Pearson s r and Chi-square tests. Dr. Christine Pereira Academic Skills Team (ASK)

Transcription

1 Pearson s r and Chi-square tests Dr. Christine Pereira Academic Skills Team (ASK) ask@brunel.ac.uk

2 Which correlation test should I use? Pearson s r Spearman s rho Chi-square Dr. Christine Pereira ASK Academic Skills ( ) 2

3 Dr. Christine Pereira ASK Academic Skills ( ) 3

4 Dr. Christine Pereira ASK Academic Skills ( ) 4

5 Variables measured using WORDS or CATEGORIES Categorical Variables measured using NUMBERS Interval/Ratio Nominal (Unranked categories) Marital Status Political Party Eye Color Ordinal (Ranked categories) Satisfaction level Level of agreement Scale Height Weight Age No. of cars No. of students Dr. Christine Pereira ASK Academic Skills ( ) 5

6 Significant Correlations A relationship, association, impact or effect Dr. Christine Pereira ASK Academic Skills ( ) 6

7 Measure the strength of a relationship They only measure association They do NOT imply causation!

8 Dr. Christine Pereira ASK Academic Skills ( ) 9

9 There s a significant relationship between BP2 (Brand Pleasure Item 2) and PI3 (Purchase Intention Item 3) Variable name in SPSS Q5_BP2 Q6_PI3 Dr. Christine Pereira ASK Academic Skills ( ) 10

10 There s a significant relationship between BP2 (Brand Pleasure Item 2) and PI3 (Purchase Intention Item 3) Scale Ordinal Nominal Dichotomous (exactly 2 groups) Scale Ordinal Nominal Pearson s r Spearman s rho Compare groups Pearson s r Spearman s rho Spearman s rho Chi-square & Cramer s V Spearman s rho Compare groups Chi-square & Cramer s V Chi-square & Cramer s V Chi-square & Cramer s V Dichotomous (exactly 2 groups) Pearson s r Spearman s rho Chi-square & Cramer s V Chi-square test & Phi Dr. Christine Pereira ASK Academic Skills ( ) 11

11 Consumer Brand Pleasure is associated with Brand Loyalty Scale Ordinal Nominal Dichotomous (exactly 2 groups) Scale Ordinal Nominal Pearson s r Spearman s rho Compare groups Pearson s r Spearman s rho Spearman s rho Chi-square & Cramer s V Spearman s rho Compare groups Chi-square & Cramer s V Chi-square & Cramer s V Chi-square & Cramer s V Dichotomous (exactly 2 groups) Pearson s r Spearman s rho Chi-square & Cramer s V Chi-square test & Phi Dr. Christine Pereira ASK Academic Skills ( ) 12

12 Whether or not customer s have contact with employees affects whether or not they make a purchase Did you speak/interact with an employee while you were shopping? Yes No Did you make a purchase? Yes No Dr. Christine Pereira ASK Academic Skills ( ) 13

13 Whether or not customer s have contact with employees affects whether or not they make a purchase Scale Ordinal Nominal Dichotomous (exactly 2 groups) Scale Ordinal Nominal Pearson s r Spearman s rho Compare groups Pearson s r Spearman s rho Spearman s rho Chi-square & Cramer s V Spearman s rho Compare groups Chi-square & Cramer s V Chi-square & Cramer s V Chi-square & Cramer s V Dichotomous (exactly 2 groups) Pearson s r Spearman s rho Chi-square & Cramer s V Chi-square test & Phi Dr. Christine Pereira ASK Academic Skills ( ) 14

14 Brand Loyalty Survey Consumer Brand Pleasure is associated with Brand Loyalty Pearson s r Dr. Christine Pereira ASK Academic Skills ( ) 15

15 Dr. Christine Pereira ASK Academic Skills ( ) 16

16 These are the 2 variables we want to correlate Brand Loyalty Survey Dr. Christine Pereira ASK Academic Skills ( ) 17

17 Brand Loyalty Survey These will always be 1. Never report these values. Dr. Christine Pereira ASK Academic Skills ( ) 18

18 Brand Loyalty Survey These will always be the same. Just report one of these. Dr. Christine Pereira ASK Academic Skills ( ) 19

19 Strength Between -1 to +1 Brand Loyalty Survey Significance (p-value) Dr. Christine Pereira ASK Academic Skills ( ) 20

20 Strong relationships Moderate/weak relationships Y Y.5 to 1 X.3 to.49 X Y Y -.3 to to -1 X X Dr. Christine Pereira ASK Academic Skills ( ) 21

21 Sign of correlation Strong Moderate Weak Very weak or None + values 0.5 to to to to values -1.0 to to to to 0 Strong & Positive Dr. Christine Pereira ASK Academic Skills ( ) 22

22 Strong & Positive Brand Loyalty Survey p < 0.05 Significant p < 0.05: There IS a significant relationship between the 2 variables p > 0.05: There is NOT a significant relationship between the 2 variables Dr. Christine Pereira ASK Academic Skills ( ) 23

23 Conclusion: There is evidence to suggest a significant strong positive association between BP and BL. Brand Loyalty Survey Strong & Positive p < 0.05 Significant Dr. Christine Pereira ASK Academic Skills ( ) 24

24 Interpretation: Consumers who experience more Brand Pleasure tend to be more Brand Loyal. People who experience more BP tend to be more BL People who experience less BP tend to be less BL Dr. Christine Pereira ASK Academic Skills ( ) 25

25 How to compute Pearson s r How to interpret the output Dr. Christine Pereira ASK Academic Skills ( ) 26

26 Customer experience survey Whether or not customer s have contact with employees affects whether or not they make a purchase Chi-square Dr. Christine Pereira ASK Academic Skills ( ) 27

27 Dr. Christine Pereira ASK Academic Skills ( ) 28

28 Customer experience survey Choose one variable as the Row and one as the column Dr. Christine Pereira ASK Academic Skills ( ) 29

29 Customer experience survey Dr. Christine Pereira ASK Academic Skills ( ) 30

30 Customer experience survey Dr. Christine Pereira ASK Academic Skills ( ) 31

31 Significance (p-value) Strength Between 0 and 1 Customer experience survey Dr. Christine Pereira ASK Academic Skills ( ) 32

32 p > 0.05 Not significant p < 0.05: There IS a significant relationship between the 2 variables p > 0.05: There is NOT a significant relationship between the 2 variables Dr. Christine Pereira ASK Academic Skills ( ) 33

33 If this is > 20% watch my tutorial on what to do next as assumptions have been violated (see later slide) Dr. Christine Pereira ASK Academic Skills ( ) 34

34 Type of data Small Moderate Strong One or both variables are Dichotomous One variable has 3 categories and the other has 3 or more Both variables have 4 or more categories Association is greater than 0.01 Association is greater than 0.07 Association is greater than 0.06 Association is greater than 0.30 Association is greater than 0.21 Association is greater than 0.17 Association is greater than 0.50 Association is greater than 0.35 Association is greater than 0.29 Strength is small Customer experience survey Dr. Christine Pereira ASK Academic Skills ( ) 35

35 Type of data Small Moderate Strong One or both variables are Dichotomous One variable has 3 categories and the other has 3 or more Both variables have 4 or more categories Association is greater than 0.01 Association is greater than 0.07 Association is greater than 0.06 Association is greater than 0.30 Association is greater than 0.21 Association is greater than 0.50 Association is greater than 0.35 When Chi Square tests table shows p > 0.05 (not significant), DO NOT report the strength Association is greater than 0.17 Association is greater than 0.29 Strength is small 3 Dr. Christine Pereira ASK Academic Skills ( ) 36

36 Conclusion: There is insufficient evidence to suggest that whether or not a customer has contact with employees effects whether or not they make a purchase. Customer experience survey p > 0.05 Not significant Dr. Christine Pereira ASK Academic Skills ( ) 37

37 Interpretation: Customers who interact with employees in a store are just as likely to make a purchase as those who do not interact with employees. Dr. Christine Pereira ASK Academic Skills ( ) 38

38 Chi-square + interpretation Chi-square + interpretation (assumptions violated) Dr. Christine Pereira ASK Academic Skills ( ) 39

39 How to compute Spearman s How to interpret the output Dr. Christine Pereira ASK Academic Skills ( ) 40

40 Dr. Christine Pereira ASK Academic Skills ( ) 41

41 SPSS Survival Manual, 4 th Edition (2010) by Julie Pallant. E-book: Library shelf location: HA32.P SPSS Survival Manual, 5 th Edition (2013) by Julie Pallant. Library shelf location: HA32.P SPSS Survival Manual, 6 th Edition (2016) by Julie Pallant. Library shelf location: HA32.P Dr. Christine Pereira ASK Academic Skills ( ) 42

42 Dr. Christine Pereira ASK Academic Skills ( ) 43