# Men and Women - Mathematical Methods in Psychology

## Men and women

Now let's see how the two groups of subjects correlate in terms of femininity - masculinity. In Ch. 1, we found that the average femininity-masculinity in the women group was 29.3, while for the group of men, it was 36.2.

We will assume that these differences exceed the random level, and the femininity-masculinity in the group of men as a whole reliably exceeds the femininity-masculinity in the group of women.

In terms of statistical hypotheses, this will look like this. The null hypothesis will assert the equality of the corresponding mathematical expectations, i.e. N 0: μx = μy. An alternative hypothesis will be to assert that the value of the mathematical expectation of femininity-masculinity in the group of men exceeds the corresponding value in the group of women, i.е. H 1: μx & lt; μy.

To compare the gender typing levels of male and female groups, we use the Student's test described in Section 2.4 (formula (2.5)). This test, as already indicated, is based on the assumption of homogeneity of variances in two general sets. To estimate this assumption and further the possibility of combining two samples in the variance estimate, we use the f-test (see formula (2.10)).

The calculations carried out in Ch. 1, showed that the variance of the femininity-masculinity index in the group of men was 27.75, and the variance of this indicator in the group of women was 24.96. As we see, the value of the dispersion in the group of men slightly exceeds the corresponding index in women. Therefore, we construct the F -relations in such a way that the variance value for the male sample will be in the numerator, and the variance for the female sample is in the denominator: If the null hypothesis confirming the equality of variances in two general populations is true, then the obtained statistics F should be described F - distribution with 19 degrees of freedom in both the numerator and the denominator (this is indicated in parentheses after a comma after F ). To estimate the statistical reliability of the obtained statistics, under the condition that our null hypothesis is true, we use the tables of/-distribution (see Appendix 4). It can be seen that the value of F for the specified number of degrees of freedom does not even enter into the 10% quantile. . This means that our null hypothesis should be preserved, and the variances of the two populations are not statistically different. Accordingly, an alternative hypothesis about the inequality of two variances should be rejected.

Therefore, it is possible to combine our data and estimate the total variance for two groups of subjects with the formulas (2.3) or (2.4): Then, using formula (2.5), we calculate t -statistics: We estimate the statistical reliability of the found value t (see Appendix 3). We see that this value certainly exceeds 1% quantile t -distributions. This means that in subsequent experiments it is unlikely to get the same (or even large) value t , assuming the null hypothesis that the averages are equal. The chances are certainly less than one per hundred. Therefore, the null hypothesis should be rejected because of the unlikely result obtained on its basis. Thus, it can be concluded that the femininity-masculinity indices in the two groups of subjects are statistically reliably different, and the men in the samples studied generally show a higher level in this indicator than women.

A similar result can be obtained if we use the statistical package SPSS Statistics.

Prepare our data for processing using the statistical package SPSS Statistics. To do this, after running the program, go to the Variables and create two variables: Group and Masculinity & quot ;. The values ​​of the fields describing these variables will be left by default with one exception. For the group variable, we specify two fixed values: 1 - "men" and 2 - "women"; (Figure 2.8).

Now go back to the Data and we introduce the results of our measurements of femininity-masculinity in two groups of subjects (Figure 2.9).

Next, choose the "Analysis" menu from the menu. - Average comparison - Τ is a criterion for independent samples ... (see Figure 2.6).

In the window that appears, select the variable "Masculinality" and add it to the Checked Variables field, then select the variable Group and add it to the Group by field. After that, click the Set Groups ... button. and in the appeared window we indicate the codes of our groups, which we used to define the variable "Group", i.e. 1 for a group of men and 2 for a group of women (Figure 2.10). Click the Continue button and return to the previous window. Fig. 2.8. Defining variables when comparing the averages in two samples using t Student test strong> Fig. 2.9. Data on femininity - masculinity in two groups of subjects for SPSS Statistics Fig. 2.10. Determining the group codes when comparing the means in SPSS Statistics

Now we have all the data to compare the average femininity indexes - masculinity in the two groups with the help of the Student test (Figure 2.11). Click OK . Fig. 2.11. Comparison of averages in two independent samples using t -test Student test in SPSS Statistics

The results of data processing are displayed in a new window, the fragment of which is shown in Fig. 2.12. Fig. 2.12. Results of the comparison of the mean of the Student's test in SPSS Statistics

Consider these data. As is evident from Fig. 2.12, the results table contains two rows. The upper part shows the results of calculating the statistics t under the condition of homogeneity of the variances, at the bottom there are results for the case when this condition is not fulfilled.

First, the results of testing the hypothesis of homogeneity of variance in two groups are given using the criterion for the equality of Livin's variances. As noted above, this criterion is a more modern analog of the F -test, discussed in the theoretical part of this chapter. Then data on t -statistics: its calculated value, the number of degrees of freedom and statistical significance, as well as the difference in the mean values ​​of the variable being investigated and some other indicators, usually not so significant for the researcher.

As you can see, the results obtained coincide exactly with those that were determined in the calculations manually. Accordingly, we can again conclude that there are reliable statistically significant differences in the indicator studied for the two groups of subjects. It should also be noted that the correction, which can be included in the evaluation of degrees of freedom under the condition of inhomogeneity of dispersions, is insignificant. This indirectly shows that our variances are really homogeneous.

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