Question

T-tests are used when you want to examine differences but you do not know everything about the population. There are three types of t-tests that you may choose to do: one-sample t-test, independent sample t-test, or dependent sample t-test. 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.

Single-sample t-tests

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, one-sample t-test

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 t-tests 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 t-statistic, degrees of freedom (n-1), significance (two-tailed), and the confidence interval

Independent sample t-test

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 t-test

Go to analyze, compare means, independent samples t-test

Your IV is the grouping variable

Click on define range and enter 1-2

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 t-statistic, the significance level, the standard error of the mean, and the confidence interval.

Dependent samples t-test

We use this t-test when we have a repeated measures design such as the same sample completes a pre and post-test and we want to know if there is a difference from one test to the other.

Go to analyze, compare means, paired sample t-test

Select two variables and move into box

Click on OK

The output will give you means for each trial (or pre-post test measure) as well as the t-statistic 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 t-test 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 t-test 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 t-test 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

Answer 1

First, do an independent sample t-test 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		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	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 p-value 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 t-test 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		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	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 p-value 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 t-test 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. (2-tailed)
		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 p-value 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.