Friday, 30 October 2015

PAIRED SAMPLE T-TEST

In this post, we will be discussing that how paired sample t-test is conducted via SPSS. Paired Sample t-test is used when we want to test the hypothesis regarding the comparison of mean of same group mostly before and after situation. Lets illustrate this with an example. 
Suppose that you want to see that if sales (in US$) is increased after a massive advertising campaign. To check this, you need to follow the steps of developing hypothesis, collecting the data, running the pair sample t-test, accepting or rejecting the hypothesis, and then arriving on conclusion.
Lets say that you have developed the following hypothesis:
Null Hypothesis=H0= The average daily sale before and after the massive advertising campaign is same
Alternative Hypothesis=H1= The average daily sale before and after the massive advertising campaign is statistically different

Lets say that to test the above hypothesis, you have collected the daily sales data in US$ before and after the massive advertising campaign which is as under.
Before: 3000, 2500, 2000, 1500, 1800, 2500. 3300, 2600, 3300, 2900, 3200, 2200, 1900, 2000, 2000, 1900, 2200, 2200, 1500, 2400
After: 3100, 2700, 3200, 2900, 3200, 2900, 2200, 2400, 1900, 2500, 3000, 3200, 3500, 3500, 4000, 1900, 3900, 4400, 1900, 2300
To run the paired t-test on this data, you need to put it in the SPSS. So in SPSS, first create the variables of ‘before’ and ‘after’; and then input the data in to it (To learn about how to input the variables and data in to SPSS please see my previous posts).


 Once variables and data is fed it to the SPSS, now you are in position to test the following hypothesis by running the following command.
Analyze---Compare Means---Paired Samples T Test




A dialogue box will appear which will show the variables of ‘before’ and ‘after’. Now click on ‘before’ variable and shift it to ‘Variable1’ and ‘after’ to ‘Variable2’ and then simply click on ‘Ok’. 


The results will appear in ‘output window’ which can be interpreted as follow.The first table with the heading ‘Paired Samples Statistics’ simply provides the mean average, number of sample and standard deviation. So in this example, the mean value for before is 2345; while the mean value for after is 2930. Both of these values show the average sales in US$. Similarly, the standard deviation shows the dispersion of mean from its central value.

The second table heading ‘Paired Samples correlations’ show the correlation or association between both variables. In this example, the value of correlation which is -.270 shows that both before and after have negative association of 27%. 
Third table with the heading of ‘Paired Samples Test’ is the main table which shows that Mean difference between before and after is -585 US$. Similarly, the value of t and sig (2-tailed) is used to test the hypothesis. In this example, the t value of -2.560 and sig value of .019 shows that the sales difference between before and after is statistically different and thus, we reject the null hypothesis and accept the alternative hypothesis. So the conclusion is that the massive advertising is indeed brining significant positive difference in daily sales. 
(Note: To accept the alternative hypothesis, the value of t should be greater than 2; while, the value of Sig should be less than 0.05. In case, t value is less than 2 and sig value is greater than 0.05, then we will accept the alternative hypothesis and reject the alternative hypothesis.)


SPSS Practice file for Paired Sample T Test is as under.

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