatively long positive tail

Outlier

an extreme score that is far removed from the rest of the scores in the distribution

Central tendency

the middle of a distribution

3 measures of central tendency

Mean, median, mode

mean

most common measure, but not good with outliers

median

Used when there are outliers

mode

Least reliable measure

Variability

the extent to which the scores in a distribution vary around their central tendency

3 measures of variability

Range, standard deviation, variance

Range

Highest-lowest score in a distribution

Standard deviation

Most commonly used

Variance

How far a set of numbers is spread out from the mean

Difference between high and low variability

Has the same mean, median, and mode, but different variability

Percentile rank

a measure of the location of a score within its distribution

Percentile rank tells the ___ of ___ below a ___ ___

percentage, scorers
particular, score

z score

measure of the location of a score within its distribution

Statistical relationship

When the average score on one variable differs across levels of another

Statistical relationships can take the form of ___ between ___ and ___ between ___

differences, groups
correlations, quantitative variables

differences between groups or conditions

means and standard deviations of groups and conditions, usually Cohen's d, and presented in bar graphs

Correlations Between Quantitative Variables

pearson's r and presented in line graphs or scatterplots

Note about Cohen's d and Pearson's r

both measures of effect size

Effect size

measures the strength of the relationship

Error bars

vertical lines that show the amount of variability around the mean in each group or condition

Error bars usually depict ___ ___

standard error

Standard error

the standard deviation divided by the square root of the sample size

Bar graph

Differences between mean scores of two or more groups or conditions

Line graph

Relationship between two quantitative variables

In a line graph for each level of the variable, theres a point representing the _ of the ___ variable

x, mean, y

Scatterplot

correlation between two quantitative variables

For each ___ on a scatterplot, theres a point representing that individuals ___ on both the ___ and ___ variables

individual, score, x, y