For the independent-measures t statistic, what is the effect of increasing the d

Question

For the independent-measures t statistic, what is the effect of increasing the difference between sample means? increase the likelihood of rejecting H_0 and increase measures of effect size increase the likelihood of rejecting H_0 and decrease measures of effect size decrease the likelihood of rejecting H_0 and increase measures of effect size decrease the likelihood of rejecting H_0 and decrease measures of effect size If other factors are held constant, which of the following sets of data would produce the smallest value for an independent-measures t statistic? The two samples both have n = 15 with sample variances of 20 and 25. The two samples both have n = 15 with variances of 120 and 125. The two samples both have n = 30 with sample variances of 20 and 25. The two samples both have n = 30 with variances of 120 and 125. Assuming that there is a 5-point difference between the two sample means, which set of sample characteristics is most likely to produce a significant value for the independent- measures t statistic? large sample sizes and small sample variances large sample sizes and large sample variances small sample sizes and small sample variances small sample sizes and large sample variances

Explanation / Answer

(21) first choice:: Increase the liklihood of rejecting H0 and increase the measure of effect size

if the difference between the samples mean is more than the t-statistics =(mean difference)/SE(mean difference) will be larger and finaly more chance of rejecting H0

For the independent samples T-test, Cohen's d is determined by calculating the mean difference between your two groups, and then dividing the result by the pooled standard deviation.

(22) Second:Two samples both have n=15 and sample variance 120 and 125

t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and n=n1+n2-2

Standard error of difference of mean= ((sp*(1/n1 +1/n2)1/2 ) for case is largest ultimately t-statistics will be smallest

(23)) first choice: large sample size and small variances

t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2

for significant t-statistic there should be large t and

for large t if difference of mean will be more and variacne of samples will be less and sample size will be more

n1 n2 s12 s22 sp2 SE 15 15 20 25 22.5 1.732051 15 15 120 125 122.5 4.041452 30 30 20 25 22.5 1.224745 30 30 120 125 122.5 2.857738

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