1

Tips on ANOVA1 Assignment

Interpreting the Output

Descriptives
Guilt
N / Mean / Std. Deviation / Std. Error / 95% Confidence Interval for Mean / Minimum / Maximum
Lower Bound / Upper Bound
Black D, Black P / 150 / 5.93 / 1.992 / .163 / 5.61 / 6.25 / 1 / 11
Black D, White P / 143 / 5.37 / 1.403 / .117 / 5.14 / 5.60 / 2 / 9
White D, Black P / 156 / 5.70 / 1.538 / .123 / 5.46 / 5.94 / 1 / 9
White D, White P / 147 / 5.90 / 1.665 / .137 / 5.63 / 6.18 / 1 / 9
Total / 596 / 5.73 / 1.676 / .069 / 5.60 / 5.86 / 1 / 11
ANOVA
Guilt
Sum of Squares / df / Mean Square / F / Sig.
Between Groups / 29.312 / 3 / 9.771 / 3.522 / .015
Within Groups / 1642.196 / 592 / 2.774
Total / 1671.508 / 595

To calculate the 2, simply divide the between groups sum of squares by the total sum of squares (yellow fill above). To get the confidence interval, see my document Using SPSS to Obtain a Confidence Interval for R2 From Regression. Here is a screen shot showing how I got the confidence interval for eta-squared. You simply enter the F value, df1, and df2 (pink highlight) into the sav file, run the script, and then look back at the data file. Eta-squared will be in the r2 column and the CI in the lr2 and ur2 columns.

Post Hoc Tests

Guilt
Group / N / Subset for alpha = 0.05
1 / 2
Ryan-Einot-Gabriel-WelschRangec / Black D, White P / 143 / 5.37
White D, Black P / 156 / 5.70 / 5.70
White D, White P / 147 / 5.90
Black D, Black P / 150 / 5.93
Sig. / .183 / .442

Any two means that are in the same subset column are NOT significantly different from each other. For these data the 5.37 is significantly different from the 5.9 and the 5.93 but not from the 5.70. This information is then transferred to an APA-style table like that one below:

Table 1

Certainty of Guilt Related to Race of the Litigants

Group / M / SD / n
Black Defendant, White Plaintiff / 5.37A / 1.40 / 143
White Defendant,Black Plaintiff / 5.70AB / 1.54 / 156
White Defendant, White Plaintiff / 5.90B / 1.66 / 147
Black Defendant, Black Plaintiff / 5.92B / 1.99 / 150

Note. Means sharing a letter in their superscript are not significantly different at the .05 level according to a REGWQ test.

The REGWQ procedure was used for pairwise comparisons, capping familywise error at .05. As shown in Table 1, certainty of guilt was significantly less when the defendant was black and the plaintiff white than for any of the other groups excepting the group where the defendant was white and the plaintiff black. All other comparisons fell short of statistical significance.

Errors Made in the Past

Presentation of the ANOVA

  • Not presenting and interpreting the results of the ANOVA. (-15)
  • Not indicating that the subjects were female, Black, mock jurors. (1)
  • Not indicating that the independent variable was the race of the litigants in a sexual harassment case. (-1)
  • Not fully describing what the four groups were. (-1)
  • Not indicating that the dependent variable was (certainty of guilt). (-1)
  • Neglecting to report the ANOVA F value. (-1)
  • Neglecting to report or incorrectly reporting the ANOVA degrees of freedom. (-1)
  • Neglecting to report the ANOVA MSE. (-1)
  • Incorrectly reporting or not reporting the p value. (-1)
  • Not giving an exact p value. See what the APA has to say on this. (-1)
  • Not indicating whether or not the ANOVA was statistically significant. (-1)
  • After obtaining a p value less than .05, indicating the ANOVA was not significant. (-2)
  • Reporting a trend analysis (polynomial contrasts). This is appropriate only when the independent variable is quantitative. The independent variable here I qualitative. (-1)
  • Incorrect solution, or no solution, for 2. (-1)
  • Reporting an 2 outside of the possible range for 2, which is 0 to 1. An 2 of 1 would mean that group membership explained 100% of the differences in the scores. (-2)
  • Reporting incorrect values for the confidence interval or failing to report the confidence interval. (-1)
  • Reporting a confidence interval for eta-squared that is beyond the range of possible values for eta-squared, 0 to 1. (-2)
  • Reporting a confidence interval for eta-squared that includes zero when the F-test was declared to be significant. (-1)

Presentation of the REGWQ

  • Not presenting the results of the REGWQ in an APA-style table with interpretation in text. (-5)
  • Not interpreting the REGWQ results in terms of differences among the groups. (-1)
  • Indicating that the Bonferroni procedure was employed. The instructions were to use the REGWQ procedure. (-1)
  • Not ordering the means in the REGWQ table. (-1)
  • Incorrectly interpreting the results of the REGWQ. (-1)
  • When describing a significant difference between groups, not emphasizing the direction of the difference. Don’t just say this mean is significant different from that mean. Say that this mean is significantly greater than that mean. (-1)
  • Not using superscripts in the REGWQ table to indicate which means differed significantly from which other means. (-1)
  • Not indicating that the REGWQ procedure was employed to make pairwise comparisons with familywise alpha capped at .05. (-1)

Other Stuff

  • Not placing statistical symbols in italic font. (-1)
  • Putting the SPSS output at the top of the document and the summary statement at the bottom. (-1)

Errors Observed Other Semesters, But Not This Semester

  • Using an 11 point font. The APA insists on use of a 12 point font. (-1/4)
  • Using the redneck plural. The plural of “juror” is “jurors,” not “juror’s.” “Juror’s” is the singular possessive. The plural possessive is “jurors’.” (-1/4)
  • Using  to stand for a sample mean. The proper symbol is M. (-1/4)
  • Not indenting the first line of each paragraph. (-.5)
  • Neglecting to put a blank space on each side of inequality and equality signs. (-.5)
  • Neglecting to put a blank space after every comma. (-.1)