Ttests are used when you want to examine differences but you do not know everything about the population. There are three types of ttests that you may choose to do: onesample ttest, independent sample ttest, or dependent sample ttest. You can calculate these by hand, in SPSS, or in Excel. The instructions below can be used for SPSS and your textbook offers instructions for using Excel.
Singlesample ttests
These tests are used when you want to determine the probability that a sample was drawn from a population with a known mean (μ) but with a standard deviation estimated from the sample.
Click on analyze, compare means, onesample ttest
Copy the variables you want to test into the Test Variables box
Type the population mean into the Test Value box
Click on options to get:
Confidence intervals (95% is default)
Exclude cases analysis by analysis
If some data is missing, this will drop the data only in analyses where that data is missing.
Exclude cases listwise
If you are doing multiple ttests and have missing data, this will drop participants who have missing data from all t tests
Click on continue, ok
The output will display the tstatistic, degrees of freedom (n1), significance (twotailed), and the confidence interval
Independent sample ttest
These tests are used when you want to determine the probability that two samples were drawn from the same population with unknown means and standard deviations; both of which are estimated from the sample. No population parameters are specified.
The data should be entered in one column and should be named as your dependent variable.
You will need another column of data to identify each group according to number. So, it is a good idea to have two columns of data (one for the IV and one for the DV).
For the IV column, you should use two consecutive numbers (I usually use 1 and 2)
Also, be sure to use variable view to name your variables (otherwise this can become very confusing)
First, we need to calculate means for the purpose of interpretation.
Go to analyze, compare means, means
Put your IV in the grouping variable box and your DV in the dependent variable box.
Click OK to get the means and standard deviations
Now, you need to calculate your ttest
Go to analyze, compare means, independent samples ttest
Your IV is the grouping variable
Click on define range and enter 12
Put the DV in the dependent variables box.
You can click on options to change the confidence interval (default is 95%)
Click on OK
The output will show you the tstatistic, the significance level, the standard error of the mean, and the confidence interval.
Dependent samples ttest
We use this ttest when we have a repeated measures design such as the same sample completes a pre and posttest and we want to know if there is a difference from one test to the other.
Go to analyze, compare means, paired sample ttest
Select two variables and move into box
Click on OK
The output will give you means for each trial (or prepost test measure) as well as the tstatistic and significance level
Let’s try a few using the data below. Be sure to attach your printouts and answer the questions below.
First, do an independent sample ttest for gender (IV) and pretest scores (DV)
Were there significant gender differences? How do you know? Interpret the results statistically and in words.
Then do an independent sample ttest for gender (IV) and posttest scores (DV)
Were there significant gender differences? How do you know? Interpret the results statistically and in words.
Now, do a paired (dependent) sample ttest for pretest and posttest scores.
Were there two scores significantly different? How do you know? Interpret the results statistically and in words.
Data Set Homework 2 (*note 1 = males, 2 = females)
Gender Pretest Posttest
1.00 50.00 80.00
1.00 50.00 70.00
1.00 80.00 70.00
1.00 80.00 50.00
1.00 70.00 50.00
1.00 70.00 50.00
1.00 60.00 60.00
1.00 60.00 80.00
1.00 90.00 80.00
1.00 90.00 90.00
1.00 90.00 80.00
1.00 80.00 90.00
1.00 80.00 90.00
1.00 70.00 70.00
1.00 70.00 80.00
1.00 50.00 80.00
1.00 50.00 70.00
1.00 50.00 70.00
1.00 60.00 60.00
1.00 70.00 80.00
2.00 50.00 70.00
2.00 40.00 50.00
2.00 40.00 80.00
2.00 70.00 80.00
2.00 50.00 70.00
2.00 50.00 80.00
2.00 50.00 90.00
2.00 60.00 90.00
2.00 70.00 90.00
2.00 40.00 80.00
2.00 40.00 80.00
2.00 30.00 70.00
2.00 30.00 70.00
2.00 50.00 60.00
2.00 60.00 80.00
2.00 40.00 80.00
2.00 70.00 80.00
2.00 50.00 70.00
2.00 60.00 70.00
2.00 70.00 90.00
First, do an independent sample ttest for gender (IV) and pretest scores (DV)
Were there significant gender differences? How do you know? Interpret the results statistically and in words.
Required SPSS output is given as below:
Group Statistics 


Gender 
N 
Mean 
Std. Deviation 
Std. Error Mean 

Pretest 
Male 
20 
68.5000 
14.24411 
3.18508 
Female 
20 
51.0000 
12.93709 
2.89282 
Independent Samples Test 


Levene's Test for Equality of Variances 
ttest for Equality of Means 

F 
Sig. 
t 
df 
Sig. (2tailed) 
Mean Difference 
Std. Error Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

Pretest 
Equal variances assumed 
.402 
.530 
4.067 
38 
.000 
17.50000 
4.30269 
8.78966 
26.21034 
Equal variances not assumed 
4.067 
37.653 
.000 
17.50000 
4.30269 
8.78702 
26.21298 
We assume the level of significance or alpha value for this test as 5% or α = 0.05.
The pvalue for above test is given as 0.00 < α = 0.05, so there is significant gender difference is observed for the pretest scores.
There is sufficient evidence to conclude that there is different average pretest scores for males and females.
Then do an independent sample ttest for gender (IV) and posttest scores (DV)
Were there significant gender differences? How do you know? Interpret the results statistically and in words.
Required SPSS output is given as below:
Group Statistics 


Gender 
N 
Mean 
Std. Deviation 
Std. Error Mean 

Posttest 
Male 
20 
72.5000 
12.92692 
2.89055 
Female 
20 
76.5000 
10.39990 
2.32549 
Independent Samples Test 


Levene's Test for Equality of Variances 
ttest for Equality of Means 

F 
Sig. 
t 
df 
Sig. (2tailed) 
Mean Difference 
Std. Error Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

Posttest 
Equal variances assumed 
1.196 
.281 
1.078 
38 
.288 
4.00000 
3.70987 
11.51025 
3.51025 
Equal variances not assumed 
1.078 
36.334 
.288 
4.00000 
3.70987 
11.52157 
3.52157 
We assume the level of significance or alpha value for this test as 5% or α = 0.05.
The pvalue for above test is given as 0.288 > α = 0.05, so we do not reject the null hypothesis that there is no any significant difference in the average posttest scores for males and females.
There is insufficient evidence to conclude that there is a significant difference in the average posttest scores for males and females.
Now, do a paired (dependent) sample ttest for pretest and posttest scores.
Were there two scores significantly different? How do you know? Interpret the results statistically and in words.
Required SPSS output is given as below:
Paired Samples Statistics 


Mean 
N 
Std. Deviation 
Std. Error Mean 

Pair 1 
Pretest 
59.7500 
40 
16.09069 
2.54416 
Posttest 
74.5000 
40 
11.75607 
1.85880 
Paired Samples Correlations 


N 
Correlation 
Sig. 

Pair 1 
Pretest & Posttest 
40 
.169 
.298 
Paired Samples Test 


Paired Differences 
t 
df 
Sig. (2tailed) 

Mean 
Std. Deviation 
Std. Error Mean 
95% Confidence Interval of the Difference 

Lower 
Upper 

Pair 1 
Pretest  Posttest 
14.75000 
18.25566 
2.88647 
20.58844 
8.91156 
5.110 
39 
.000 
We assume the level of significance or alpha value for this test as 5% or α = 0.05.
The pvalue for above test is given as 0.00 < α = 0.05, so we reject the null hypothesis H_{0.}
There is sufficient evidence to conclude that there is a significant difference in the average pretest score and average posttest score.
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