1. www.handels.gu.se E 45 Johan Brink, IIE 24 November Quantitative data analysis Lecture 6 2015-06-11

2. www.handels.gu.se Agenda Chapter 14 Univariate analysis Bivariate analysis Multivariate analysis Contingency Pearson’s correlation t-test Chi square Factor & cluster analysis

3. www.handels.gu.se Univariate analysis One variable at a time Frequency tables – Bar charts Grouping of ration & interval variables: 20-29, 30-39… - Histograms Arithmetic mean = Sum of all values/ # Values =33.6 Median = Mid point of distribution of values Mode =the most frequent value in the distribution Interval/ Ratio – Scale & distance Ordinal - ranked Nominal – can’t be ranked MeanYesNo -used anyhow No MedianYes No ModeYes

4. www.handels.gu.se Dispersion Range: Min to Max (7 & 3) Variance =standard deviation² s²= Σ (x-M)²/ (n-1) = 1,5 ->Standard deviation =1,22 Point(x-M)² 150 250 3610 450 541 641 774 834 961 Sum4512 Variance = 12/(9-1) =1,5

5. www.handels.gu.se Spurious correlation Relationship between two variables are caused by a thirds, underlying factor Intervening variable Chain of relationships Moderating variable The relationship between A & B only exist if C is percent Multivariate analysis AB C ABC AB C

6. www.handels.gu.se Analyzing data Correlation & relationship Between variables (questions, groups, items) Does the answers on question 1 correlate with answers on question 2? - Different questions/items for the same construct or does it capture a relationship Test – significant differences Between variables -Questions, groups items -Across time/treatments Is the mean different enough given the standard deviations? t-test ( Chi-squared (nominal scales) Differences from the expected value?

7. www.handels.gu.se Constructs & Items Variable 1 Variable 2 Variable 3 Variable 4 Variable 5 Variable 6 Cronbach α is a measure of how well variables measures the same underlying phenomena Construct 1Construct 2 Item Question 1 Item Question 2 Item Question 3 Item Question 4 Item Question 5 Item Question 6 Org. CulturePerformance

8. www.handels.gu.se Hypothesis testing H0 There is no difference between group A and group B H1 There is a difference between group A and B H0 There is no connection between variable X and Y H1 There is a connection between variable X and Y Real relationship (unknown) H0 trueH0 false Result of statistical test H0 rejectedType 1 error Correct H0 not rejected CorrectType 2 error In order to reduce the risk of type 1 error, by increasing the level of significance from 5% to 1%,the risk of committing type 2 error increases!

9. www.handels.gu.se Bivariate analysis NominalOrdinalInterval/rationDichotomus Nominal – Can’t be ranked Contingency table, Chi square, Cramer’s V Ordinal -RankedContingency table, Chi square, Cramer’s V Spearman’s rho Interval/ratio – scale & distance Contingency table, Chi square, Cramer’s V Spearman’s rhoPearson’s rSpearman’s rho Dichotomus – Yes/No Contingency table, Chi square, Cramer’s V Spearman’s rho Phi

10. www.handels.gu.se Contingency tables Reasons MaleFemale #%#% Relaxation37613 Fitness15361633 Lose weight8192552 Build strength 163812 Total4210048100

11. www.handels.gu.se Pearson's correlation For interval/ratio variables Measure of the strength of association between two variables r = Between -1 and +1, 0= no correlation & 1= perfect correlation r²*100% = Variation caused /explained XY 12 23 34 45 55 56 77 78 89 98 R=0,969

12. www.handels.gu.se Pearson's correlation

13. www.handels.gu.se Pearson's correlation

14. www.handels.gu.se Pearson's correlation

15. www.handels.gu.se t-test: A statistical test to see if there is a difference between two samples n1=25 n2=24 Mean1=64Mean2=56 S1=10S2=8 Df=n1+n2-2=47 t= (Mean1-Mean2)/√[((n1-1)s1²+ (n2- 1)s2²)/(n1+n2-2))*(1/n1+1/n2))] t= (641-56)/√[((25-1)10²+ (24-1)8²)/(25+24- 2))*(1/25+1/24))] =3,08 Statistic table t(df=47, 0,05)=2,012 3,08>2,012 thus reject H0, there is a difference! Hypothesis: H0, the true means is equal Alternative, H1, there is a difference

16. www.handels.gu.se Chi square Is there a difference between age groups (young, middle and old) and preference for A or B? Nominal scales! 40 respondents Chi²= Σ (observed-expected)²/expected

17. www.handels.gu.se Chi square YoungMiddle age OldΣ A205025 B55515 Σ2510540

18. www.handels.gu.se Chi square YoungMiddle age OldΣ A20 (15,625)5 (6,25)0 (3,125)25 B5 (9,375)5(3,75)5 (1,875)15 Σ2510540

19. www.handels.gu.se Chi square Chi²= (20-15,625)²/15,625+ (5-6,25)²/6,25+ (0-3,125)²/3,125+ (5-9,375)²/9,375+ (5-3,75)²/3,75+ (5-1,875)²/1,875=12,27 Df= (r-1)*(c-1)= 2-1*3-1=2 Chi²0,05, df=2 =>5,99 12,27> 5,99 Thus reject H0, there is a difference between A and B and age group.

20. www.handels.gu.se Factor analysis and Cluster analysis Reduce the data Variables which measures the same thing Underlying factors