FORE SCHOOL OF MANAGEMENT

Business Research MethodsProjectOne-Way ANOVA

Submitted to:

Prof Alok Kumar

FORE School of Management

Qutub Institutional Area, New Delhi

Submitted by:

Arun Behl231034

FMG23-A

12nd March 2015

ACKNOWLEDGEMENT

The success of any project depends largely on the encouragement and guidelines of many people. I take this opportunity to express my gratitude to the people who have been instrumental in completion of this project. I would like to show my greatest appreciation to Prof. ALOK KUMAR (FORE School of Management). I can't thank him enough for his tremendous support and help. Without his encouragement and guidance this project would not have got materialized. I would also like to thank my friends for their support and cooperation. My appreciation also goes to the FORE School Of Management for allowing me access to various resources, and to the College Library.

Table of Contents

ACKNOWLEDGEMENTi

One-way ANOVA in SPSS Statistics1Introduction1QUESTION2Goal3Solution3SPSS OUTPUT6POST HOC TESTS7

One-way ANOVA in SPSS StatisticsIntroductionThe one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of two or more independent (unrelated) groups (although you tend to only see it used when there are a minimum of three, rather than two groups). For example, you could use a one-way ANOVA to understand whether exam performance differed based on test anxiety levels amongst students, dividing students into three independent groups (e.g., low, medium and high-stressed students). Also, it is important to realize that the one-way ANOVA is anomnibustest statistic and cannot tell you which specific groups were significantly different from each other; it only tells you that at least two groups were different. Since you may have three, four, five or more groups in your study design, determining which of these groups differ from each other is important. You can do this using a post-hoc test.The ANOVA tests thenull hypothesisthat samples in two or more groups are drawn from populations with the same mean values. To do this, two estimates are made of the population variance. These estimates rely on certain assumptions. The ANOVA produces an F-statistic, the ratio of the variance calculated among the means to the variance within the samples. If the group means are drawn from populations with the same mean values, the variance between the group means should be lower than the variance of the samples, following thecentral limit theorem. A higher ratio therefore implies that the samples were drawn from populations with different mean values.Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by at-test. When there are only two means to compare, thet-testand theF-testare equivalent; the relation between ANOVA andtis given byF=t2.There are several types of ANOVA. Many statisticians base ANOVA on thedesign of the experiment,especially on the protocol that specifies therandom assignmentof treatments to subjects; the protocol's description of the assignment mechanism should include a specification of the structure of the treatments and of anyblocking. It is also common to apply ANOVA to observational data using an appropriate statistical model.Some popular designs use the following types of ANOVA: One-way ANOVAis used to test for differences among two or moreindependentgroups (means) e.g. different levels of urea application in a crop, or different levels of antibiotic action on several bacterial species,or different levels of effect of some medicine on groups of patients. Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by at-test.When there are only two means to compare, thet-testand the ANOVAF-testare equivalent; the relation between ANOVA andtis given byF=t2. FactorialANOVA is used when the experimenter wants to study the interaction effects among the treatments. Repeated measuresANOVA is used when the same subjects are used for each treatment (e.g., in alongitudinal study). Multivariate analysis of variance(MANOVA) is used when there is more than oneresponse variable.

EXAMPLE

Evaluation of training programs.A manager wants to raise the productivity at his company by increasing the speed at which his employees can use a particular spreadsheet program. As he does not have the skills in-house, he employs an external agency which provides training in this spreadsheet program. They offer 4 courses (each with a unique training method): a beginner, intermediate, expert and advanced course. He is unsure which course is needed for the type of work they do at his company, so he sends 4 employees on the beginner course, 4 on the intermediate, 4 on the expert and 4 on the advanced course. When they all return from the training, he gives them a problem to solve using the spreadsheet program, and times how long it takes them to complete the problem. He then compares the four different methods used by four different courses (beginner, intermediate, expert, advanced) to see if there are any differences in the average time it took to complete the problem.

Following are the observations for various training program methods. The values inside tells the learning time.

Method 1Method 2Method 3Method 4

10111318

916823

59925

46727

TABLE 1: Method is an independent variable. Learning time is the dependent variable.

GoalTo see if there is significant difference in learning time using different training methods.

SolutionBy looking at the question we can deduce that Learning Time is a dependent variable. It depends on the Training Method used. Training Method is an independent variable. To perform one-way ANOVA, for the data listed in the data table which contain 4 independent random samples, we should follow the listed steps.

STEP1. Enter the dependent variable values and the independent variable (factor variable) values in the Date Editor. In the SPSS Data Editor sheet, it contains a data sheet for a one-way layout design with four treatment groups. The data in the following picture were scores from four training methods. Method is the dependent variable and learning time is the dependent variable.

STEP2. Click through the following menu selection: Analyze / Compare Means / One-Way ANOVA.

STEP3. Select the dependent or response variable and put into the Dependent List box, and put the method or treatment variable into Factor box.

STEP4. Click Options button, check Descriptive and Homogeneity-of-Variance box, and click Continue and click OK.

STEP5. To perform multiple comparisons, in the ANOVA dialog box, click the Post Hoc button and check Tukey or any other method and click Continue and OK.

SPSS produces two tables. The multiple comparisons table containing confidence intervals can help us to understand the difference between each pairs of means. If interval doesnt cover zero, it implies that the difference between the pair of means are statistically significant.

SPSS OUTPUT

Descriptives

Learning Time

NMeanStd. DeviationStd. Error95% Confidence Interval for MeanMinimumMaximum

Lower BoundUpper Bound

147.002.9441.4722.3211.68410

2410.504.2032.1023.8117.19616

349.252.6301.3155.0713.43713

4423.253.8621.93117.1029.401827

Total1612.507.2391.8108.6416.36427

ObservationP-value indicates equal variancesTest of Homogeneity of Variances

Learning Time

Levene Statisticdf1df2Sig.

.285312.835

ANOVA

ObservationP-value indicating significant differences between Training MethodsLearning Time

Sum of SquaresdfMean SquareFSig.

Between Groups641.5003213.83317.758.000

Within Groups144.5001212.042

Total786.00015

POST HOC TESTS

Multiple Comparisons

Dependent Variable: Learning Time Tukey HSD

(I) Training Method Used(J) Training Method UsedMean Difference (I-J)Std. ErrorSig.95% Confidence Interval

Lower BoundUpper Bound

12-3.5002.454.508-10.783.78

3-2.2502.454.796-9.535.03

4-16.250*2.454.000-23.53-8.97

213.5002.454.508-3.7810.78

31.2502.454.955-6.038.53

4-12.750*2.454.001-20.03-5.47

312.2502.454.796-5.039.53

2-1.2502.454.955-8.536.03

4-14.000*2.454.000-21.28-6.72

4116.250*2.454.0008.9723.53

212.750*2.454.0015.4720.03

314.000*2.454.0006.7221.28

*. The mean difference is significant at the 0.05 level.

Homogeneous subsetThe homogenous subsets table can help us to divide the four groups into homogenous subgroups. Within each subgroup the difference in means is statistically insignificant. The difference between average learning time of Methods 1, 2 and 3 are statistically insignificant and their means are significantly different from the mean from Method 4.

Learning Time

Tukey HSD

Training Method UsedNSubset for alpha = 0.05

12

147.00

349.25

2410.50

4423.25

Sig..5081.000

Means for groups in homogeneous subsets are displayed.

a. Uses Harmonic Mean Sample Size = 4.000.