Lesson 3: Graphical Display of Multivariate Data.Lesson 2: Linear Combinations of Random Variables.1.5 - Additional Measures of Dispersion.Lesson 1: Measures of Central Tendency, Dispersion and Association.Next 7.1.16 - Summary of Basic Material ».« Previous 7.1.14 - The Multivariate Case.The counterfeit notes can be distinguished from the genuine notes on at least one of the measurements.Īfter concluding that the counterfeit notes can be distinguished from the genuine notes the next step in our analysis is to determine upon which variables they are different. The sample variance-covariance matrix for the real or genuine notes appears below: Note: You can also perform this entire paired samples t-test by simply using the Paired Samples t-test Calculator.The sample mean vectors are copied into the table below: We have sufficient evidence to say that the mean max vertical jump of players is different before and after participating in the training program. Since this p-value is less than our significance level α = 0.05, we reject the null hypothesis. Step 4: Calculate the p-value of the test statistic t.Īccording to the T Score to P Value Calculator, the p-value associated with t = -3.226 and degrees of freedom = n-1 = 20-1 = 19 is 0.00445. H 1: μ 1 ≠ μ 2 (the two population means are not equal).H 0: μ 1 = μ 2 (the two population means are equal).We will perform the paired samples t-test with the following hypotheses: s: sample standard deviation of the differences = 1.317.x diff: sample mean of the differences = -0.95.Step 1: Calculate the summary data for the differences. To determine whether or not the training program actually had an effect on max vertical jump, we will perform a paired samples t-test at significance level α = 0.05 using the following steps: Then, we may have each player use the training program for one month and then measure their max vertical jump again at the end of the month. To test this, we may recruit a simple random sample of 20 college basketball players and measure each of their max vertical jumps. Suppose we want to know whether or not a certain training program is able to increase the max vertical jump (in inches) of college basketball players. There should be no extreme outliers in the differences.The differences between the pairs should be approximately normally distributed.The participants should be selected randomly from the population.Paired Samples t-test: Assumptionsįor the results of a paired samples t-test to be valid, the following assumptions should be met: If the p-value that corresponds to the test statistic t with (n-1) degrees of freedom is less than your chosen significance level (common choices are 0.10, 0.05, and 0.01) then you can reject the null hypothesis. s: sample standard deviation of the differences.We use the following formula to calculate the test statistic t: H 1 (left-tailed): μ 1 μ 2 (population 1 mean is greater than population 2 mean).H 1 (two-tailed): μ 1 ≠ μ 2 (the two population means are not equal).The alternative hypothesis can be either two-tailed, left-tailed, or right-tailed: H 0: μ 1 = μ 2 (the two population means are equal).Paired Samples t-test: FormulaĪ paired samples t-test always uses the following null hypothesis: In both cases we are interested in comparing the mean measurement between two groups in which each observation in one sample can be paired with an observation in the other sample. the response time of a patient is measured on two different drugs. A measurement is taken under two different conditions – e.g. the max vertical jump of college basketball players is measured before and after participating in a training program.Ģ. A measurement is taken on a subject before and after some treatment – e.g. An example of how to perform a paired samples t-test.Ī paired samples t-test is commonly used in two scenarios:ġ.The assumptions that should be met to perform a paired samples t-test.The formula to perform a paired samples t-test.The motivation for performing a paired samples t-test.A paired samples t-test is used to compare the means of two samples when each observation in one sample can be paired with an observation in the other sample.
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