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Since μ d is assumed to 0, then we simply take the mean, d, and divide it by the standard error. This gives us a standard deviation of 4.64. Next, we get the standard deviation, s d, of the paired differences. To calculate the mean, we take all the paired differences, add them together, and divide them by the number of paired data samples, which in thisĬase is 10. So, in order to calculate the test statistic from this data, there is a number of steps we must do.Īs we did above, we had to take the first value of the paired data sample and minus the second value from it. If textbook B is better, we should get a negative paired difference value. If textbook A is better, we should get a positive paired difference value.
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If the methods are exactly equal, we should get a paired difference of 0. So these paired difference values now supersede the actual scores themselves, and this will be the new data we work with going forward. Therefore, we get the paired difference for each paired data sample. The difference between the scores is actually what's important, because we're doing a comparison to However, it's not the actual scores that we're interested in. So we have our paired data samples from each group (the group studying with Textbook A vs the group studying with Textbook B). With have similar subjects being compared (reading ability, grades, etc.), we want to see which textbook is better fit to train students So, as you can see, the data are in pairs. Let's say that the following table below are the scores of the students. Receive based on a previous agreement with the students that they would grant permission to the scores. The second group will train for the exam using Textbook B.Īfter the training occurs and the students have taken the board exam, the prep center are notified of all the grades that the students The first group will train for the exam using Textbook A. Grades, reading ability, study habits, etc so that it's relatively even between each group. The pairs are matched up according to their Therefore, the prep instructor subdivides the 20 trainees up into 2 groups, making 10 pairs. The prep instructor wants to determine if Textbook A or Textbook B is better at training students for the exam. To determine what is the best approach to train students so that they can get the highest score possible on the exam. The person who runs this prep class wants This is a brand new prep class that isn't established yet in terms of its teaching method. This prep class is to prepare engineering students for the national board exam to become Let's say that we are running a new prep class. To illustrate this, let's now go over an example of a paired t-test scenario, which can be seen in real life.
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The sample size is the number of paired data samples. S d is the standard deviation of of the paired differences. To 0, and the alternative hypothesis is that μ d 0, or ≠ 0. When testing paired data, the null hypothesis is that μ d is equal Μ d is the population mean of all paired differences. The formula to calculate the test statistic of paired data samples is, Paired tests are used when you want to minimize the chance of the treatment and control groups being too different. In the sample are either paired up in some way (such as a husband and wife) or the same people are used twice (for example, preprocedure and postprocedure). The paired t-test is used when the variable is numerical in nature (for example, the height of a person or the weight of a person) and the individuals With this calculator, a user can enter up to 100 paired data samples. This paired t-test calculator calculates the test statistic for a given set of paired data samples. Paired t-test Calculator Enter Up to 100 Paired Data SamplesĪdd 10 More Paired Data Samples Add 10 More Paired Data Samples Add 10 More Paired Data Samples Add 10 More Paired Data Samples Add 10 More Paired Data Samples Add 10 More Paired Data Samples Add 10 More Paired Data Samples Add 10 More Paired Data Samples Add 10 More Paired Data Samples