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Descriptive Statistics. Printing information at: www.msu.edu/service/mlab.web Class website: www.msu.edu/course/psy/475/. Moving from broad research. Begin with broad question Generate specific hypothesis Narrow basic topic Specific prediction about relationship Operationalize hypothesis
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Descriptive Statistics Printing information at: www.msu.edu/service/mlab.web Class website: www.msu.edu/course/psy/475/
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
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
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
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
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)
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
Descriptive Statistics: Frequency Distribution • Choose handful blocks: • 10” • 8” • 8” • 10” • 6” • 4” • 10”
Frequency Distribution: Summarize Data • Length # Blocks 10” 3 8” 2 6” 1 4” 1
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
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
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
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)
