6. Anova and pairwise comparison SPSS PDF

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ANOVA and pairwise comparisons – SPSS Instructions Background This data represents a case study where a farmer wanted to investigate increasing the yield of barley with the use of fertilizers. The data is the weight of barley per unit area (kg/1000m -2) harvested from 60 plots (15 for each treatment).

Initial exploration of the data The data file is ANOVA_data.sav. The value labels have already been added for you. On the Data View you can use this button to toggle between factor numbers and labels: In the Variable view tab, check that all of the variables are set to the correct data type (scale or nominal). The first thing that you should always do is ‘get a feel’ for the data you have. Have a look at the Descriptive Statistics for all of the treatments and look at a plot of the data. Use Graphs > Legacy dialogs > Error bar > Simple > Define > Variable: Harvest Category axis: Treatment > OK.

What does this tell you about the likely result of a test for difference between the 4 treatments? Do the treatments appear to have similar variability?

Kolmogorov-Smirnov test for normality Since ANOVA is a parametric test you should test to see if your data is approximately normally distributed before you decide that ANOVA is appropriate for your data. Analyze > Nonparametric Tests > Legacy Dialogs > 1-Sample K-S > put all 4 treatments in the Test Variable List > OK. One-Sample Kolmogorov-Smirnov Test Nitrogen N Normal Parametersa,b

Most Extreme Differences

15 Mean

Phosphorus 15

Potassium

Control

15

15

107.6000

99.8667

95.1333

89.8000

5.99762

4.65781

4.98378

4.58569

Absolute

.193

.190

.184

.149

Positive

.158

.190

.182

.149

Negative

Std. Deviation

-.193

-.104

-.184

-.117

Kolmogorov-Smirnov Z

.748

.736

.713

.578

Asymp. Sig. (2-tailed)

.630

.650

.690

.892

a. Test distribution is Normal. b. Calculated from data.

Levene test for equal variances Since ANOVA works by comparing the variability between samples with the variability within samples, it is very important that you test for homogeneity of variance before you apply an ANOVA test. You can select this test under Options when you run the ANOVA

ANOVA test for difference with a post hoc pairwise comparison test Analyze > Compare means > One-Way ANOVA > Dependent List: Harvest Factor: Treatment Options > select Homogeneity of Variance Test > Continue Post Hoc > select Tukey > Continue

SPSS Output Oneway Test of Homogeneity of Variances Harvest Levene Statistic

df1

.960

df2 3

Sig. 56

.418

ANOVA Harvest Sum of Squares

df

Mean Square

Between Groups

2565.933

3

855.311

Within Groups

1449.467

56

25.883

Total

4015.400

59

F

Sig.

33.045

.000

Post Hoc Tests Multiple Comparisons Dependent Variable: Harvest Tukey HSD (I) Treatment

(J) Treatment

Mean Difference

Std. Error

Sig.

(I-J)

Phosphorus

1.85772

.001

2.8143

12.6524

Potassium

12.46667*

1.85772

.000

7.5476

17.3857

Control

17.80000*

1.85772

.000

12.8810

22.7190

Nitrogen

-7.73333*

1.85772

.001

-12.6524

-2.8143

4.73333

1.85772

.063

-.1857

9.6524

*

1.85772

.000

5.1476

14.9857

*

-12.46667

1.85772

.000

-17.3857

-7.5476

-4.73333

1.85772

.063

-9.6524

.1857

*

1.85772

.029

.4143

10.2524

*

1.85772

.000

-22.7190

-12.8810

*

-10.06667

1.85772

.000

-14.9857

-5.1476

-5.33333*

1.85772

.029

-10.2524

-.4143

Potassium

Nitrogen Phosphorus Control Nitrogen Control

Upper Bound

7.73333

Control

Potassium

Lower Bound *

Phosphorus Nitrogen

95% Confidence Interval

Phosphorus Potassium

10.06667

5.33333 -17.80000

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

Homogeneous Subsets Harvest Tukey HSD Treatment

N

Subset for alpha = 0.05 1

2

3

Control

15

Potassium

15

95.1333

Phosphorus

15

99.8667

Nitrogen

15

Sig.

89.8000

107.6000 1.000

.063

1.000

Means for groups in homogeneous subsets are displayed. a. Uses Harmonic Mean Sample Size = 15.000.

Questions 1. What was the result of the test for normality? Was it significant? 2. What was the result of the test for homogeneity of variance? Was it significant? 3. Based on the results of these two tests, was a parametric test for difference appropriate? 4. Why were ANOVA and the post hoc pairwise comparison test used, rather than using multiple t-tests? 5. The results could be reported as follows. Make sure that you can identify where to find each of the values, for each of the 4 tests, in the SPSS output tables.    

There was no significant deviation from a normal distribution for any of the treatments (Kolmogorov-Smirnov tests: Nitrogen: Z = 0.748, p > 0.05; Phosphorous: Z = 0.736, p > 0.05; Potassium: Z = 0.713, p > 0.05; Control: Z = 0.578, p > 0.05). There was no significant difference between the variances (Levene: F = 0.96, p > 0.05) so a parametric test was appropriate. There was a significant difference in yield of barley between the 4 treatments (ANOVA, F3,56 = 33.05, p < 0.001). A post hoc Tukey test showed that there was no significant difference between phosphorous and potassium (p = 0.063) but all other pairwise combinations were significantly different (p < 0.05).

6. Add to these results by making at least 2 interesting statements about differences between the treatments. Support your statements by reporting means, with units and with a measure of variability such as standard error if appropriate.

Kruskal-Wallis test If the data is not interval scale; the sample sizes are not approximately equal; any of the samples of data are not normally distributed or the sample variances are not approximately equal then the data does not meet the assumptions for a parametric test. The non-parametric test for a difference between 3 or more samples is a Kruskal-Wallis test. Try applying this test to the same set of data and compare the results: Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples Select Kruskal-Wallis H Test Variable List: Harvest Grouping Variable: Treatment Define Range: Minimum: 1 Maximum: 4 Continue > OK When you report the results of a Kruskal-Wallis test you can call the test statistic either chisquare or H...