Comparing Means:T-Test

PSYC 301 /SPSSSPRING 2014

t-tests• Used to determine whether there is a significant difference

between two sets of scores

• Main types of t-tests:• One sample t-test• Independent groups t-test• Repeated-measures t-test

t-tests

Assumptions

• Scale of measurement is interval or ratio• Random sampling• Normality

The one-sample t-test• Only one sample (one set of scores)

• Whether the sample mean is different from the population mean You should know the population mean!

Working example: «Data for training study»

Question: Is the IQ score of our sample different from the whole population?Population IQ: Mean = 100; SD = 15

The one-sample t-testOne sample t-test

One sample: It is your sample and you are comparing it with the population (or any fixed value)

• Analyze – Compare means – One-Sample t-test• Select the variable (IQ) and move to test variables box• In test value, type the population mean (100, for this example)

• If p < .05, the difference is significant

The one-sample t-test• How to report the result in APA format:Question:

Is the IQ score of our sample different from the whole population?(Is our sample representativeof the population?)

Reporting in APA Style

The sample mean is significantly different from the population mean, (t(23) = -2.26 , p < .05). More specifically, IQ scores in our sample (M = 95.08 , SD = 10.66) was found to be lower then the population mean (M = 100 , SD = 15).

The repeated measures t-test• Dependent-samples, within subjects or paired t-test

• Only one group again, but now they have two treaties!

• Within-subjects design: same subjects perform in two conditions/at two different times…etc.

• Two different scores for the same participants)• Testing at two different times: Pretest-posttest Test-retest• Testing for two distict, but related abilities: Math-Literacy test

• Now you are comparing the two sets of scores from the same participants.

The repeated measures t-test• Research question:• Does the training have an effect on the test performance?

Working example: «Data for training study»

• Analyze – Compare means – Paired-Samples t-test• Select the variables (Time1 – Time2) and move to paired variables

box - Click OK

• If p <.05, the difference is significant

• How to report:• There is a significant difference in the participants’ test scores before and

after the training, (t(23) = -10.17 , p < .05). We can conclude that the given training improved the test performance such that scores at time 2 (M = 90.20 , SD = 9.30) are significantly greater than time 1 (M = 75.87 , SD = 11.65)

The independent groups t-test

• Between-subjects design• Different participants in two conditions,

• We have two groups treated differently (or they are inherently different)• Gender (male vs female)• Manipulation (Drug A vs Drug B) or (Drug A vs Control)• Age groups (Adolescents vs children)

The independent groups t-test• Additional assumptions:• Independence of groups (related to research design)• Homogeneity of variance (tested in the analysis),

• SPSS has the Levene test for equality of variances.• If p > .05 variances are equal.

• Why p value should be greater than .05 for Levene’s test?• Levene test assess whether the variance in two groups are

different?• H0: Variance in two groups are equal to each other• H1: Variance in two groups are significantly different than each other.

• So, if the requirement is variance in two groups should be equal, then we want H0 to be accepted!

The independent groups t-test• Research Question:• Does the initial IQ scores differ for participants assigned to training 1 and

training 2?

• Analyze – Compare means – Independent-Samples t-test• Select the variable (IQ) and move to test variable(s) box• Select the grouping variable (training) and move it to the grouping variable • Click on define groups, enter lowest value to group 1 (1) and the second value to group2 (2), Continue and OK

• First check the Levene’s test!• Levene’s test, p > .05, variances are equal for both groups, then, t-test is appropriate.

The independent groups t-test• Research Question:• Does the initial IQ scores differ for participants training 1 and training 2?

• The IQ scores of the participants assigned to training 1 and training 2 were found to be significantly different, t(22) = 2.93, p < .05) such that the participants assgined to training 1 (M = 101.09 , SD = 8.14). had higher IQ scores than the ones assigned to training 2 (M = 90.00 , SD = 10.09).

The independent groups t-test• Research Question:• Does the performance at time 1 differ for participants assigned to training 1 and training 2?

• The test perfomormance at time 1 was found to be different for the participants assigned to training 1 and training 2, t(22) = -2.86, p < .05) such that the participants assgined to training 2 (M = 80.23 , SD = 8.34) performed better than than the ones assigned to training one (M = 70.72 , SD = 7.84).

The independent groups t-test• Research Question:• Does the performance at time 2 differ for participants assigned to training 1 and training 2?

• The test perfomormance at time 2 did not differ for participants assigned to training 1 and training 2, t(22) = -1.61, p > .05).

• In general, you do not need to report the mean and SDs if the test is insignificant.

The independent groups t-testWhat if the Levene test is significant?

• Then report the t-statistics for the Levene’s test and then proceed reporting as usual.

• However, this time you have to report the df and t-values based the bottom level. That is, for the Time 1 variable: t(21.97) = 2.98, p < .05).

Summary • Do not forget to test relevant assumptions (e. g., homogenity)

• Use One-sample t-test to compare the mean of one sample and a given population mean

• Use Repeated-measures t-test when the same subject has two different scores

• Use Independent-groups t-test when the data is gathered from two different groups

• Report t value, degrees of freedom (df), and p value, and also mean and SDs for each set of scores.