1. P Values - part 2 Samples & Populations Robin Beaumont 11/02/2012 With much help from Professor Chris Wilds material University of Auckland

2. Aspects of the P value

3. Resume P value = P(observed summary value + those more extreme |population value = x) A P value is a conditional probability considering a range of outcomes Sample value Hypothesised population value

4. The Population Ever constant at least for your study! = Parameter Sample estimate = statistic P value = P(observed summary value + those more extreme |population value = x)

5. One sample Many thanks Professor Chris Wilds at the University of Auckland for the use of your material

6. Size matters – single samples Many thanks Professor Chris Wilds at the University of Auckland for the use of your material

7. Size matters – multiple samples Many thanks Professor Chris Wilds at the University of Auckland for the use of your material

8. We only have a rippled mirror Many thanks Professor Chris Wilds at the University of Auckland for the use of your material

9. Standard deviation - individual level = measure of variability within sample 'Standard Normal distribution' Total Area = 1 0 1 = SD value 68% 95% 2 Area: Between + and - three standard deviations from the mean = 99.7% of area Therefore only 0.3% of area(scores) are more than 3 standard deviations ('units') away. - But does not take into account sample size = t distribution Defined by sample size aspect ~ df Remember the previous tutorial

10. Sampling level -‘accuracy’ of estimate From: http://onlinestatbook.com/stat_sim/sampling_dist/index.htmlhttp://onlinestatbook.com/stat_sim/sampling_dist/index.html = 5/√5 = 2.236 SEM = 5/√25 = 1 We can predict the accuracy of your estimate (mean) by just using the SEM formula. From a single sample Talking about means here

11. Example - Bradford Hill, (Bradford Hill, 1950 p.92) mean systolic blood pressure for 566 males around Glasgow = 128.8 mm. Standard deviation =13.05 Determine the ‘precision’ of this mean. SEM formula (i.e 13.5/ √566) =0.5674 “We may conclude that our observed mean may differ from the true mean by as much as ± 1.134 (.5674 x 2) but not more than that in around 95% of samples.” page 93. [edited] All possible values of mean 125126127128129130131 x

12. We may conclude that our observed mean may differ from the true mean by as much as ± 1.134 (.5674 x 2) but not more than that in around 95% of samples.” That is within the range of 127.665 to 129.93 125126127128129130131 x The range is simply the probability of the mean of the sample being within this interval P value = P(observed summary value + those more extreme |population value = x) P value of near 0.05 = P(getting a mean value of a sample of 129.93 or one more extreme in a sample of 566 males in Glasgow |population mean = 128.8 mmHg ) in R to find P value for the t value 2*pt(-1.99, df=566) = 0.047

13. Variation what have we ignored!

14. Sampling summary The SEM formula allows us to: predict the accuracy of your estimate ( i.e. the mean value of our sample) From our single sample Assumes we have a Random sample

15. Aspects of the P value