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In parametric statistics, when we have to compare means of two samples there are several test where 2 samples are dependent and independent 2 Sample T Test are used to compare the means of 2 sample which are not dependent on each other and have equal variance (determined by F test) which is normally distributed. Example: If we want to compare performance of two team (sales performance) Comparing the runs scored by two different team Outcome of a drug testing on 2 independent groups Wherein Paired Sample T test is performed to compare means of 2 samples which are dependent (paired) which is normally distributed. Two means could be : Comparison pre and post-performance different times Comparison performance due to change in conditions so on Examples: Comparing the sales pre and post advertisement Comparing performance of employee per and post refresher training Person’s health before and after a treatment Benefits of using Paired T test Paired T test is a powerful tool due to the below reasons: 1) Since the sample used before and after are the same hence eliminated variation between the samples Same set of employee before and after training Same bike before and after servicing Same product before and after a marketing campaign 2) Its best tool to measure the effectiveness of some factor on a sample, industries where it could be best in use are: Service Sector – measure performance of people before and after a training Sales – Effectiveness of awareness program/advertisement (pre and post sales value and volume) Pharma- effectiveness of medicine on patient’s health Automobile – Efficiency of automobile pre and post changing fuel efficiency So, we can find its utility in all fields where ever comparative study is required on a paired Sample 3) Increase in the degree of freedom, in 2 sample T-Test df is “n1+n1-2 : as there are two different samples”, But in Paired it n-1 as the sample are same (decrease in df required high t power) 4) Time and cost is minimized as the sample size remains the same (unlike 2 sample T test wherein 2 independent samples are collated 5) The outcome of the two groups are co-related

Benchmark Six Sigma Expert View by Venugopal R When we have to compare the averages for two samples, it could be for different reasons: 1. To estimate whether two existing populations are different with respect to their average values of the characteristics of interest. Examples: To compare the average life span of bulbs produced by two different companies Average marks scored by male students vs that of female students 2. To estimate whether the effect of some change on a given population is significant or not. Examples: Performance of a group before training and after training Average mileage of cars for one type of fuel vs another From the above, we can see that for point-1, the two samples being compared can never be the same, since the reason for comparison is a difference based on the very nature of the sample itself. In such situations, we have to use 2-sample 't' test, and no ‘pairing' is possible. For the point-2, we have a possibility of subjecting the same set of samples to the first treatment and then to the second treatment and compare the difference in performance for each same sample. In such situations, Paired ‘t’ test is the ideal comparative statistical tool to be used. We may also come across some situations, where the paired sampling would not be practically possible. For example, let’s take the case of evaluating the average life of bulbs from the same company before and after doing a process improvement. Since the life testing of bulbs is a destructive test, the same samples will not be available for doing a paired 't' test and hence we have to use a different set of samples, and hence, only 2-sample 't' test. Another example would be to compare the effect of two vaccines on a set of people. Once they are subject to vaccine-1, they would have developed immunity and we cannot subject the same set of people to vaccine-2, ruling out the possibility of a paired 't' test. A paired ‘t’ test is recommended over 2-sample ‘t’ test whenever the situation permits, considering the advantages. Let me statistically illustrate certain advantages of paired test using the below example. As part of a medical research study, the heart rates of 20 athletes were studied before and after subjecting them to a running program. Since heart rates of the same athletes were studied before and after the treatment, a paired test is possible. We will however, carryout the paired test and the unpaired 2-sample 't' test for the same sets of data and compare the results. The mean heart rate before the treatment was 74.5 and after treatment was 72.3. The Minitab outputs for both the tests are given below: From the above results, it can be seen from the p values that for the same set of data, the paired t test has shown significance, where as the 2-sample t test has not shown significance. Thus, the 2-sample t test for the same data exhibits higher ‘Type 2’ error. Now, let us fix the required power of the test as 0.8 and determine the sample size requirements for both these tests, all data remaining same: The above information are the outputs based on ‘Power & Sample size’. For both the type of tests, the sample size was determined based on a difference of 2, target power of 0.8 and standard deviation of 4.29. The paired test requires a sample of 39 whereas the 2-sample test requires a sample of 74. Hence, the paired t test is preferable, whenever practically possible, from the sampling size requirement as well.

Two Sample T Tests are statistical tests that are used to compare the mean values of two independent samples/groups to determine if there is a significant difference between the means of 2 samples in reference. Two samples are considered to be independent if the selection of individuals/objects of one sample does not influence the selection of individuals/objects in the other sample in any way. The data from both samples should be normally distributed to apply the Two Sample T Test. On the other hand, a Paired T Test is a statistical test that is used to compare the mean values of two related samples/groups to determine if there is a significant difference between the means of 2 samples in reference. A Paired T test is also called as a Dependent T Test/Repeated Measures T Test. Here the groups can be related by being the same group of people, same item, or being subjected to the same conditions. Hence by using the same participants or item eliminates variation/individual differences that occur between the participants .Thus, Paired T tests are considered to be more powerful. This implies that we are more likely to detect a difference, if one does exist using a Paired T test over a Two Sample T Test. The differences between the values of the two related groups should be normally distributed to apply the Paired T Test. Hypotheses of Paired T Test: The null hypothesis (H0) states that there is no significant difference between the means of two groups. The alternative hypothesis (H1) states that there is a significant difference between the means of two groups Examples/Applications of Paired T Test : Performance of a group of students in a test conducted before and after a Training course. The before and after effect of a pharmaceutical treatment on the same group of participants. Body temperature using two different thermometers on the same group of participants. Body Weights of a group of participants before and after an exercise-training program. Body Weights of a group of participants before and after a diet counselling course