Descriptive Statistics: Describing Variables and the Relations among Them
● The levels of a nominal scale are simply different categories or groups that have no intrinsic
numerical properties. For example, two different kinds of therapies for depression would be
nominal categories. Variables using an ordinal scale rank order the levels from lowest to highest
(or least to most), but the intervals between each rank order are not equal. A list of the top ten
restaurants in Halifax would use an ordinal scale. For an interval scale, the distances between
each level are equivalent in size.In contrast, ratio scales have equal intervals in addition to a true
zero point. Response time and age are examples of ratio scales.
● The statistical procedures used to analyze data with interval and ratio variables are identical.
Importantly, data measured on interval and ratio scales can be summarized using an arithmetic
average, or what is known as the mean.
● The mean is used in many statistical analyses. Variables measured on interval and ratio scales are
often referred to as continuous variables because the values represent an underlying continuum
Distributions
● A frequency distribution indicates the number of participants who receive or select each possible
score on a variable. Frequency distributions can be created for variables using any scale of
measurement
● any outliers: scores that are unusual, unexpected, impossible, or very different from the scores of
other participants. An outlier might reflect a data-entry error that can be corrected
Bar Graphs
● A bar graph uses a separate and distinct bar for each piece of information. Bar graphs are
commonly used for comparing group means but can also be used for comparing percentages
Pie Charts
● A pie chart divides a whole circle, or “pie,” into “slices'' that represent relative percentages. Pie
charts are particularly useful when representing data on a nominal scale. Instead of using a bar
graph for the data we could have divided a circle into five sections corresponding to the five
response options.
Histograms
● A histogram uses bars to display a frequency distribution for a continuous variable. In this case,
the values along the x-axis are continuous and show increasing amounts of a variable, such as
blood pressure, reaction time, or number of correct response
● a normal distribution, a distribution of scores that is frequently observed, and rather important for
statistics. In a normal distribution, the majority of the scores cluster around the mean.This
distribution is only possible for continuous variables
● (SD) is a common measure of variability, or how the scores are spread out with respect to the
mean
Frequency Polygons
● an alternative to histograms, use a line to represent frequencies for continuous variables (i.e.,
interval or ratio scales). Frequency polygons are especially helpful when you want to examine
frequencies for multiple groups simultaneously
Descriptive Statistics
● main types of descriptive statistics are (1) measures of central tendency and (2) measures of
variability. Measures of central tendency try to capture how participants scored overall, across the
entire sample, in various ways. In contrast, measures of variability attempt to summarize how
● The levels of a nominal scale are simply different categories or groups that have no intrinsic
numerical properties. For example, two different kinds of therapies for depression would be
nominal categories. Variables using an ordinal scale rank order the levels from lowest to highest
(or least to most), but the intervals between each rank order are not equal. A list of the top ten
restaurants in Halifax would use an ordinal scale. For an interval scale, the distances between
each level are equivalent in size.In contrast, ratio scales have equal intervals in addition to a true
zero point. Response time and age are examples of ratio scales.
● The statistical procedures used to analyze data with interval and ratio variables are identical.
Importantly, data measured on interval and ratio scales can be summarized using an arithmetic
average, or what is known as the mean.
● The mean is used in many statistical analyses. Variables measured on interval and ratio scales are
often referred to as continuous variables because the values represent an underlying continuum
Distributions
● A frequency distribution indicates the number of participants who receive or select each possible
score on a variable. Frequency distributions can be created for variables using any scale of
measurement
● any outliers: scores that are unusual, unexpected, impossible, or very different from the scores of
other participants. An outlier might reflect a data-entry error that can be corrected
Bar Graphs
● A bar graph uses a separate and distinct bar for each piece of information. Bar graphs are
commonly used for comparing group means but can also be used for comparing percentages
Pie Charts
● A pie chart divides a whole circle, or “pie,” into “slices'' that represent relative percentages. Pie
charts are particularly useful when representing data on a nominal scale. Instead of using a bar
graph for the data we could have divided a circle into five sections corresponding to the five
response options.
Histograms
● A histogram uses bars to display a frequency distribution for a continuous variable. In this case,
the values along the x-axis are continuous and show increasing amounts of a variable, such as
blood pressure, reaction time, or number of correct response
● a normal distribution, a distribution of scores that is frequently observed, and rather important for
statistics. In a normal distribution, the majority of the scores cluster around the mean.This
distribution is only possible for continuous variables
● (SD) is a common measure of variability, or how the scores are spread out with respect to the
mean
Frequency Polygons
● an alternative to histograms, use a line to represent frequencies for continuous variables (i.e.,
interval or ratio scales). Frequency polygons are especially helpful when you want to examine
frequencies for multiple groups simultaneously
Descriptive Statistics
● main types of descriptive statistics are (1) measures of central tendency and (2) measures of
variability. Measures of central tendency try to capture how participants scored overall, across the
entire sample, in various ways. In contrast, measures of variability attempt to summarize how
