Statistics Quick Reference Guide Notes

General Notes

  • Data should be organized in a table format.

    • Subjects/observations as rows and variables as columns.

    • Example:

      • Subject # | Group | Variable 1 | Variable 2

      • 1

      • 2

      • 3

  • Group is a categorical variable.

    • May be an existing grouping (e.g., gender or ethnicity).

    • Or an assigned variable (e.g., experimental condition).

  • Variables should be represented numerically.

    • Ratio and interval scales of measurement are preferred.

    • Ordinal or categorical scales require different statistical tests.

  • Variables should have brief but informative names.

    • Write down an explanation of variable names for later reference.

  • Set your  α\,\alpha level in advance (most often .05) and stick to it!

  • Recommended website for calculating statistics:

    • www.socscistatistics.com

Descriptive Statistics

  • Used for evaluating the general characteristics of data (central tendency, spread of distribution).

  • Key Statistics:

    • N (Number of observations)

      • Function: =COUNT(range of cells)=COUNT(range\ of\ cells)

      • Notes: Counts valid entries

    • Mean

      • Description: Average score; center of the distribution based on values of scores.

      • Function: =AVERAGE(range)=AVERAGE(range)

      • Notes: Most susceptible to outliers; if long-tailed distribution, use median instead.

    • Median

      • Description: Center of the distribution based on ranking of scores.

      • Function: =MEDIAN(range)=MEDIAN(range)

    • Mode

      • Description: Most common score.

      • Function: =MODE(range)=MODE(range)

    • Maximum

      • Description: Highest score.

      • Function: =MAX(range)=MAX(range)

    • Minimum

      • Description: Lowest score.

      • Function: =MIN(range)=MIN(range)

    • Standard Deviation

      • Description: Average distance between any score and the mean value.

      • Function: =STDEV(range)=STDEV(range)

      • Notes: Sample estimate of population parameter.

    • Cohen’s d

      • Description: Measure of effect size of a difference between two means.

      • Function: =(Mean1−Mean2)/AVERAGE(SD1,SD2)=(Mean1 - Mean2) / AVERAGE(SD1, SD2)

      • Notes: Assumption of equal variance for distributions; only compare across the same variable.

Inferential Statistics

  • Used for testing relationships between different variables.

  • Key Statistics:

    • Pearson’s r

      • Description: Test of correlation between two variables.

      • Function: =CORREL(range1,range2)=CORREL(range1, range2)

      • Notes:

        • Only provides r value.

        • Use SocSciStats to obtain p value.

        • N = number of paired observations; discount missing data.

        • Df = N-2

    • Student’s t

      • Description: Test of difference between means of a single variable for two groups.

      • Notes:

        • SocSciStats is preferred; provides both t statistic and p value.

        • In worksheet: =TTEST(range1,range2,tails,type)=TTEST(range1, range2, tails, type); only provides p value.

        • See notes below.

    • One-way ANOVA

      • Description: Analysis of Variance; tests for differences between three or more independent groups.

      • Notes:

        • SocSciStats One-way ANOVA calculator.

        • N = number of total observations.

        • Df1 = # of groups - 1

        • Df2 = N – df1

        • Follow up with individual t-tests.

  • Student’s t-test Tails and Types:

    • Most hypotheses will use 2 tails.

    • Only directional hypotheses use 1 tail.

    • Type 1: Dependent means

      • Scores are different measures of the same individuals (within-subjects design).

        • N = number of paired observations, df = N-1; discard any unpaired observations.

    • Type 2: Independent means

      • Scores are measures of different individuals (between-subjects design), assuming same variance for different distributions.

        • N = number of total observations, df = N-2.

    • Type 3: Independent means without same variance for different distributions

      • N = number of total observations, df = N-2

Reporting Statistics

  • Commonly used abbreviations:

    • N = number of participants (or observations).

    • M = mean.

    • SD = standard deviation.

    • p = probability value.

  • Pearson’s r example:

    • “There was a negative correlation between number of words recalled (M = 3.6, SD = 1.2) and reported hunger (M = 4.2, SD = 1.6), r (24) = -.41, p = .042.”

  • Student’s t example:

    • “Participants rated their feelings of anger (M = 4.3, SD = 1.6) more strongly than their feelings of suspicion (M = 2.6, SD = 0.8), t (14) = -2.91, p = .011.”

  • ANOVA example:

    • “There was an observed difference in number of puzzles solved based on the room to which participants were assigned, F (2, 42) = 13.49, p =.000. Post-hoc t-tests showed that participants in the green room solved significantly more puzzles (M =10.39, SD = 2.86) than those in the yellow room (M = 4.87, SD = 2.98), t (48) = -5.17, p = .000. Those in the orange room also solved more puzzles (M = 8.11, SD = 2.93) than those in the yellow room, t (48) = -3.001, p = .006. Numerically, participants in the green room solved more puzzles than those in the orange room, t (48) = 2.156, p = .040, but with a Bonferroni corrected  α\,\alpha value of .017 this difference was no longer significant.”