Word version of Cluster Analysis Output

The material in this document is organised in the following sections.Section 1 Cluster analysis resultsSection 2 Cluster Profiles Section 2a Profiles using target variablesSection2b Profile using nominal use of budget variableSection2c Profiles using total scale scores

Section 1 Cluster Analysis ResultsTable 1 Initial Cluster Centres

FactorCluster

123

Ease of use-2.458971.32641-1.75815

Social influence-1.815441.98563.31065

Benefits of online grocery shopping 1.58265.95027-2.98908

This is just the starting point for the iterative procedure. It describes the three cluster centres in terms of scores on the three factors.It is not essential for the analysis

Table 2 Iteration HistoryIterationChange in Cluster Centers

123

12.2421.9342.199

2.312.274.221

3.170.184.079

4.072.073.045

5.070.023.045

6.098.011.082

7.165.045.091

8.118.018.089

9.101.037.054

10.062.035.014

This is a summary of the iterative procedure. It is not essential for the analysis.

Table 3 Final Cluster Centres

FactorCluster

123

Ease of use.40421.10858-.55197

Social influence-1.01152.88842-.33981

Benefits of online grocery shopping .60845.31152-1.05053

This is essential. It defines the final solution in terms of the location of cluster centres in terms of scores on the three factors. It is essential for the profile analysis. See later

Table 4 Results of ANOVA Test

FactorClusterErrorFSig.

Mean SquaredfMean Squaredf

Ease of use21.8482.86631125.230.000

Social influence103.5512.341311304.105.000

Benefits of online grocery shopping 73.0542.537311136.135.000

This is essential. The ANOVA tests that there are significant differences between final cluster centres on each of the target variables (factors). The ANOVA is a test based on the following hypotheses:H0: The cluster centre values (average factor scores) are equalH1: The cluster centre values (average factor scores) are not equalFor a specific solution we would expect significant differences between cluster centres on all the target variables (factors)

Table 5 Number of Cases in Each Cluster

Cluster NumberPercent

Cluster188.00028.0

2135.00043.0

391.00029.0

Valid314.000100.0

Missing19.000

This is essential. This information tells us about cluster membership. The SPSS output only gives the number of online grocery shoppers in each cluster. It is more useful for inference to express cluster membership in terms of percentage composition. The Percent column has been added

Section 2 Cluster ProfilesThe third element of cluster analysis is to establish the characteristics or profile of each cluster. In this analysis the profiles are established fromTarget variables: Based upon the average scores for each cluster on the three factors from Table3 Final Cluster CentresBehavioural variables: Based upon a nominal measure concerned with use of a budget Scale variables Based upon total scores for:Attitudes to online grocery shoppingShopping enjoyment in a storeSatisfaction with online grocery shoppingRepeat purchase intentions

Section 2a Profiles using target variablesThe profile is based upon the average factor scores for each cluster,Remember that you need to translate the factor scores with reference to the original data that is based upon a seven-point score (1 = Not at all, 7 = Completely)Table 3 Final Cluster CentresFactorCluster

123

Ease of use.40421.10858-.55197

Social influence-1.01152.88842-.33981

Benefits of online grocery shopping .60845.31152-1.05053

Section 2b Profile using nominal measure of use of a budget

Statistical Test: Chi-square contingency testH0: Cluster identity and profile variable are independentH1: Cluster identity and profile variable are associated

Sequence of testUse significance level of 5% (.050)Check Table 6b Chi-square Statistics tableCheck the Pearson Chi-square results in Decide whether to accept or reject H0 at the 5 percent significance levelIf H0 is rejected interpret the association between cluster and profile variable from Table 6a Crosstab for Cluster Identity and Use of BudgetInterpretation should use percentages and not numerical counts.

Note that these tests produce two tables for each test. The information is an essential part of the analysis but we need to find a more efficient way of summarising the information to present it in the main text. Table 6a Crosstab for Cluster Identity and Use of Budget

Use of budgetTotal

YesNo

Cluster identityCluster 1Count563288

% within Cluster identity63.6%36.4%100.0%

Cluster 2Count7659135

% within Cluster identity56.3%43.7%100.0%

Cluster 3Count395291

% within Cluster identity42.9%57.1%100.0%

TotalCount171143314

% within Cluster identity54.5%45.5%100.0%

Table 6b Chi-Square Statistics

ValuedfAsymp. Sig. (2-sided)

Pearson Chi-Square8.111a2.017

Likelihood Ratio8.1392.017

Linear-by-Linear Association7.7981.005

N of Valid Cases314

Section 2c Profiles using total scale scores

Statistical Test: One-way ANOVAH0: Average scores are equal for the three clustersH1: Average scores are not equal for the three clusters

Note that there are quite a few tables to work through here. Be patient, read the notes carefully and work your way through them.Table 12 shows you how to summarise the whole lot in a single table.

Sequence:Identify mean scores for each group and total score from Table 7 Descriptive StatisticsInterpret the Levene test for homogeneity of variances from Table 8Use a significance level of 5% (.050)Interpret the ANOVA (Table 9) or Browne Forsythe test (Table 10) for the results of the test for mean scoresIf the null hypothesis is rejected, interpret the test for multiple comparisons from Tables 11a -11d to identify why scores are not equal

Table 7 Descriptive Statistics

NMeanStd. DeviationStd. Error95% Confidence Interval for MeanMinimumMaximum

Lower BoundUpper Bound

Total attitude scoreCluster 18829.17057.42196.7911827.597930.743010.0042.00

Cluster 213531.81485.05815.4353430.953832.675814.0042.00

Cluster 39023.12225.76862.6080721.914024.33048.0036.00

Total31328.57197.00426.3959027.792929.35098.0042.00

Total shopping enjoyment scoreCluster 18719.24146.58392.7058717.838220.64465.0035.00

Cluster 213322.87225.54105.4804721.921823.82265.0032.00

Cluster 39019.95565.35883.5648718.833221.07796.0033.00

Total31021.00656.01239.3414820.334521.67845.0035.00

Total satisfaction scoreCluster 18731.40236.51199.6981630.014432.790211.0042.00

Cluster 213332.24065.73420.4972231.257133.22416.0042.00

Cluster 39025.88895.13294.5410624.813826.96407.0040.00

Total31030.16136.40690.3638929.445330.87736.0042.00

Total repeat purchase scoreCluster 18713.21844.27656.4585012.306914.12983.0021.00

Cluster 213315.12783.59590.3118014.511015.74463.0021.00

Cluster 39011.07783.65423.3851910.312411.84313.0019.00

Total31013.41614.16229.2364012.951013.88133.0021.00

There is a lot of information here. All you need is the average score for each scale for each cluster in the column headed Mean. Note that the score for the Total row is simply the average score for all groups

Table 8 Levene Test for Homogeneity of Variances

MeasureLevene Statisticdf1df2Sig.

Total attitude score10.0902310.000

Total shopping enjoyment score3.3232307.037

Total satisfaction score2.4982307.084

Total repeat purchase score2.8882307.057

Null hypothesis is that the true variances are equal between groupsAlternative hypothesis is that true variances are not equal between groupsAssume a significance level of 5% (.050)

If Significance statistic (Sig) in the table is less than the significance level reject H0

If Significance statistic (Sig) in the table is greater than the significance level accept H0

Table 9 ANOVA Results

Sum of SquaresdfMean SquareFSig.

Total attitude scoreBetween Groups4124.16322062.08257.165.000

Within Groups11182.46931036.072

Total15306.633312

Total shopping enjoyment scoreBetween Groups833.4072416.70312.376.000

Within Groups10336.58030733.670

Total11169.987309

Total satisfaction scoreBetween Groups2351.82621175.91334.940.000

Within Groups10332.10930733.655

Total12683.935309

Total repeat purchase scoreBetween Groups885.1862442.59330.410.000

Within Groups4468.13330714.554

Total5353.319309

Note that this test can only be used if the test for the homogeneity of variance indicates that group variances are equal (See Table 8 Test for Homogeneity of Variances). From Table 8 we see that this only applies in the case of the scores Total satisfaction score and Total repeat purchase score.In the case of the scores Total attitude score and Total shopping enjoyment score we have to use the Browne-Forsythe robust test for the equality of means. See Table 10.

Null hypothesis is that the true mean scores of the set of dependent variables are equal between groupsAlternative hypothesis is that true mean scores of the set of dependent variables are not equal between groupsIf Significance statistic (Sig) in the table is less than the significance level reject H0

If Significance statistic (Sig) in the table is greater than the significance level accept H0

Table 10 Browne-Forsythe Robust Test for the Equality of Means

Statisticadf1df2Sig.

Total attitude scoreBrown-Forsythe52.9712233.872.000

Total shopping enjoyment scoreBrown-Forsythe12.0622260.846.000

Total satisfaction scoreBrown-Forsythe34.5972265.280.000

Total repeat purchase scoreBrown-Forsythe29.4912262.312.000

This test is used instead of the ANOVA test if the Levene test (Table 8) indicates that the group variances are not the same. This applies to the scores Total attitude score and Total shopping enjoyment scores.Null hypothesis is that the true mean scores of the set of dependent variables are equal between groupsAlternative hypothesis is that true mean scores of the set of dependent variables are not equal between groupsIf Significance statistic (Sig) in the table is less than the significance level rejects H0

If Significance statistic (Sig) in the table is greater than the significance level accept H0

Post Hoc Tests

Note that ANOVA is an omnibus test. It determines whether at least two mean scores in the set of dependent variables are significantly different but does not identify which ones they are.The Post Hoc Test allows us to identify which group means differ.The tests are conducted for the significance of differences between each pair of groups for the three clusters: Cluster 1 (C1), Cluster 2 (C2) and Cluster 3 (C3). The comparisons are:C1 with C2C1 with C3C2 with C3The test results that is used depends on the results of Levene test for equality of variances (See Table 8)Use Bonferroni results if variances are equalUse Games-Howell if variances are not equal

The hypotheses are Null hypothesis is that the true mean scores are equal between the two groupsAlternative hypothesis is that true mean scores are not equal between groupsLook at the significance statistic (Sig) in the table.

Adopt a significance level of 5% (.050)

If Significance statistic (Sig) is less than the significance level reject H0

If Significance statistic (Sig) in the table is greater than the significance level accept H0

Note that the material in this section has been presented in a different way compared to the SPSS Output.

I have presented separate tables for each score. The SPSS output presents a single table. Its just that the original table is too big to fit on a single page.

Post Hoc Test for Total Attitude Score

Table 11a Multiple Comparisons for Total Attitude Score(I) Cluster identity(J) Cluster identityMean Difference (I-J)Std. ErrorSig.95% Confidence Interval

Lower BoundUpper Bound

BonferroniCluster 1Cluster 2-2.64436*.82287.004-4.6250-.6637

Cluster 36.04823*.90040.0003.88098.2155

Cluster 2Cluster 12.64436*.82287.004.66374.6250

Cluster 38.69259*.81732.0006.725310.6599

Cluster 3Cluster 1-6.04823*.90040.000-8.2155-3.8809

Cluster 2-8.69259*.81732.000-10.6599-6.7253

Games-HowellCluster 1Cluster 2-2.64436*.90304.011-4.7837-.5050

Cluster 36.04823*.99786.0003.68818.4083

Cluster 2Cluster 12.64436*.90304.011.50504.7837

Cluster 38.69259*.74784.0006.924710.4605

Cluster 3Cluster 1-6.04823*.99786.000-8.4083-3.6881

Cluster 2-8.69259*.74784.000-10.4605-6.9247

See results from Table 8: H0 is rejectedCovariances are not equalUse Games-Howell Results

Post Hoc Test for Shopping Enjoyment Score

Table 11b Multiple Comparisons for Total Shopping Enjoyment Score

(I) Cluster identity(J) Cluster identityMean Difference (I-J)Std. ErrorSig.95% Confidence Interval

Lower BoundUpper Bound

BonferroniCluster 1Cluster 2-3.63080*.80010.000-5.5568-1.7048

Cluster 3-.71418.872421.000-2.81421.3859

Cluster 2Cluster 13.63080*.80010.0001.70485.5568

Cluster 32.91662*.79200.0011.01014.8231

Cluster 3Cluster 1.71418.872421.000-1.38592.8142

Cluster 2-2.91662*.79200.001-4.8231-1.0101

Games-HowellCluster 1Cluster 2-3.63080*.85388.000-5.6507-1.6109

Cluster 3-.71418.90406.710-2.85231.4239

Cluster 2Cluster 13.63080*.85388.0001.61095.6507

Cluster 32.91662*.74157.0001.16524.6680

Cluster 3Cluster 1.71418.90406.710-1.42392.8523

Cluster 2-2.91662*.74157.000-4.6680-1.1652

See results from Table 8: H0 is rejectedCovariances are not equalUse Games-Howell Results

Post Hoc Test for Satisfaction Score

Table 11c Multiple Comparisons for Total Satisfaction Score(I) Cluster identity(J) Cluster identityMean Difference (I-J)Std. ErrorSig.95% Confidence Interval

Lower BoundUpper Bound

BonferroniCluster 1Cluster 2-.83830.79993.886-2.76391.0873

Cluster 35.51341*.87223.0003.41387.6130

Cluster 2Cluster 1.83830.79993.886-1.08732.7639

Cluster 36.35171*.79183.0004.44568.2578

Cluster 3Cluster 1-5.51341*.87223.000-7.6130-3.4138

Cluster 2-6.35171*.79183.000-8.2578-4.4456

Games-HowellCluster 1Cluster 2-.83830.85712.592-2.86521.1886

Cluster 35.51341*.88327.0003.42427.6026

Cluster 2Cluster 1.83830.85712.592-1.18862.8652

Cluster 36.35171*.73483.0004.61698.0866

Cluster 3Cluster 1-5.51341*.88327.000-7.6026-3.4242

Cluster 2-6.35171*.73483.000-8.0866-4.6169

See results from Table 8: H0 is accepted Covariances are equalUse Bonferroni Results

Post Hoc Tests for Repeat Purchase Score

Table 11d Multiple Comparisons for Repeat Purchase Score(I) Cluster identity(J) Cluster identityMean Difference (I-J)Std. ErrorSig.95% Confidence Interval

Lower BoundUpper Bound

BonferroniCluster 1Cluster 2-1.90943*.52604.001-3.1757-.6432

Cluster 32.14061*.57359.001.75993.5213

Cluster 2Cluster 11.90943*.52604.001.64323.1757

Cluster 34.05004*.52071.0002.79665.3035

Cluster 3Cluster 1-2.14061*.57359.001-3.5213-.7599

Cluster 2-4.05004*.52071.000-5.3035-2.7966

Games-HowellCluster 1Cluster 2-1.90943*.55447.002-3.2211-.5978

Cluster 32.14061*.59882.001.72473.5566

Cluster 2Cluster 11.90943*.55447.002.59783.2211

Cluster 34.05004*.49557.0002.87935.2207

Cluster 3Cluster 1-2.14061*.59882.001-3.5566-.7247

Cluster 2-4.05004*.49557.000-5.2207-2.8793

See results from Table 8: H0 is rejectedCovariances are equalUse Bonferroni Results

Summary Table for One-Way ANOVA ResultsThis is to demonstrate an efficient way of summarising the tests in a single table.Read table notes 1 and 2 first

Table 12. Summary Table for One-Way ANOVA ResultsTotal scoreMean Scores1Test result2

Cluster1Cluster 2Cluster 3Total

Total attitude29.170ab31.815ac23.122bc28.572F(2,233.9)= 52.971, sig = .000

Total shopping enjoyment19.241a22.872ab19.956b21.006F(2,260.8)= 12.062, sig = .000

Total satisfaction31.402a32.241b25.889ab30.161F(2.307) = 34.940, sig = .000

Total repeat purchase13.218ab15.128ac11.078bc13.416F(2,307) = 30.410, sig = .000

Notes1. In comparing any pair of means, if each mean has the same letter as a superscript, the difference is statistically significant. If not, the difference is not statistically significant. 2. Test results for Total attitude and Total shopping enjoyment are based on the Browne-Forsythe Robust Test. The test results for Total satisfaction and Total repeat purchase are based upon the ANOVA test.

Writing about ANOVA in the textReport the results of the ANOVA test F statistics. F(df1, df2) = F value, p=sig valueReport and interpret the results of the post hoc tests for the equality of means for group pairs from the table Multiple Comparisons including group means.

Example for Total AttitudeOne-way analysis of variance resulted in the rejection of the null hypotheses that the group means were equal (F(2, 233.9)= 52.971, sig = .000). The Games-Howell post hoc test reveal significant differences in the means of all three group comparisons. Cluster 1 (29.170) has less positive attitudes to online grocery shopping than Cluster 2 (31.815) and more positive attitudes than Cluster 3 (23.122). Cluster 2 has more positive attitudes to online grocery shopping than Cluster 3. In absolute terms Cluster 2 has the most positive attitude while Cluster 3 has the least positive attitude.

24