annotated word version of cluster anaysis output 2014-2015 version 2(1)
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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
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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
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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
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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
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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.
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