WHAT IS THE T-TEST?

The t-test was developed by a statistician, W.S. Gossett (1878-1937) who worked in a brewery in Dublin, Ireland. His pen name was ‘student’ and hence the term ‘student’s t-test’ which was published in the scientific journal, Biometrika in 1908. The t-test is a statistical tool used to infer differences between small samples based on the mean and standard deviation.
In many educational studies, the researcher is interested in testing the differences between means on some variable. The researcher is keen to determine whether the differences observed between two samples represents a real difference between the populations from which the samples were drawn. In other words, did the observed difference just happen by chance when, in reality, the two populations do not differ at all on the variable studies.
For example, you have conducted an experiment to compare the Lecture Method and the Disovery Method in the teaching of science. Based on the science achievement test, students taught using the Discovery Method scored 43.0 marks while students taught using the Lecture Method scored 38.0 marks.  How do you determine whether the difference between the two teaching methods represents a real difference and not due to chance?
THE HYPOTHESIS TESTED USING THE T-TEST

How do we go about establishing whether the differences in the two means are statistically significant or due to chance? We begin by formulating a hypothesis about the difference. This hypothesis states that the two means are equal or the difference between the two means is zero and is called the null hypothesis. [Refer to "Hypothesis Testing" discussed earlier].

Under the null hypothesis, we begin our test of significance by saying:
  • "There is no difference in the score obtained in science between the Lecture Method Group and the Discovery Method Group". 
  • More commonly the null hypothesis may be stated as follows:
                  a)    Ho :  U1  =  U2                [43.0 = 38.0]
                 b)    Ho :   U1  - U2   =  0        [43.0 -  38.0 = 0]

                                    
  • If you reject the null hypothesis, it means that the difference between the two means have statistical significance
  • If you do not reject the null hypothesis, it means that the difference between the two means are NOT statistically significant and the difference is due to chance.

Note: For a null hypothesis to be accepted, the difference between the two means need not be equal to zero since sampling may account for the departure from zero. Thus, you can accept the null hypothesis even if the difference between the two means is not zero provided the difference is likely to be due to chance. However, if the difference between the two means appears too large to have been brought about by chance, you reject the null hypothesis and conclude that a real difference exists.
At the end of this topic, you should be able to"
  • explain the rationale for using the t-test
  • differentiate between the tools for using independent and dependent t-test
  • justify when to use a one-tailed and two-tailed test of significance
  • show the steps of using SPSS when applying the t-test
  • interpret the SPSS output for the t-test

Multiple Regression
SELF-CHECK
a) What is the t-test?
b) State the null hypothesis tested using the t-test.
c) What meant when you reject or do not reject the null hypothesis?
T-test
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