Friday, 30 October 2015

ONE SAMPLE T-TEST USING SPSS

There are different types of t-tests which are used in different situations. In this post, we will be discussing one sample t-test and relevant hypothesis procedure. One sample t-test is used when a researcher want to know that whether the mean value of a sample is same or different from the mean value of population. For this purpose, we construct hypothesis, collect the data from sample, conduct one sample t-test, then accept or reject the hypothesis and thus arrive on some conclusion. Let’s illustrate this with an example. 
Imagine that you are a manager of a busy fast food restaurant and you want to know that whether the average time of serving a customer is 30 Minutes or more or less than that. To test this, you collect data from 20 customers by observing serving times. Lets say that the data you collected is as follow: 45, 35, 35, 45, 50, 25, 22, 15, 20, 25, 35, 45, 35, 45, 50, 35, 25, 30, 20, and 25 (in Minutes Units)
If you calculate mean of these twenty values, you will get 33.10 Minutes; however, the question is that whether this 33.10 minutes is statistically different from the test value of 30 minutes. For this purpose, we run the one sample t-test. Here we develop the following null and alternative hypothesis. 
H0= The average serving time to the customers is 30 minutes
H1= The average serving time to the customers is different from 30 minutes
Now, just put this variable (Serving Time) and data (20 values) in to SPSS (For details on how to input variable and data in to SPSS, please see my previous posts). 






Once you have put the data, now just run the one sample t-test for which the command is as under.

Analyze---Compare Means---One Sample t-test



A dialogue box will appear which will show you the variables in to the left hand side. 




Now just select the variable (Serving time) and shift it to the selection box at right hand side. Then in the test value box just enter the test or hypothetical value which in this example is 30 minutes. And then just press OK.



Results will appear in Output Window in two tables. The first table with the heading ‘One-Sample Statistics’ provides some basic information. For example, the value of N shows that data consist of 20 samples. Similarly, the mean column shows the average or mean for full sample data which in this case is 33.10 minutes which we already calculated above. The standard deviation is also a regularly used measure which shows the data dispersion from its mean which in this case is 10.81. In this example, the mean serving time of 33.10 minutes with 10.81 standard deviation shows that there is some big variation in serving times (you can also see this from simply looking at data).



In second table heading ‘One-Sample Test’, there are various information. The value of t shows the t statistics value which is used to accept or reject the hypothesis. In this example, the value of t is 1.28 which is quite lower than the standard value of 2. The Sig value in the fourth column is also .215 which is greater than the standard value of .05. Therefore, based on this information we can reject the alternative hypothesis. Thus, conclusion is that average serving time is not statistically different from 30 minutes of serving. (Note: if t value is greater than 2 and sig value is less than 0.05 then you will reject the null hypothesis and accept the alternative hypothesis).

 Practice SPSS file is as under.

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