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Understanding Descriptive Statistics: Measurement, Variables, and Central Tendency

This guide covers essential concepts in descriptive statistics, emphasizing the transition from broad research questions to specific hypotheses. It explains different types of variables—categorical and continuous—and their operationalization. Learn about frequency distributions, measures of central tendency (mean, median, mode), and variance (standard deviation). Discover how to effectively analyze psychological data, using rating scales and considering outliers to choose the most appropriate measures. A comprehensive overview for those studying statistical analysis in psychology or related fields.

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Understanding Descriptive Statistics: Measurement, Variables, and Central Tendency

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  1. Descriptive Statistics Printing information at: www.msu.edu/service/mlab.web Class website: www.msu.edu/course/psy/475/

  2. Moving from broad research • Begin with broad question • Generate specific hypothesis • Narrow basic topic • Specific prediction about relationship • Operationalize hypothesis • How will we measure the constructs in our hypothesis • How you operationalize hypothesis may lead to different results

  3. Types of variables • Categorical variables (also called nominal) • Has discrete categories • Ex: variable = sex (1=female, 2=male) • Values assigned to categories are meaningless • Continuous variables • Many levels or values that have meaning

  4. Three types of continuous variables • Ordinal • Numbers indicate order but distance between numbers not equal • Ex: race winners; birth order • Interval • Distance between numbers equally spaced • Ex: temperature; extraversion • Ratio • Includes a value of zero which indicates the absence of a quality • Ex: income

  5. Continuous or Categorical • Many psychological variables are rating scales • Ex: 1=not at all, 2=somewhat, 3=moderately, 4=very much, 5=extremely • Each case falls into one of these categories • But we assume that the distance between 1 & 2 is equal to the distance between 4 & 5 • So treat this as a continuous variable

  6. Continuous or Categorical • Rule of thumb with rating scales • 2 categories: categorical • 3 categories: either depending on number of cases in each category • If number of cases in each category fairly equal, ok to treat as categorical • If number of cases in each category unequal, treat as continuous • 4+ categories: continuous (approximates a continuum) • Exception: if variable with 4 categories is truly categorical (e.g., marital status, state live in)

  7. Statistics Terms • Population • Every member in a group that you want to study • Sample • Representative subset of the whole population • Case • Single item or individual in your sample

  8. Descriptive Statistics: Frequency Distribution • Choose handful blocks: • 10” • 8” • 8” • 10” • 6” • 4” • 10”

  9. Frequency Distribution: Summarize Data • Length # Blocks 10” 3 8” 2 6” 1 4” 1

  10. Descriptive Statistics: Central Tendency • Mean • Arithmetic average • Mode • Most frequently occurring value • Median • Value of the middle case in the sample if cases arranged in order from smallest to largest

  11. Uses for Measure of Central Tendency • Usually the mean is the best measure • It takes into account the values of all the cases in the sample, unlike the mode and median • When the mean is not the best measure of central tendency • When there are outliers (extreme values) • Will skew the mean towards the outlier • So use median instead; not influenced by outliers • When your data are categorical • Then the mean is not meaningful • Use the mode instead

  12. Measures of variance • Tells you how much the values of your variable are spread out (vary) • The average deviation from the mean • Standard deviation & variance

  13. Variance & Standard Deviation • Calculate by: • Getting sample mean • Subtract each value from the mean to get deviation • Square deviation so all signs positive • Take the average of squared deviations • Variance is not in original units (is inches squared) • Can take the square root of the variance to get the standard deviation, which is in our original units (inches)

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