An experimenter at the University of California at San Diego conducted a study o

Question

An experimenter at the University of California at San Diego conducted a study of sex differences in nonverbal sensitivity using an independent-sample design, with 32 women and 32 men. Her results showed that the women were significantly better than the men at decoding nonverbal cues, t = 2.34, df = 62, p < .05 two-tailed, and Cohen’s d = 0.594 and reffect size = .28. Suppose the experimenter added an additional 30 women and 30 men, randomly selected from the same population as the original sample. When the analysis is recalculated with the extra participants, should the new t be larger, smaller, or about the same size? Should the p value be larger, smaller, or about the same size? Should Cohen’s d and the reffect size be larger, smaller, or about the same size relative to the original effect size values? Should the 95% confidence interval be wider, narrower, or about the same size?

Explanation / Answer

1. The first experiment has already shown that p-value<0.05 that is the null hypotheses is rejected i.e. we reject the hypotheses that there is no difference between men and women. This means in the population there is significant difference between men and women population. If we go on and sample further then this difference will be more pronounced. Mathematicall, t is the ratio of mean difference to the scaled pooled variance. We find that t is 2.34 now with 62 df. Since we expect the diff to still remain in the data so at 62 + 60 = 122 df the t-value should increase to increase gap from the critical value i.e. more surely reject the null hypotheses. (Since higher the df the lower the t-critical value)

2. If t-value increases and the t-critical value decreases (due to increase in the degrees of freedom) then the probability that the t-distribution takes a value more extreme than the observed value of t decreases, i.e p-value decreases.

3. Chen's D is difference between the 2 means divided by the pooled S.D. With increase in the number of observations the S.D increases because there is a wide gap between the male and female population, However the individual means should almost remain same, hence the numerator of Cohen'D remains same with increase in the denominator. Hence Cohen'D decreases. The r-effect as given by the correlation coeffecient between the 2 population can't be inferred because we have knowledge only on the difference between the population, but no information on the movement of one population with another.

4. the confidence interval for the difference in the means becomes narrow. With more data coming in we are more confident of the Confidence interval and hence 95% CI can be achieved in a much smaller gap than earlier. In fact mathematically the CI length is a decreasing function of N. A CI is always like mean - s.d/n, mean + s.d/n. So if n increases then the factor s.d/n decreases and hence the gap reduces.

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