spss with t-test & analysis of variance
TRANSCRIPT
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
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