Descriptive Statistics Printing information at: Class website:

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”  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 1. When there are outliers (extreme values) Will skew the mean towards the outlier So use median instead; not influenced by outliers 2. 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)