SPSS WITH T-TEST &

ANALYSIS OF VARIANCE

BY- DINESH KUMAR,

PHD, DEPARTMENT OF PHYSICAL EDUCATION AND SPORTS SCIENCES

UNIVERSITY OF DELHI

CONTENTS:

1. T-Test and its uses

a) APPLICATION OF T-Test

b) Two-Sample t-Test with SPSS

c) Interpretation of the Outputs

2. ANOVA and its implication.

a) Type of ANOVA

b) Program in SPSS for ANOVA

c) Interpretation of the Outputs

T-Test and its uses

The t-test is used to determine whether the difference between means of two groups or

conditions is due to the independent variable, or if the difference is simply due to chance.

This test is used if the population standard deviation is not known and the distribution of the

population from which the sample has been drawn is normally distributed. Usually t-test is

used for small sample size (n < 30) in a situation where population standard deviation is not

known.

The t-statistic is tested for its significance by finding its corresponding p value. If p value is

less than .05, the t-statistic becomes significant, and we reject the null hypothesis against the

alternative hypothesis.

NOTE- The p value is the probability of wrongly rejecting the null hypothesis

APPLICATION OF T-Test

1. One-Sample Test: the authorities may be interested to test whether the bank’s processing

time in all their branches is equal to 4 h or not.

2. Two-Sample t-Test: comparing the effect of two different diets on weights, the effect of two

teaching methodologies on the performance, or the IQ of boys and girls.

a) Case 1: Two-Tailed Test: it is desired to see the impact of different kinds of music on the

hours of sleep. The two groups of the subjects are randomly selected, and the first group is

exposed to classical music, whereas the second group is exposed to Jazz music for 1 h before

sleep for a week. To test whether average sleep hour remains same or different in two

different kinds of music groups.

b) Case 2: One-Tailed Test: whether frustration level is less among those employees whose

jobs are linked with incentives in comparison to those whose jobs are not linked with the

incentives

Two-Sample t-Test with SPSS

QUESTION: An experiment was conducted to

assess delivery performance of the two pizza

companies. Customers were asked to reveal the

delivery time of the pizza they have ordered

from these two companies. Following are the

delivery time in minutes of the two pizza

companies as reported by their customers. Can it

be concluded that the delivery time of the two

companies is different? Test your hypothesis at

5% level.

STEPS TO BE FOLLOWED IN SPSS

1. Preparing Data File:

2. SPSS Commands for Two-Sample t-Test

Analyze ⇨ Compare means ⇨ Independent-

Samples t test

3. Selecting options for computation:

4. Getting the Output:

Interpretation of the Outputs.

1. The mean, standard deviation, and standard error of the mean for the data on delivery time of both the

pizza companies. The mean delivery time of the company B is less than that of the delivery time of

company A. However, whether this difference is significant or not shall be revealed by looking to the t-

value and its associated p value.

2. One of the conditions for using the two-sample t-ratio for unrelated groups is that the variance of the two

groups must be equal. To test the equality of variances, Levene’s test was used. F-value is .356 which is

insignificant as the p value is .557 which is more than .05. Thus, the null hypothesis of equality of

variances may be accepted, and it is concluded that the variances of the two groups are equal.

3. It can be seen that the value of t-statistic is 3.028. This t-value is significant as its p value is 0.007 which is

less than .05. Thus, the null hypothesis of equality of population means of two groups is rejected, and it

may be concluded that the average delivery time of the pizza in both the companies is different. Further,

average delivery time of the company B is less than that of the company A, and therefore, it may be

concluded that the delivery of pizza by the company B to their customers is faster than that of the company

A.

ANOVA and its implication.

As with the t-test, ANOVA also tests for significant differences between groups. But while the t-

test is limited to the comparison of only two groups, one-way ANOVA can be used to test

differences in three or more groups.

In one-way ANOVA, group means are compared by comparing the variability between groups

with that of variability within the groups. This is done by computing an F-statistic.

NOTE: As per the central limit theorem, if the groups are drawn from the same population, the

variance between the group means should be lower than the variance within the groups. Thus, a

higher ratio (F-value) indicates that the samples have been drawn from different populations.

- example: Consider a study in which it is required to compare the responses of the students

belonging to north, south, west and east regions towards liking of mess food in the university.

Type of ANOVA

1. One-Way ANOVA: It is used to compare the means of more than two independent groups. In one-way ANOVA,

the effect of different levels of only one factor on the dependent variable is investigated. Ex: anxiety of the

employees can be compared in three different units of an organization

2. Factorial ANOVA: A factorial design is the one in which the effect of two factors on the dependent variable is

investigated. Here each factor may have several levels and each combination becomes a treatment. Usually

factorial ANOVA is used to compare the main effect of each factor as well as their interaction effects across the

levels of other factor on the criterion variable.

Ex: Consider a situation where the effect of different combination of duration and time on learning efficiency is to

be investigated. The duration of interest is 30 and 60 minutes and the subjects are given training in the morning and

evening sessions for a learning task. The four combinations of treatments would be morning time with 30 minutes

duration, morning time with 60 minutes duration, evening time with 30 minutes duration and evening time with 60

minutes duration. In this case neither the main effect nor the interaction effects are of interest to the investigator

rather just the combinations of these levels form four levels of the independent treatment.

Continue ……

3. Repeated Measure ANOVA: It is used when same subjects are given different treatments at different

time interval. In this design, same criterion variable is measured many times on each subject.

Ex: in order to see the impact of temperature on memory retention, a subject’s memory might be tested once

in an air-conditioned atmosphere and another time in a normal room temperature.

4. Multivariate ANOVA: Multivariate ANOVA is used when there are two or more dependent variables.

Multivariate analysis of variance is also known as MANOVA.

Multivariate ANOVA is used to compare the effects of two or more treatments on a group of dependent

variables. The dependent variables should be such so that together it conveys some meaning. Consider an

experiment where the impact of educational background on three personality traits honesty, courtesy, and

responsibility is to be studied in an organization. The subjects may be classified on the basis of their

educational qualification; high school, graduation or post-graduation.

Program in SPSS for ANOVA

QUESTION : A human resource department of an organization conducted a study to know the status of occupational stress among their employees in different age categories. A questionnaire was used to assess the stress level of the employees in three different age categories: <40, 40–55, and >55 years. The stress scores so obtained are shown in Table

STEPS TO BE FOLLOWED:

STEP 1: Preparing data file:

STEP 2: SPSS commands for one-way ANOVA for unequal sample size.Analyze ➾ Compare Means ➾ One-Way ANOVA

STEP 3: Selecting options for computation: Click the tag Post Hoc

STEP 4: Getting the output:

Descriptive statistics for the data

ANOVA table for the data

Post hoc comparison of group means using Scheffe’s test Mean scores on data

Interpretation of the Outputs:

Table 2 gives the value of calculated F. The p value attached with the F is .000 which is less than .05

as well as .01; hence, it is significant at 5% as well as 1% levels. Since the F-value is significant, the

null hypothesis of no difference in the occupational stress among the employees in all the three age

categories is rejected. The post hoc test is now used to compare the means in different pairs.

It can be seen that the difference between occupational stress of the employees in group A (<40

years) and group B (40–55 years) is significant at 5% as well as at 1%. Similarly, the mean

difference between occupational stress of the employees in group B (40–55 years) and group C (>55

years) is also significant at 5% as well as 1%. However, there is no significant difference between

the occupational stress of the employees in group A (<40 years) and group C (>55 years) because

the p value is .606.

On the basis of the results obtained above, it may be inferred that the occupational stress among the

employees in the age category 40–55 years is maximum

THANKYOU