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# When reporting your results make sure you specify

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When reporting your results, make sure you specify which technology you used, as different software use different degrees of freedom. You will also need to watch for the direction of subtraction that the software uses automatically (often alphabetical by group name). There is also a version of the two-sample t -test that makes an additional assumption the population standard deviations are equal. The standardized statistic has the following form: 2 1 2 1 0 / 1 / 1 n n s x x t p ² ± where 2 ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 ± ± ± ² ± n n s n s n s p , a pooled estimate of the common SD. This “ pooled t -test ” has some advantages (namely higher power), when the population standard deviations are equal. However, this additional condition can be difficult to assess from your sample data. The benefits do not appear to outweigh the risks of applying this assumption when you shouldn’t. So in this text we will focus on “unpooled t - tests” only. Technology Detour ± Two-Sample t -Test (unpooled, summary data) In R The iscamtwosamplet function takes the following inputs: o Group 1 mean, standard deviation, sample size (in that order) o Group 2 mean, standard deviation, sample size (in that order) o Optional: hypothesized difference (default is zero) o Optional: alternative (“less”, “greater”, or “two.sided”) o Optional: conf.level For example: iscamtwosamplet(x1=75, sd1=15, n1=888, x2=66, sd2=15, n2=99, alt="greater") In Minitab x Choose Stat > Basic Statistics > 2-Sample t . x Use the pull0down menu to select Summarized data . x Enter the summary statistics. x Press Options and specify direction of Alternative. x Press OK twice.

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Chance/Rossman, 2015 ISCAM III Investigation 4.2 266 Theory-Based Inference applet x Use the pull- down menu to select “Two means.” x Specify the summary statistics. Press Calculate . (You will see a visual representation of the sample means and standard deviations.) x Check the box for Test of Significance. Specify the hypothesized difference and the direction of the alternative hypothesis. x Press Calculate . Technology Detour - Two-Sample t -Test (unpooled, raw data) Theory-Based Inference applet x Use the pull- down menu to select “Two means.” x Copy the data to the clipboard, check the Paste data box, select the Stacked box if that’s the data format (explanatory variable in first column), press Clear , click in the data window and paste the data. Press Use data . x Check the Test of Significance box. x Specify the hypothesized difference and the direction of the alternative hypothesis. x Press Calculate . In R (note, if you have attached the data, you don’t need the “with”) > with(NBASalaries2014, t.test(salary~conference, alt="two.sided", var.equal=FALSE)) In Minitab x Choose Stat > Basic Statistics > 2-Sample t . x Stacked data: Select “Both samples are in one column” from the pull -down menu. Enter response variable in Samples and explanatory variable in Subscripts.
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• Spring '14
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