1. Stats Questions We Are Often Asked

2. Stats questions we are often asked
When can I use r and R 2 ?
When can I make a ‘causal-type’ claim?
Why should I be careful with a media reported margin of error?
When can I say a confidence interval gives support to a claim?

3. Stats questions we are often asked
When can I use r and R 2 ?
When can I make a ‘causal-type’ claim?
Why should I be careful with a media reported margin of error?
When can I say a confidence interval gives support to a claim?

4. r – little r – what is it?
r is the correlation coefficient between y and x
r measures the strength of a linear relationship
r is a multiple of the slope

5. r – when can it be used? Only use r if the scatter plot is linear
Don’t use r if the scatter plot is non-linear! x y *
r = 0.99

6. r – what does it tell you?
How close the points in the scatter plot come to lying on the line
r = 0.99 x y *
r = 0.57

7. R 2 – big R 2 – what is it? R 2 is the coefficient of determination
Measures how close the points in the scatter plot come to lying on the fitted line or curve x y *

8. R 2 – big R 2 – when can it be used?
When the scatter plot of y versus x is linear or non-linear x y *

9. R 2 – what does it tell you? ˆ Dotplot of the y ’s
Shows the variation in the y ’s x y ˆ x
Dotplot of the y ’s Shows the variation in the y ’s ˆ

10. R 2 – what does it tell you? ˆ ˆ Variation in fitted values
Variation in the y ’s
This amount of variation can be explained by the model ˆ x
We see some additional variation in the y ’s.
The excess is not explained by the model. 2
Variation in y 's ˆ
Variation in fitted values
Variation in y values Variation in y 's R =

11. R 2 – what does it tell you?
When expressed as a percentage, R 2 is the percentage of the variation in Y that our regression model can explain
R 2 near 100%  model fits well
R 2 near 0%  model doesn’t fit well

12. R 2 – what does it tell you? R 2 = 90%x y *
R 2 = 90%
90% of the variation in Y is explained by our regression model.

13. R 2 – pearls of wisdom!
R 2 and r 2 have the same value ONLY when using a linear model
DON’T use R 2 to pick your model
Use your eyes!

14. R 2 and Excel & Graphics Calculators

15. Damaged for life by too much TV

16. Damaged for life by too much TV
N Z Herald (04/10/2005)

17. Damaged for life by too much TV

18. Damaged for life by too much TV
Causal relationship?
r =
Health Score
TV watching

19. Causal relationships
Two general types of studies: experiments and observational studies
In an experiment, the experimenter determines which experimental units receive which treatments.

20. Damaged for life by too much TV
Causal relationship?
r =
Health Score
TV watching

21. Causal relationships
Two general types of studies: experiments and observational studies
In an experiment, the experimenter determines which experimental units receive which treatments.
In an observational study, we simply compare units that happen to have received different levels of the factor of interest.

22. Causal relationships
Only well designed and carefully executed experiments can reliably demonstrate causation.
An observational study is often useful for identifying possible causes of effects, but it cannot reliably establish causation

23. Causal relationships - Summary
In observational studies, strong relationships are not necessarily causal relationships.
Correlation does not imply causation.
Be aware of the possibility of lurking variables.

24. Damaged for life by too much TV

25. Margin of Error Sunday Star Times: National 44% Labour 37.2%
NZ First 4.7%
margin of error: 4.4%
(n = 540)
Herald on Sunday:
Labour 42%
National 38.5%
NZ First 5.5%
margin of error: 4.9%
(n = 400)

26. Margin of Error Herald on Sunday: Labour 42% National 38.5%
NZ First 5.5%
margin of error: 4.9%
(n = 400)

27. Margin of Error Confidence Interval: estimate ± margin of error
Herald on Sunday:
Labour 42%
National 38.5%
NZ First 5.5%
margin of error: 4.9%
(n = 400)

28. Margin of Error
Survey
Errors
Sampling Error
Nonsampling Errors

29. Margin of Error Survey Errors Sampling Error Nonsampling Errors
caused by the act of sampling
has potential to be bigger in smaller samples
can determine how large it can be – margin of error
unavoidable (price of sampling)

30. Margin of Error Survey Errors Sampling Error Nonsampling Errors
e.g., nonresponse bias, behavioural, . . .
can be much larger than sampling errors
impossible to correct for after completion of survey
impossible to determine how badly they affect results

31. Margin of Error Herald on Sunday: Labour 42% National 38.5%
NZ First 5.5%
margin of error: 4.9%
(n = 400)

32. Margin of Error
Approx. 95% confidence interval for p:

33. Margin of Error
Margin of error (single proportion)

34. Margin of Error Sunday Star Times: National 44% Labour 37.2%
NZ First 4.7%
margin of error: 4.4%
(n = 540)
Herald on Sunday:
Labour 42%
National 38.5%
NZ First 5.5%
margin of error: 4.9%
(n = 400)

35. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6

36. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6
With 95% confidence, the mean dissatisfaction score for Canterbury customers is somewhere between 0.5 and 20.7 larger than the mean dissatisfaction score for Auckland customers.

37. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6
With 95% confidence, the mean dissatisfaction score for Canterbury customers is somewhere between 0.5 and 20.7 larger than the mean dissatisfaction score for Auckland customers.

38. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6
With 95% confidence, the mean dissatisfaction score for Auckland customers is somewhere between 9.8 less than and 6.6 greater than the mean dissatisfaction score for Wellington customers.

39. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6
With 95% confidence, the mean dissatisfaction score for Auckland customers is somewhere between 9.8 less than and 6.6 greater than the mean dissatisfaction score for Wellington customers.

40. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6
Does this confidence interval support the proposition that there is a difference between the two population means?
Supports mA – mW  0 ?
No, it doesn’t support the proposition.
Since 0 is in the confidence interval, then 0 is a believable value for the difference. There could be no difference between the two means.
mA – mW = 0 (no diff)
mA – mW  0 (a diff)

41. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6
Does this confidence interval support the proposition that there is NO difference between the two population means?
Supports mA – mW = 0 ?
No, it doesn’t support the proposition.
Since there are non-zero numbers in the interval mA – mW could be non-zero, there could be a difference.
mA – mW = 0 (no diff)
mA – mW  0 (a diff)

42. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6
Does this confidence interval support the proposition that there is a difference between the two population means?
Supports mA – mW  0 ?
Yes, it does support the proposition.
Since zero is not in the interval, it is not believable that the difference is zero. No difference between the means is not believable.
mA – mW = 0 (no diff)
mA – mW  0 (a diff)

43. Bank Dissatisfaction Scores – 95% CIs
mC – mA: to mA – mW: – 9.8 to 6.6
Does this confidence interval support the proposition that there is NO difference between the two population means?
Supports mA – mW = 0 ?
No, it doesn’t support the proposition.
In fact, it provides evidence against it. 0 is not in the interval. No difference between the means is not believable.
mA – mW = 0 (no diff)
mA – mW  0 (a diff)