In our last post, we talked about single sample t-tests, which is a way of comparing the mean of a population with the mean of a sample to look for a difference. With two-sample t-tests, we are now trying to find a difference between two different sample means. More specifically,\u00a0independent t-tests<\/strong> involve comparing the means of two samples which are distinctly different from one another in regards to the individuals within each sample. For example, a group of pet owners vs. a group of folks who don’t own pets. These two groups are completely independent of one another. This distinction will be important in a later post.<\/p>\n A more technical explanation of the difference between a single sample and two-sample is that a\u00a0<\/b>single sample t-test revolves around drawing conclusions about a treated population based on a sample mean and an untreated population mean (no standard deviation). An i<\/span>ndependent sample t-tests are all about comparing the means of two samples (usually a control group\/untreated group and a treated group) to draw inferences about how there might be differences between those two groups in the broader population<\/span><\/p>\n There are some distinct advantages and disadvantages to this approach when compared to other approaches. To avoid confusion, we won’t describe the other approaches here but will just mark the advantages and disadvantages of this one here for your consideration:<\/p>\n Advantages:<\/p>\n Disadvantages:<\/span><\/p>\n The null and alternative hypotheses for this kind of test are as follows:<\/span><\/p>\n H<\/span>0<\/span>: \u00b5<\/span>1<\/span> – \u00b5<\/span>2<\/span> = 0 (no difference in the population means)<\/span><\/p>\n H<\/span>1<\/span>: \u00b5<\/span>1<\/span> – \u00b5<\/span>2<\/span> \u2260 0 (there is a mean difference)<\/span><\/p>\n Steps of calculating an independent samples t-test (from this point forward, if there is a larger formula you’re looking for, see our formula guide post or pdf)<\/span>:<\/span><\/p>\n Assumptions of independent sample t-tests:<\/p>\n To calculate the estimated standard error, you need to first calculate pooled variance, especially because not all treatment or non-treatment groups will have the same number of scores, and so you need to weight in both groups before coming to terms with the overall estimated standard error. Remember that the e<\/span>stimated standard error is how we calculate the standard error when there\u2019s no population mean to go off of.<\/span><\/p>\n In essence, the steps for calculating a t-test by hand are:<\/p>\n We use Cohen\u2019s d to get effect size. For this particular test, it\u2019s mean 1 minus mean 2 all divided by the square root of the pool variance calculated earlier. In this case, instead of comparing the effects of a sample to the population (asking, is this practically significant rather than just statistically significant?), we’re comparing the effects of two different samples.\u00a0<\/span><\/p>\n Hartley’s F-max test\u00a0<\/strong>is a statistical test to evaluate the homogeneity assumption.\u00a0<\/span>To compute, you need to compute the sample variance of each sample individually. Then, you need to make a fraction with the biggest variance on top and the smallest one on the bottom. Finally, compute. The F-max value computed for the sample data is compared with the critical value found in an F-max table. If the sample value is larger than the table value, then you can conclude that the homogeneity assumption is not valid.<\/span><\/p>\n <\/p>\n If you’re looking for more help on learning the concept of the independent samples t-test or how to calculate it, check out this series on youtube: part 1<\/a>, part 2<\/a>, part 3<\/a>, part 4<\/a>, part 5<\/a>, part 6<\/a>. It may seem like a lot of videos, but each video is only 5 minutes long.<\/p>\n","protected":false},"excerpt":{"rendered":" Independent t-test In our last post, we talked about single sample t-tests, which is a way of comparing the mean of a population with the mean of a sample to look for a difference. With two-sample t-tests, we are now trying to find a difference between two different sample means. More specifically,\u00a0independent t-tests involve comparing […]<\/p>\n","protected":false},"author":1347,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[151,153,148,152,158,155,156,150,159,160],"tags":[4,3,5,68,76,57,74,8,75,7,6],"_links":{"self":[{"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/posts\/81"}],"collection":[{"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/users\/1347"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/comments?post=81"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/posts\/81\/revisions"}],"predecessor-version":[{"id":121,"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/posts\/81\/revisions\/121"}],"wp:attachment":[{"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/media?parent=81"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/categories?post=81"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubalt.edu\/mathsupportcenter\/wp-json\/wp\/v2\/tags?post=81"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n
Hypothesis Testing with Independent t-tests<\/h2>\n
\n
\n
Estimated Standard Error and Pooled Variance<\/h2>\n
\n
Effect Size of Independent Samples t-test<\/h2>\n
Hartley’s F-Max Test<\/h2>\n