T-Test statistics, which is also known as student’s T-Test, was first developed by William Sealy Gosset in the year 1908. It refers to a statistical analysis technique that is used to compare the means of the two groups. T-Test statistics is a type of parametric method. This means that it is a statistical technique where one can define the probability distribution of the variables and thus can make the inferences about the parameters of the distribution.
2 Types of T-Tests statistics
- Independent T-Test and,
- Paired T-Test.
Independent T-Test is used when two groups that are under comparison are independent of each other. Paired T-Test is used when the two groups under the comparison are dependent on each other.
The T-Test statistics is usually used in cases where the experimental subject can be divided into two independent groups, group A and Group B. The researcher using this technique can acquire two types of the results from each of the group i.e. prior to treatment and post-treatment. ‘Treatment’ here refers to the experiment which is conducted on one of the groups.
Assumptions of T-Test statistics
The T-Test statistics method is subject to certain assumptions. It is not possible to carry out the test without these assumptions, which are as follows.
- The scale of measurement: the first assumption regarding T-Test relates to the scale of measurement. This means that the data collected should follow a continuous or ordinal scale.
- Sampling distribution: Data should be in the simple random sample, i.e., data collected should be randomly selected portion of the total population.
- Curve shape: The thirst assumption relates to the shape of the curve which means that data when potted should result in a normal distribution i.e. bell-shaped curve.
- Sample size: Under this assumption, the sample size used should be large. Larger sample size will imply that the distribution of results should approach a normal bell-shaped curve.
- No significant outliers: Outliers refer to data points that do not follow the usual pattern. The major issue with the outliers is that they tend to have a negative impact on the independent T-Test results i.e. reducing their validity.
- Homogenous: the final assumption relates to the homogeneity of variance. Homogenous or the equal variances exists when the standard deviations of the given samples are approximately equal.
Benefits of using T-Test statistics
- The simplicity of interpretation: the results of the independent sample T-Test presents the difference in the mean values of one sample group from the mean of other groups and also tells that whether the difference is statistically significant or not.
- Ease of gathering data: the independent sample T-Test normally requires very little data. The T-Test is also valid when even with the small number of subjects.
- Ease of calculation: these days although, even the T-Test are done with the computer aid. But the statistical formula of the independent sample T-Test is also very simple. And especially appealing for the people who have less statistical training.
The statistical formula of T-Test
The statistical formula for the T-Test is as follows:
Procedure for conducting T-Test statistics in SPSS
The execution and applicability of T-Test statistics can be explained with the help of the following example.
The government of India has been paying special focus on promoting vocational education in the schools. In this respect, the government of India has launched a scheme known as Rashtriya Madhyamik Shiksha Abhiyan which focuses on the rationalization of secondary and higher secondary education in India. Therefore, the researcher wants to investigate the impact of the program on the students’ academic performance through evaluation of their test scores. In order to compare the test results of the students taught through vocational teaching style and the students taught through the traditional method, the researcher opted the technique of T-Test.
The test was conducted with 70 students divided into two groups of 35 each:
- Group A consisted of students who were taught through the vocational teaching style.
- Group B consisted of students taught using the traditional teaching style.
The steps below show how to analyze the data using an independent T-Test in SPSS software.
Steps to conduct T-Test in SPSS software
Import the data from the MS Excel to SPSS by pasting the data on the ‘Data View’ page. Then click on the Analyze > Compare means > Independent-Samples T-Test as shown in figure 1 below.
A dialogue box will appear as shown in figure 2 below.
Next, transfer the dependent variable data i.e. scores of the students into the ‘Test Variable(s):’ box.
Transfer the independent variable data i.e. the groups into the ‘Grouping Variable’ box.
This is shown in figure 3 below.
The next step in the process is defining the groups. In order to do this, click on ‘Define groups’ button as shown in Figure 3 above. A ‘Define Groups’ box will appear as shown in figure 4 below.
Next, enter ‘A’ in Group 1 which represents the students taught using vocational teaching style. Enter ‘B’ in the Group 2 which represents the students taught using the traditional teaching style. This is shown in figure 5 below.
Click on ‘Continue’.
Click on ‘OK’ as shown in figure 6 below. This step represents the last step in the process. After this, the results will appear.
Interpretation of T-Test statics results
The SPSS Statistics tend to generate two main output tables while conducting the independent T-Test. The following section will show the interpretation of those tables.
Table 1- descriptive statistics
|Group statistics||Groups||N||Mean||Std. Deviation||Std. Error Mean|
The table above represents the descriptive statistics. As shown in the table above the mean scores of Group A which was taught using the vocational teaching style is 33.42 with the standard deviation of 3.6. On the other hand, the mean average scores of the students taught using the traditional teaching style were equal to 29.40 with the standard deviation equal to 2.9. The mean values indicate that the results are in favour of the students taught using the vocational teaching style.
Levene’s test for equality of variances
In order to derive the significance of this test, Levene’s Test for Equality of Variances and T-Test for equality of means is conducted. The results for this are presented in the table below.
To minimize the chances of error while the computation of the results, the significance level was set at 0.05 level. The significance level helps to determine whether the null hypothesis is true or not.
The rule is that the value of null hypothesis is rejected if the resultant significance value came out to be greater than the set level of 0.05.
For the present study in order to derive the significance, the researcher first conducted the Levene’s test for equal variances. As shown in the table above the significance value came out to be .070 which is greater than the set criteria value of 0.05. This implies that while conducting the T-Test for equality of means the researcher will now focus only on the values of the column (equal variance not assumed).
T-Test for equality of means- in order to reach the result, the significance 2 tailed value will be used. Which is basically the 2 tailed p-value. The rule, in this case, is the same as specified above. As shown in the table above the sig 2 tailed value at the level of equal variance not assumed was .000 which is less than the set criteria value of 0.05.
Thus vocational teaching style has a significant impact on the students’ results. Therefore, the null hypothesis is rejected.