1. One way ANOVA
One way Analysis of Variance (ANOVA) is used to test the significance difference of mean of one dependent variable across more than two categories (situation) of one independent variable.
To use the one way ANOVA, the dependent variables should be quantitative and measured in either interval or ratio scale. Some time researcher also consider the dependent variable which is measured in ordinal scale.
The independent variable should be qualitative with more than two categories and measured in nominal scale. Some time researcher also consider the independent variable which is measured in ordinal scale. For example, ANOVA can be used to test the following model i.e. impact of development regions on income level of peoples.
IV=
Development region
DV=
Income

2. Assumption of one way ANOVA
F-test is used to test the overall significance of the model. If p-value is less than significance level then we can conclude that the model is statistical significant. If F –test suggest that the model is significant then follow-up test will be conducted. The follow up test measures the significance difference of mean of dependent variable between various possible groups of the independent variable. SPSS calls post hoc multiple comparisons for these follow up test.
Assumption of one way ANOVA
The dependent variable is normally distributed for each of the population as defined by the different level of independent variable.
The variances of the dependent variable are the same for all population as defined by the different level of independent variable.
The cases represent random samples from the population and the scores on the dependent variable are independent of each other.

3. For post hoc multiple comparisons test:
After an ANOVA you need a further analysis to find out which groups differ significantly
When you have equal sample sizes and groups variances are similar then use REGWQ or Tukey
If sample sizes are slightly different and groups variances are similar then use Gabriel’ procedure,
If sample sizes are Very different and groups variances are similar then use Hochberg GT2.
If there is any doubt about the homogeneity of variance then use the Games-Howell procedure.

4. Effect size statistics for the ONE Way ANOVA
SSM= Variance explained by the Model(independent variable) or Between groups)
SSE= Unexplained variance (Within groups)
SST = SSM +SSE
Small effect (this effect explains 1% of the total variance)
Medium effect (this effect explains 9% of the total variance)
Large effect (this effect explains 25% of the total variance)

5. One way ANOVA -test in SPSS
Use the Sales database
From the Sales database think one research question/research model and test the validity of the research question that your have generated and make the conclusions and discuss the implication of research question.
Research question: The sales of pairs of shoes is differ across the types of location of the shops.
DV=
Sales
IV=
Locations

6. One way ANOVA -test in SPSS
DV=
Sales
IV=
Locations
Analyze
Compare mean
One way ANOVA
Then from comprehensive list of variables in the left side of the box select the DEPENDENT variable and send to right dependent list box and select the independent variable and send to right factor box. Then click on OPTION and select the descriptive check box and homogeneity of variance test check box and click on continue. Then click on post hoc box and select the appropriate test from the list and then click on continue and OK.
Then following output will generate by SPSS

7. Test of Homogeneity of Variances
Descriptives
Pairs of shoes sold per day N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
Suburban 12
42.33
8.217
2.372
37.11
47.55 30 59
Mall
37.67
10.325
2.981
31.11
44.23 22 53
Downtown
25.83
4.988
1.440
22.66
29.00 17 33
Total 36
35.28
10.590
1.765
31.69
38.86
Test of Homogeneity of Variances
Pairs of shoes sold per day
Levene Statistic
df1
df2
Sig.
4.769 2 33
.015

8. Post Hoc Tests Multiple Comparisons
ANOVA
Pairs of shoes sold per day
Sum of Squares df
Mean Square F
Sig.
Between Groups
SSM = 2
MSM =
13.087
.000
Within Groups
SSE = 33
MSE =
Total
SST = 35
Post Hoc Tests
Multiple Comparisons
Pairs of shoes sold per day Games-Howell
(I) Locations
(J) Locations
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Suburban
Mall
4.667
3.809
.452
-4.94
14.27
Downtown
16.500*
2.775
.000
9.42
23.58
-4.667
-14.27
4.94
11.833*
3.310
.007
3.29
20.38 *
-23.58
-9.42 *
-20.38
-3.29

9. Findings from ONE WAY ANOVA
A one way ANOVA is conducted to evaluate the relationship between sales of shoes and locations of the store. The independent variable is location and dependent variables is sales. The sales of shoe is significantly different across the locations at the 0.05 significance level, F(2,33) = , P=0.000 < The effect size of 0.44 indicate the strong effect of location on sales of shoe i.e. Location of store accounts for 44% of variance of sales .
Follow up test is conducted to evaluate pair wise differences among the mean sales of shoe. The variance of sales are not equal in three locations so for post hoc test is conducted using Games-Howell test.
The sales of shoes is NOT significantly different between suburban than Mall , P= > 0.05.
The sales of shoes is significantly higher in suburban than downtown, P= < 0.05.
The sales of shoes is significantly higher in Mall than downtown, P= < 0.05.
The findings reveals that sales of shoes is significantly higher in Suburban (M = 42.33, SE = 2.372), and Mall (M = 37.67, SE = 2.981) than downtown (M = 25.83, SE = 1.44)

10. Two way ANOVA
Two way Analysis of Variance (ANOVA) is used to test the significance difference of mean of one dependent variable when two independent categories variables are involved in the analysis.
To use the two way ANOVA, the dependent variables should be quantitative and measured in either interval or ratio scale. Some time researcher also consider the dependent variable which is measured in ordinal scale.
The both independent variables should be qualitative with two or more categories and measured in nominal scale. Some time researcher also consider the independent variable which is measured in ordinal scale.
IV1=
Location
DV=
Sales
IV2=
Competitors
Fig: Statistical Model for Two Way ANOVA

11. F-test is used to test the Main effect of the first and second independent variables on the dependent. If the corresponding p-value of the independent variables in ANOVA Table is less than significance level then we can conclude that the model is statistical significant. If F –test suggest that the model is significant then follow-up test will be conducted. The follow up test measures the significance difference of mean of dependent variable between various possible combination groups of the independent variable. SPSS calls post hoc multiple comparisons for these follow up test. The Two way ANOVA will evaluate the following hypothesis
Main effect of location: The sales of shoe is significantly differ across the location of store
Main effect of competitors: The sales of shoe is significantly differ by Number of competitors

12. Assumption of TWO way ANOVA
The dependent variable is normally distributed for each of the population as defined by the different level of independent variables.
The variances of the dependent variable are the same for all population as defined by the different level of independent variable.
The cases represent random samples from the population and the scores on the dependent variable are independent of each other.

13. Effect size statistics for the TWO Way ANOVA
SSM= Variance explained by the Model(independent variable) or Between groups)
SSE= Unexplained variance (Within groups)
SST = SSM for first factor+ SSM for second factor +SSE
Small effect (this effect explains 1% of the total variance)
Medium effect (this effect explains 9% of the total variance)
Large effect (this effect explains 25% of the total variance)

14. TWO way ANOVA -test in SPSS
Use the Sales database
From the sales database think one research question/research model and test the validity of the research question that your have generated and make the conclusions and discuss the implication of research question.
IV1=
Location
DV=
Sales
IV2=
Competitors
Research question1 :
Main effect of location: The sales of pairs of shoes is differ across the types of location of the shops.
Research question2
Main effect of competitors : The sales of pairs of shoes is differ across the number of competitors

15. TWO way ANOVA -test in SPSS
Analyze
General linear model
Univariate
Then from comprehensive list of variables in the left side of the box select the DEPENDENT variable and send to right dependent list box and select the independent variables and send to right fixed factor box. Then click on OPTION and select the descriptive check box, homogeneity test and estimates of effect size check box and click on continue. Click on Model and select custom button then send the variable one by one to the model box (make sure that main effect is selected in build term box and then clink on continue. Then click on post hoc box and select the appropriate test from the list and then click on continue and OK (this time tukey).
Then following output will generate by SPSS

16. Between-Subjects Factors Levene's Test of Equality of Error Variancesa
Value Label N
Locations 1
Suburban 12 2
Mall 3
Downtown
Number of Competitors
No Competotors 9
One Competitors
2 Competitors 4
3 & More Competitors
Levene's Test of Equality of Error Variancesa
Dependent Variable:Pairs of shoes sold per day F
df1
df2
Sig.
.755 11 24
.678

17. Descriptive Statistics
Dependent Variable:Pairs of shoes sold per day
Locations
Number of Competitors
Mean
Std. Deviation N
Suburban
No Competotors
38.67
7.767 3
One Competitors
36.00
4.359
2 Competitors
52.67
5.686
3 & More Competitors
42.00
Total
42.33
8.217 12
Mall
26.00
4.583
31.33
3.215
47.33
3.055
46.00
6.083
37.67
10.325
Downtown
26.67
21.33
4.041
27.67
1.528
25.83
4.988
30.44
8.575 9
29.56
7.316
42.56
11.876
38.56
9.369
35.28
10.590 36

18. Tests of Between-Subjects Effects
Dependent Variable:Pairs of shoes sold per day
Source
Type III Sum of Squares df
Mean Square F
Sig.
Partial Eta Squared
Corrected Model
2814 5
563 15
0.000
0.717
Intercept
44803 1
44802
1210
0.976
Locations
SSM1 = 1736 2
868 23
0.610
Competitors
SSM2 = 1078 3
359 10
0.493
Error
SSE = 1111 30 37
Total
48728 36
Corrected Total
SST = 3925 35
R Squared = .717 (Adjusted R Squared = .670)

19. Post Hoc Tests Multiple Comparisons
Pairs of shoes sold per day Tukey HSD
(I) Locations
(J) Locations
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Suburban
Mall
4.67
2.484
.162
-1.46
10.79
Downtown
16.50*
.000
10.38
22.62
-4.67
-10.79
1.46
11.83*
5.71
17.96
-16.50*
-22.62
-10.38
-11.83*
-17.96
-5.71

20. Post Hoc Tests Multiple Comparisons
Pairs of shoes sold per day Tukey HSD
(I) Number of Competitors
(J) Number of Competitors
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
No Competotors
One Competitors
.89
2.868
.989
-6.91
8.69
2 Competitors
-12.11*
.001
-19.91
-4.31
3 & More Competitors
-8.11*
.039
-15.91
-.31
-.89
-8.69
6.91
-13.00*
.000
-20.80
-5.20
-9.00*
.019
-16.80
-1.20
12.11*
4.31
19.91
13.00*
5.20
20.80
4.00
.512
-3.80
11.80
8.11*
.31
15.91
9.00*
1.20
16.80
-4.00
-11.80
3.80

21. Findings from TWO WAY ANOVA
The two way ANOVA is conducted to evaluate the main effect of locations and competitors on the sales of shoes. The independent variables are locations and competitors and the dependent variables is sales.
The main effect of location on sales is significant at the 0.05 significance level, F(2,30) = 23, P=0.000 < The effect size of 0.61 indicate the strong effect of location on sales of shoe i.e. Location of store accounts for 61% of variance of sales .
The main effect of competitors on sales is significant at the 0.05 significance level, F(3,30) = 10, P=0.000 < The effect size of 0.49 indicate the strong effect of location on sales of shoe i.e. Competitors accounts for 49% of variance of sales .
The overall effect size of the model is R-square = 0.717, indicate the high effect on sales i.e. 71.7% of the total variance of sales is explained by the model i.e. by location and competitors.

22. Follow up test is conducted to evaluate pair wise differences among the mean sales of shoe. The variance of sales are equal in three locations so for post hoc test is conducted using Tukey test.
Result of post hoc for Multiple comparison: Competitors
The sales of shoes is significantly higher in those area where there are 2 competitors than no competitors , P= < 0.05.
The sales of shoes is significantly higher in those area where there are 3 or competitors than no competitors , P= < 0.05.
The sales of shoes is significantly higher in those area where there are 2 competitors than having only one competitor , P= < 0.05.
The sales of shoes is significantly higher in those area where there are 3 or competitors than having only one competitor , P= < 0.05.

23. Result of post hoc for Multiple comparison: Locations
The sales of shoes is significantly higher in suburban than downtown, P= < 0.05.
The sales of shoes is significantly higher in Mall than downtown, P= < 0.05.
Conclusions:
1. The best place for the high sales of shoes is the Suburban where only two competitors is there.
2. The best place for the high sales of shoes is the Mall where only two competitors are there.
3. The best place for the high sales of shoes is the Mall where 3 or more competitors are there.

24. Two Way ANOVA With Interaction Or Moderation effect in SPSS
IV1=
Location
DV=
Sales
IV2=
Competitors
Interaction=
Location*competitors
Fig: Statistical Model for Two Way ANOVA with Moderation (interaction ) effect