Question 3

Chapter 4: Results

4.3. Objective 2

4.3.1. Question 3

Does the sex of an individual determine how attractive or masculine they find certain male faces and body odours?

Visual Stimulus Attractiveness

The Friedman’s two-way ANOVA comparing rankings of stimuli items between the sexes was not significant both before a bootstrap was applied (χ²= 7, df =5, NS) as well as after (𝜃_𝑥²=5.37, df=5, NS). Therefore, the null hypothesis was not rejected and the conclusion that there was no significant difference between the ranked stimuli items, drawn. However, as there were no significant differences between the ranked items it can be assumed that men and women ranked the items differently.

Although the Friedman’s test implies a difference between the average rank of the medians between men and women, a 𝑊̃ test indicates significant agreement both before and after a bootstrap for both the sexes combined. However, although the agreement is significant it is small, and furthermore the 𝑊̃ statistic decreases after the bootstrap. In addition, the maximum agreement estimated by the upper confidence limit suggests that we can be 95%

certain that the 𝑊̃ population will not be greater than 0.286, which indicates a small yet significant window of agreement. Men in the initial sample did not significantly agree on which of the VS they considered visually attractive, however after a bootstrap was applied the men showed small but significant agreement. Women showed moderate significant concordance regarding the VS. This result may support the Friedman’s test. However, after a bootstrap was applied with the sample size of the sexes equated both men and women, independent of each other, showed agreement in their rankings of VA. However, in this instance women still showed more agreement regarding rankings of VA. Please see table 15 for a summary of the 𝑊̃ findings.

Table 15: Summary of bootstrapped (B=10000) 𝑾̃ for rankings of visual attractiveness for the sexes

Sex 𝑊̃ P 𝜃_𝑊̃ P SE Lower

confidence limit

Upper confidence

limit Decision Both

sexes

combined 0.18 <0.001 0.143 <0.001 0.062 0.045 0.284 Reject Women 0.33 <0.001 0.362 <0.001 0.116 0.142 0.597 Reject

Men 0.063 NS 0.107 0.05 0.062 0.026 0.266 Reject

The histograms below indicate the distributions of 𝜽_𝑾̃ for all significant aggreements in rankings of VA. The first histogram indicates the distribution of 𝜽_𝑾̃ statistics for both sexes combined, as is evident in the graph the distribution is slightly skewed and the confidence limits are quite narrow as indicated by the graph and table 15 above. Due to the slight skewness and narrow confidence limits interpretations must be regarded tenuously. The second histogram represents the distribution of 𝜽_𝑾̃ for women. As is visible in the graph, the distribution of scores is almost normal and the confidence interval is much wider, therefore, inferences regarding the female sample may be made with more rigour as the population estimation deduced from the bootstrap is normally distributed. The histogram regarding male rankings of VA is quite skewed and the confidence interval quite narrow, this may however be due to the reduction in variance caused by the oversampling procedure and thus must be interpreted cautiously.

Figure 15: Histograms representing the distribution of bootstrapped θ_W ̃ VA scores for both sexes combined (left), women (centre), and men (right)

0 1 2 3 4 5 6 7

0 0.2 0.4

Density

Normal(0.143,0.062)

0 0.5 1 1.5 2 2.5 3 3.5

0 0.2 0.4 0.6 0.8

Density

Normal(0.366,0.116)

0 1 2 3 4 5 6 7 8 9

0 0.2 0.4 0.6

Density

Normal(0.108,0.063)

Visual Stimulus Masculinity

A Friedman’s test indicated no significant difference between the ranked stimulus items when contrasting the sexes (χ²=6.86, df=5, NS), this was also not significant after bootstrapping was applied (𝜃_𝑥²= 6.02, df=5, NS). Therefore, the null hypothesis that there is no significant difference between the ranked items was not rejected, and the conclusion that men and women may rank the items differently was drawn.

As before, the Friedman’s result is not congruent with the measures of 𝑊̃ as agreement between the sexes was indicated to be significant although this agreement was very small and only just significant (see table 16). Subsequently, although men and women combined may have indicated significant agreement, men and women independently, did not show significant concordance before the bootstrap was applied. However, once bootstrapped, 𝜃_𝑊̃

for both sexes independently and both sexes combined indicated significant concordance. The bootstrap increased the degree of agreement amongst all the groups. Men showed greater agreement with regards to VM, sustaining predictions made earlier.

Table 16:Summary of bootstrapped (B=10000) 𝑾̃ for rankings of visual masculinity for the sexes

Sex 𝑊̃ P 𝜃_𝑊̃ P SE Lower

confidence limit

Upper confidence

limit Decision Men and

women

combined 0.072 0.05 0.107 0.001 0.047 0.034 0.213 Reject

Women 0.065 NS 0.108 0.05 0.055 0.026 0.237 Reject

Men 0.163 NS 0.201 0.001 0.089 0.057 0.4 Reject

The histograms indicating the distributions for 𝜽_𝑾̃ for VM for both sexes combined and independent are slightly positively skewed, therefore conclusions must be drawn tentatively regarding all the results. The confidence intervals for both sexes combined and women are slightly narrower than the confidence interval for the male sample, indicating a wider 95%

confidence interval for the estimation of the real world 𝜽_𝑾̃ statistic for men.

Figure 16: Histograms representing the distribution of bootstrapped θ_W ̃ VM scores for both sexes combined (left), women (centre), and men (right)

Scent Stimulus Attractiveness

In comparing the sexes for a difference in the rankings of stimulus items a Friedman’s test found no significant difference both before the bootstrap (χ²= 0.21, df=5, NS) and after (𝜃_𝑥²=3.4, df=5, NS). Thus, indicating that the null hypothesis should fail to be rejected and that there is no significant difference between the SA ranked items and thus, possibly a difference between the sexes.

This result is supported by the 𝑾̃ statistics reported in table 17. Per these results, men and women do not rank the attractiveness of scent concordantly and this result is sustained after the application of bootstrapping. Furthermore, before the bootstrap, both men and women independently were not concordant in their rankings of scent attraction, however, once bootstrapped, significant agreement was indicated, although the degree of agreement for both men and women was small.

Table 17: Summary of bootstrapped (B=10000) 𝑾̃ for rankings of scent attractiveness for the sexes

Sex 𝑊̃ P 𝜃_𝑊̃ P SE Lower

confidence limit

Upper confidence

limit Decision Men and

women

combined 0.019 NS 0.029 NS 0.020 0.005 0.081 fail to

reject

Women 0.086 NS 0.129 0.02 0.056 0.038 0.254 Reject

Men 0.061 NS 0.106 0.05 0.066 0.022 0.280 Reject

0 1 2 3 4 5 6 7 8 9

0 0.1 0.2 0.3

Density

Normal(0.107,0.047)

0 1 2 3 4 5 6 7 8

0 0.2 0.4

Density

Normal(0.108,0.055)

0 1 2 3 4 5

0 0.2 0.4 0.6

Density

Normal(0.202,0.089)

The histograms in figure 17 below, represent the distribution of 𝜃_𝑊̃ for women and men. For women, the distribution is positively skewed, although, much less skewed than the distribution for men. The confidence interval however is somewhat narrower than the confidence interval for men, as indicated in table 18. For men, the distribution is quite skewed with most of the distribution falling at the lower end of the confidence interval. These resultant distributions estimated to represent the population by the bootstrap are not normally distributed indicating that the results should be compared tenuously given the assumption that the population is normally distributed.

Figure 17: Histograms representing the distribution of bootstrapped θ_W ̃ SA scores women (left), and men (right)

Scent Stimulus Masculinity

The Friedman’s test for the masculinity of scent between stimulus items for the sexes indicated that both before bootstrapping (χ²=4.71, df=5, NS) and after bootstrapping (𝜃_𝑥²=5.133, df=5, NS) the distribution of stimulus items were not significantly different, therefore a conclusion can be tenuously drawn that men and women ranked the masculinity of the scent differently.

According to the summary of 𝑊̃ statistics for the agreement between the sexes regarding the masculinity of scent, there was no significant agreement amongst sexes combined, men or women. Furthermore, the only original outcome that was not sustained by the bootstrap was concordance amongst men and women combined which increased with the bootstrap and is only just significant with a very small degree of agreement.

0 1 2 3 4 5 6 7 8

0 0.1 0.2 0.3 0.4

Density

Normal(0.129,0.056)

0 1 2 3 4 5 6 7 8

0 0.2 0.4 0.6

Density

Normal(0.106,0.066)

The distribution of 𝜃_𝑊̃ regarding masculinity rankings for both sexes combined is illustrated in figure 18 adjacent, indicates a slight positively skewed distribution. This indicates that most estimated 𝜃_𝑊̃ statistics lie below the mean and closer to the lower confidence limit. A skewed distribution violates the assumption of normality and therefore any conclusions drawn cannot be substantially indicative of the real-world population. Furthermore, the confidence interval is quite narrow providing a small

window for which to be 95% certain of a real-world estimate.