Results

ANOVA

The table below shows the main ANOVA summary table. We should routinely look at the robust Fs. Let’s assume we’re using 𝛼= 0.05, because the observed significance of Welch’s F is less than 0.05 we can say that there was a significant effect of mobile phones on the size of tumour. At this stage we still do not know exactly what the effect of the phones was (we don’t know which groups differed). Because there were no specific hypotheses I carried out post hoc tests and using the standard procedure. Each group of participants is compared to all of the remaining groups (see post-hoc tests for continuation of analysis).

ANOVA - tumour
95% CI for ω²
Homogeneity Correction Cases Sum of Squares df Mean Square F p ω² Lower Upper
Welch usage 450.664 5.000 90.133 414.926 < .001 0.918 0.892 0.936
Residuals 38.094 44.390 0.858  
Note.  Type III Sum of Squares

Descriptives

Descriptives - tumour
usage N Mean SD SE Coefficient of variation
0 hours 20 0.018 0.012 0.003 0.691
1 hour 20 0.515 0.284 0.064 0.552
2 hours 20 1.261 0.492 0.110 0.390
3 hours 20 3.022 0.766 0.171 0.253
4 hours 20 4.888 0.696 0.156 0.142
5 hours 20 4.731 0.782 0.175 0.165

Bar plots

The plot below displays the error bar chart of the mobile phone data. Note that in the control group (0 hours), the mean size of the tumour is virtually zero (we wouldn’t actually expect them to have a tumour) and the error bar shows that there was very little variance across samples - this almost certainly means we cannot assume equal variances. Above is the table of descriptive statistics. The means should correspond to those plotted. These diagnostics are important for interpretation later on.

Post Hoc Tests

First, the control group (0 hours) is compared to the 1, 2, 3, 4 and 5 hour groups and reveals a significant difference in almost cases (almost all the values in the column labelled ptukey are less than 0.05). In the next part of the table, the 1 hour group is compared to all other groups. Again all comparisons are significant (all the values in the column labelled ptukey are less than 0.05). In fact, all of the comparisons appear to be highly significant except the comparison between the 4 and 5 hour groups, which is non-significant because the value in the column labelled ptukey is larger than 0.05.

Games-Howell

Games-Howell Post Hoc Comparisons - usage
Comparison Mean Difference SE t df ptukey
0 hours - 1 hour -0.497 0.064 -7.819 19.069 < .001 ***
0 hours - 2 hours -1.244 0.110 -11.298 19.023 < .001 ***
0 hours - 3 hours -3.004 0.171 -17.546 19.010 < .001 ***
0 hours - 4 hours -4.870 0.156 -31.277 19.012 < .001 ***
0 hours - 5 hours -4.713 0.175 -26.963 19.009 < .001 ***
1 hour - 2 hours -0.746 0.127 -5.874 30.402 < .001 ***
1 hour - 3 hours -2.507 0.183 -13.728 24.139 < .001 ***
1 hour - 4 hours -4.373 0.168 -26.005 25.160 < .001 ***
1 hour - 5 hours -4.216 0.186 -22.669 23.937 < .001 ***
2 hours - 3 hours -1.760 0.204 -8.649 32.415 < .001 ***
2 hours - 4 hours -3.626 0.191 -19.021 34.194 < .001 ***
2 hours - 5 hours -3.469 0.207 -16.797 32.020 < .001 ***
3 hours - 4 hours -1.866 0.231 -8.065 37.663 < .001 ***
3 hours - 5 hours -1.709 0.245 -6.986 37.984 < .001 ***
4 hours - 5 hours 0.157 0.234 0.672 37.503 0.984
 *** p < .001
Note.  Results based on uncorrected means.

Using a mobile phone significantly affected the size of brain tumour found in participants, 𝐹Welch (5, 44.39) = 414.93, p < 0.001, 𝜔2 = 0.92 [0.89, 0.93]. The effect size indicated that the effect of phone use on tumour size was substantial. Games-Howell post hoc tests with Tukey corrected p-values revealed significant differences between all groups (p < 0.001 for all tests) except between 0 and 1 hours (p = 0.079) and 4 and 5 hours (p = 0.984).