Introduction
A ttest for independent groups is useful when the same variable has been measured in two independent groups and the researcher wants to know whether the difference between group means is statistically significant. “Independent groups” means that the groups have different people in them and that the people in the different groups have not been matched or paired in any way.
Objectives
The independent ttest compares the means of two unrelated/independent groups measured on the Interval or ratio scale. The SPSS ttest procedure allows the testing of hypothesis when variances are assumed to be equal or when are not equal and also provide the tvalue for both assumptions. This test also provide the relevant descriptive statistics for both of the groups.
Assumptions
 Variable can be classified in two groups independent of each other.
 Variable is Measured on interval or ratio scale.
 Measured variable is approximately normally distributed
 Both groups have similar variances (variances are homogeneity)
Data
Suppose a researcher want to discover whether left and right handed telephone operators differed in the time it took them to answer calls. The data for reaction time were obtained (RT’s measured in seconds):
Subject no.  RTs (Left)  Subject no.  RTs (Right) 
1  500  11  392 
2  513  12  445 
3  300  13  271 
4  561  14  523 
5  483  15  421 
6  502  16  489 
7  539  17  501 
8  467  18  388 
9  420  19  411 
10  480  20  467 
Mean 
476.5 
430.8 

Variance Ŝ^{2 } 
5341.167 
5298.84 
The mean reaction times suggest that the lefthanders were slower but does a ttest confirm this?
Independent Sample t Test using SPSS
Perform the Following step by running the SPSS and entering the data set in SPSS data view
 Click Analyze > Compare Means > IndependentSamples T Test… on the top menu as shown below.
 Select continuous variables that you want to test from the list.
 Click on the arrow to send the variable in the “Test Variable(s)” box. You can also double click the variable to send it in “Test Variable” Box.
 Select the categorical/grouping variable so that group comparison can be made and send it to the “Grouping Variable” box.
 Click on the “Define Groups” button. A small dialog box will appear asking about the name/code used in variable view for the groups. We used 1 for males and 2 for females. Click Continue button when you’re done. Then click OK when you’re ready to get the output. See the Pictures for Visual view.
Output
First Table in output is about descriptive statistics concerning your variables. Number of observations, mean, variance, and standard error is available for both of the groups (male and female)
Second Table in output is important one concerning testing of hypothesis. You will see that there are two ttests. You have to know which one to use. When comparing groups having approximately similar variances use the first ttest. Levene’s test checks for this. If the significance for Levene’s test is 0.05 or below, then it means that the “Equal Variances Not Assumed” test should be used (second one), Otherwise use the “Equal Variances Assumed” test (first one). Here the significance is 0.287, so we’ll be using the “Equal Variances” first row in the second table.
In output table “t” is calculated tvalue from test statistics, in example tvalue is 1.401
df stands for degrees of freedom, in example we have 18 degree of freedom
Sig (two tailed) means two tailed significance value (PValue), in example sig value is greater than 0.05 (significance level).
Decision
As the Pvalue 0.178 id greater than our 0.05 significance level we fail to reject the null hypothesis. (two tailed case)
As the Pvalue 0.089 id greater than our 0.05 significance level we fail to reject the null hypothesis. (one tail case with 0.05 significance level)
As the Pvalue 0.089 id smaller than our 0.10 significance level we reject the null hypothesis and accept the alternative hypothesis. (one tail case with 0.10 significance level). In this case, it means that left handler have slower reaction time as compared to right handler on average.
Other links to study Independent Sample t test using SPSS
 http://libguides.library.kent.edu/SPSS/IndependentTTest
 https://statistics.laerd.com/spsstutorials/independentttestusingspssstatistics.php
thanks for lessons. please update more with some basic and advance statistics. Do also provide some lecture for mathematical statistics… thanks…