Cross_Tabs_lecture.ppt
- 2. Cross Tabulation • Tests whether a relationship exists in data collected • i.e. tests whether there is a contingency between two variables • Tests whether there are any differences or similarities in the responses between 2 or more variables
- 3. • Usually only do cross tabs between 2 variables that make sense • Most common x-tabs are by personal characteristics: such as?….. - Gender - Age - Income level - Marital status - Place of residence - Ethno-cultural background - Type of household - Educational background
- 4. Example • Conducting research on the number of accident claims for a car insurance company • Want to see if the number of claims varies by different types of respondents • What would be some other meaningful x- tabs for insurance claims other than personal characteristics?
- 5. Meaningful x-tabs • Type of car (sports, family, mini-van) • Whether the driver has any previous driving convictions • Whether the driver has taken driving lessons as a youth • Quality of vision • Colour of hair (but would this one be meaningful?)
- 6. Number of insurance claims by gender, NDJ insurance 2015 Number of claims Males Females Total 0 10 032 13 478 23 510 1 2 156 1 430 3 586 2 129 25 145 3 13 4 17 Total 12 321 14 937 27 258 • is there a difference between the number of claims made by gender? • difficult to tell by absolute numbers
- 7. Number of insurance claims by gender, NDJ 2015 Number of claims Males % Females % 0 81.4 90.2 1 17.5 9.6 2 1.1 0.2 3 0.1 0.0 Total 100.0 100.0 • Conclusion? Yes there is a difference…but is it statistically significant? Need to do a chi- square test to determine
- 8. Chi-square test • It enables you to find out if the values for the two variables are independent or associated • If they are independent, there is no relationship, i.e. the number of claims does not vary significantly by gender • If they are associated, there is a relationship, i.e. the number of claims does vary significantly by gender
- 9. 2 Requirements for Chi-square test 1 Try at least to get 50 cases in each sub- group of the variables being cross tabulated E.g. want to examine relationship between age and number of claims would need at least 50 cases in each age group i.e. 18-24, 25-34, 35-44, 45-54, 55-64, 65+ if not, collapse sub-groups: 18-34, 35-54, and 55+
- 10. 2 Requirements for Chi-square test 2 No more than 20% of cells have less than 5 expected responses therefore try to collapse the number of cells whenever possible example….
- 11. Example Number of Holidays per year 18-24 years 25-34 years 35-44 years 45+ years 0 12 4 7 10 1 8 12 7 5 2 8 29 10 4 3 3 2 14 6 4 16 2 11 4 5 4 14 4 7 6 6 13 2 2 7-10 2 2 4 1 11 or more 0 1 4 2 • Number of cells = 36, lots with less than 5 (i.e. more than 20% in fact 50%) • Thus collapse number of categories...
- 12. Thus... Number of Holidays per yr 18-34 years 35 + years 0 16 17 1-2 57 26 3-4 23 35 5+ 40 26 • Number of cells = 8, none less than 5 • Now meets both requirements
- 13. How to check if relationship of 2 variables is associated... • Run the cross tab for your 2 variables • Check the chi-square value and the degrees of freedom • If p value less than .05, your two variables are said to be associated, i.e. there is a relationship between the two variables • You can then statistically be confident in saying that the number of claims is related to gender
- 14. Running a cross tab in Minitab (similar in SPSS and others)
- 15. Example of coded data
- 17. Tip – make sure independent variable like age/gender are in the row
- 18. If p value less than 0.05 there is a relationship, that is satisfaction levels vary significantly by gender in this example
- 19. In this example we don’t meet the 20% rule, that is more than 20% of our cells (there are 8 in the example 4 residence categories x 2 satisfaction scores), have less than 5 – it tells you below that 3 do, so we have to collapse the residence categories from 4 down to 2 – the computer will re-code for you…
- 21. Re-code into new blank column not over the same data you never want to lose your original data
- 22. Here I re-coded data into a blank column 25 And now values are only 1 and 2 instead of 1-4
- 23. Now we can run a cross tab of residence and satisfaction, p value less than 0.05 therefore residence has significant influence on satisfaction levels, here our domestic tourists (coded as 1) are much more satisfied (69.2%) than overseas visitors (coded as 2) – 42.5%!!