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3. The t statistic, the t distribution, and sample size The average duration of labor from the first contraction to the birth of the baby in women over 35 who have not previously given birth and who did not use any pharmaceuticals is 16 hours. Suppose you have a sample of 29 women who exercise daily, and who have an average duration of labor of 17.8 hours and a sample variance of 77.4 hours. You want to test the hypothesis that women who exercise daily have a different duration of labor than all women. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is SM= statistic is Now suppose you have a larger sample size n 73. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same standard deviation as above, but with the larger sample size. The new estimated standard error is statistic is The new t Note that the t statistic becomes The t as n becomes larger. Use the Distributions tool to look at the t distributions for different sample sizes. To do this, choose the Degrees of Freedom for the first sample size on the slider, and click the radio button with the single orange line. Move the orange vertical line to the right until the number below the orange line is located on the t statistic. The probability of getting that t statistic or one more extreme will appear in the bubble with the orange type. Now repeat the process for the other sample.

t Distribution Degrees of Freedom-52 AA -3.0 -1.0 0.0 1.0 2.0 What is the probability of getting the t statistic or something more extreme for the sample size of n = 29?p= getting the t statistic or something more extreme for the sample size of n = 73?p= 3.0 What is the probability of The t distribution is with a smaller n. (Hint: To best see this, click the radio button in the tool with no vertical lines. Slowly move the Degrees of Freedom slider from the smallest value to the largest value, and observe how the shape of the distribution chaninne

6. Effect size - Cohen's d and r squared An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist's findings is that one year after the workshop, a sample of 81 job seekers who received training on resume writing worked more than 30 hours per week an average of 8.7 months in the last year, with a standard deviation of 4.1. The typical job seeker works 7.4 months. The psychologist finds that the estimated Cohen's d is 2.853 the t statistic is 2.83, and r² is 0.091 treatment treatment effect. (Hint: Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a effect. Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a When using Cohen's guidelines for interpreting the effect size, if the value lies between two categories, then specify the range covered by both categories, for example, medium to large.) Another one of the psychologist's findings is that a sample of 81 job seekers who received training on dressing for interviews scored an average of 8.1 as measured on a 9-point job search motivation scale, with a standard deviation of 0.8. The typical job seeker scores 7.4 points. She finds that the estimated Cohen's dis the t statistic is 7.78, and r² is Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a treatment effect. Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a treatment effect.

size a and squar An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist's findings is that one year after the workshop, a sample of 81 job seekers who received training on resume writing worked more than 30 hours per week an average of 8.7 months in the last year, with a standard deviation of 4.1. The typical job seeker works 7.4 months. The psychologist finds that the estimated Cohen's d is 2.853, the t statistic is 2.83, and r² is 0.091 Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a effect. Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a When using Cohen's guidelines for interpreting the effect size, if the value lies between two categories, the categories, for example, medium to large.) Another one of the psychologist's findings is that a sample of 81 job seekers who received training on dres as measured on a 9-point job search motivation scale, with a standard deviation of 0.8. The typical job se medium very large small treatment treatment effect. (Hint: range covered by both views scored an average of 8.1 4 points. She finds that the estimated Cohen's d is, the t statistic is 7.78, and r² is Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a treatment effect. Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a treatment effect.