Results

ANOVA

Looking at the means (descriptives table/plot) we can see that Rue Morgue had the highest mean number of murders (M = 2.92) and Ruskin Avenue had the smallest mean number of murders (M = 0.83). The main ANOVA table below shows us the Welch F-statistic for predicting mean murders from location. Let’s assume we’re using 𝛼 = 0.05. Because the observed significance value is less than 0.05 we can say that there was a significant effect of street on the number of murders. However, at this stage we still do not know exactly which streets had significantly more murders (we don’t know which groups differed). To investigate, we can look at the Descriptives plot with confidence intervals, or we can conduct hypothesis tests using post hoc tests, where each street is compared to all of the remaining streets. To have a more robust result, we can use bootstrapped confidence intervals.

ANOVA - murder
95% CI for ω²
Homogeneity Correction Cases Sum of Squares df Mean Square F p ω² Lower Upper
Welch street 29.167 2.000 14.583 4.595 0.023 0.226 0.011 0.437
Residuals 76.833 19.285 3.984  
Note.  Type III Sum of Squares

Descriptives

Descriptives - murder
street N Mean SD SE Coefficient of variation
Ruskin Avenue 12 0.833 0.718 0.207 0.861
Acacia Avenue 12 1.250 1.138 0.329 0.911
Rue Morgue 12 2.917 2.275 0.657 0.780

Descriptives plots

Post Hoc Tests

If we look at the values in the column labelled ptukey we can see that the two significant comparisons are between Ruskin Avenue and Rue Morgue (ptukey = 0.006) and between Acacia Avenue and Rue Morgue (ptukey = 0.03). The BCa 95% confidence intervals corroborate this result, since the intervals do not contain 0 for these two comparisons. Combined with the observed means in the Descriptives table/plot, this tells us that Rue Morgue had the highest number of murders, compared to Ruskin Avenue and Acacia Avenue. Note that values from your bootstrap will slightly differ, since the bootstrap uses random number generation; in order to have these values fluctuate less, you can opt to use more bootstrap replicates (I set mine to 5000).

Standard (HSD)

Bootstrapped Post Hoc Comparisons - street
95% bca† CI
Mean Difference Lower Upper SE df bias t ptukey
Ruskin Avenue Acacia Avenue -0.400 -1.214 0.299 0.379 33 0.008 -0.669 0.783
  Rue Morgue -2.077 -3.425 -0.745 0.684 33 -0.003 -3.344 0.006 **
Acacia Avenue Rue Morgue -1.669 -3.091 -0.215 0.732 33 -0.011 -2.676 0.030 *
 * p < .05, ** p < .01
† Bias corrected accelerated.
Note.  Bootstrapping based on 5000 successful replicates.
Note.  Mean Difference estimate is based on the median of the bootstrap distribution.
Note.  P-value adjusted for comparing a family of 3 estimates.