Responding to: Disc1 Various Forms of the t Test In what research situations should the paired samples t test be used rather than the independent samples t test?
Based on the information that was provided by Warner (2013) a t TEST is a procedure that is used for comparing a set of sample means to see if there is evidence between two population means. A t test will determine if the two population means differ from each other and it will also tell how much it will differ from each other if any difference. Something that would use a t test that is stated in Warner (2013) is treatment a have a higher rate of recovery than treatment b. Paired sample t test is used to compare two population mean where you have two sample and the one sample can be paired with the other sample that is being observed. For example you would use a paired sample t test would be drinking water. You can compare a certain zinc value from bottle water and tap water. Independent sample t test is a test that compares the means of two groups to find out if there is evidence that population means are different. An example of that would be comparing two different states on what they spend a week on fast food.
Warner, R. M. (2013). Applied Statistics: From Bivariate Through Multivariate Techniques, 2nd Edition. [Bookshelf Online]. Retrieved from https://online.vitalsource.com/#/books/9781483305974/
Various Forms of the t Test
A t test is a statistic that is used to test hypotheses about scores on quantitative variables (Warner, 2013). A paired sample t test is indicated when scores come from a repeated measures study a pretest/posttest design, matched samples or other design in which scores are paired in some way. An independent t test is a parametric test that is best used when groups being compared are between-subjects or independent group. When it comes to choosing which to use a paired t test should be chosen over an independent t test if the data comes from a within-subjects or repeated measures design a paired sample t test should be chosen.
Applied Behavior Analysis
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, Calif.: SAGE Publications.
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Two Versions of Independent Samples t Test
Analyze why there are two different versions (“Equal variances assumed” and “Equal variances not assumed”) of the ttest on the SPSS printout and how you decide which one is more appropriate.
There are two different versions of the t-test on the SPSS printout. One version states, “equal variances assumed” while the other reports “equal variances not assumed”. In order to determine which version of the t-test should be utilized, the Levene test should be used (Warner, 2013). Using the Levene test to determine which t-test should be used is the best way to decipher whether or not “equal variance assumed” or “equal variance not assumed”. If a researcher looked at the Levene test and saw that there was no severe and/or significant violation, then the researcher would be able to determine that “equal variance assumed” (Warner, 2013). When there is “equal variance assumed”, it is important to remember that there is always a risk for Type 1 error (Warner, 2013). In order for researchers to determine “equal variance assumed”, they must also make sure that the population is not small and unequal (Warner, 2013). If there was a tiny, uneven population and/or group being measured, then the risk of Type 1 error becomes higher (Warner, 2013).
In order to determine “equal variances not assumed”, researchers must once again look at the Levene test (Warner, 2013). If the population and/or group being tested displayed skewed correlations and different variances, then the researchers would deem “equal variances not assumed” (Warner, 2013). Another time that researchers may decide that “equal variances not assumed” would be if the f value on the Levene test was very small (Warner, 2013). If it was f value did not show statistical significance, then the test would once again be reported as “equal variances not assumed” (Warner, 2013). This would also be true if the p-value was determined to be small (ie. p<.05 or p<.01) (Warner, 2013).
Warner, R. M. (2013). Applied Statistics From Bivariate Through Multivariate Techniques (2nd ed.). Thousand Oakes, CA: SAGE Publications.
Equal variance assumed is when in a sample the two independent samples are assumed that are drawn for populations that are identical in their variances, in this t test it is assume equal variances (Warner, 2013). Equal variances not assumed is when two independent samples are assumed that are drawn from populations that are unequal in variances, in this case it is not assume equal variances (Warner, 2013). In the SPSS output, we have both equal variances, to determine which variance is going to be used we need to rely on what the Levene’s test indicates. For example, if the Levene’s test indicates that the variance is equal in both groups then the equal variances assumed is appropriate, but if indicates that both groups are not equal then the equal variances not assume would be appropriate. When utilizing equal variances are assumed the researcher utilizes the calculation of pooled variances (Warner, 2013). Instead when equal variances cannot be assumed, researcher would use calculation un-pooled variances and a correction to the degrees of freedom (Warner, 2013).
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: Sage.