Results

Data from Daniels (2012). The authors investigated the impact of sexualized images on women's self-evaluations.

picture: performance athletes or sexualized athletes
theme_present: absent or present
self_evaluation: the number of counts that fell in particular combinations of categories

Contingency Tables

The Cells tab is used to ask for the information displayed in the contingency table. It is important that you ask for expected counts because this is how we check the assumptions about the expected frequencies. It is also useful to have a look at the row, column and total percentages because these values are usually more easily interpreted than the actual frequencies and provide some idea of the origin of any significant effects. There is another option that is useful for breaking down a significant effect (should we get one): select standardized residuals.

Let’s check that the expected frequencies assumption has been met. We have a 2 × 2 table, so all expected frequencies need to be greater than 5. If you look at the expected counts in the contingency table, we see that the smallest expected count is 34.6 (for women who saw pictures of performance athletes and did self-evaluate). This value exceeds 5 and so the assumption has been met.

The expected counts and observed counts help us say which observations occured more, or less, often than expected under the null hypothesis (which states that there is no association between the two variables). For example, for Performance Athletes, there were 97 cases where the theme was absent in what they wrote, while we would expect only 87.4 counts if theme and picture would be unrelated. The standardized residual is positive, which indicates that indeed the observed count was higher than expected. For Sexualized Athletes, this was the other way around, and there were fewer occurrences where the theme was absent in what they wrote. Whether these differences are significant is indicated by the Pearson's chi-square test below.

Contingency Tables
		theme_present
picture		Absent	Present	Total
Performance athletes	Count	97.000	20.000	117.000
	Expected count	82.401	34.599	117.000
	% within row	82.906 %	17.094 %	100.000 %
	% within column	53.591 %	26.316 %	45.525 %
	% of total	37.743 %	7.782 %	45.525 %
	Standardized residuals	4.007	-4.007
Sexualized athletes	Count	84.000	56.000	140.000
	Expected count	98.599	41.401	140.000
	% within row	60.000 %	40.000 %	100.000 %
	% within column	46.409 %	73.684 %	54.475 %
	% of total	32.685 %	21.790 %	54.475 %
	Standardized residuals	-4.007	4.007
Total	Count	181.000	76.000	257.000
	Expected count	181.000	76.000	257.000
	% within row	70.428 %	29.572 %	100.000 %
	% within column	100.000 %	100.000 %	100.000 %
	% of total	70.428 %	29.572 %	100.000 %

Chi-Squared Tests
	Value	df	p
Χ²	16.057	1	< .001
N	257

Pearson’s chi-square test examines whether there is an association between two categorical variables (in this case the type of picture and whether the women self-evaluated or not). The value of the chi-square statistic is 16.057. This value is highly significant (p < .001), indicating that the type of picture used had a significant effect on whether women self-evaluated.

The highly significant result indicates that there is an association between the type of picture and whether women self-evaluated or not. In other words, the pattern of responses (i.e., the proportion of women who self-evaluated to the proportion who did not) in the two picture conditions is significantly different. Below is an excerpt from Daniels’s (2012) conclusions:

Odds Ratio
		95% Confidence Intervals
	Odds Ratio	Lower	Upper	p
Odds ratio	3.233	1.796	5.823
Fisher's exact test	3.219	1.737	6.148	< .001

The effect size for 2x2 contingency tables is the odds ratio: How much more likely is it to observe absent in Performance athletes, compared to Sexualzed athletes? The odds ratio here is about 3.2, and we saw from the contingency table above that Performance athletes tended to have the theme be absent in what they wrote more often then expected, so then we know the direction in which to interpret this effect:

Performance athletes are 3.2 times more likely to have self-objectification be absent from their writing, compared to Sexualized athletes. But we can also phrase it the other way around:

Sexualized athletes are 3.2 times morel likely to have self-objectification be present in the writing, compared to Performance athletes.

The odds ratio is computed as the ratio within each row, and then we take the ratio of those ratio's:

For Performance athletes, absent occurred 97/20 = 4.85 times more than present.

For Sexualized athletes, absent occurred 84/56 = 1.5 times more than present.

So for Performance athletes, absent is 4.85/1.5 = 3.2 times more likely to occur over present, than it does for Sexualized athletes. This ratio significantly differs from 1 (see Fisher's exact test), which corroborates the result from Pearson's chi-square test.

Nominal
		Value
Phi-coefficient		0.250
Cramer's V		0.250