Upload
donal
View
33
Download
0
Embed Size (px)
DESCRIPTION
P Values - part 2 Samples & Populations. Robin Beaumont 11/02/2012 With much help from Professor Chris Wilds material University of Auckland. probability. Aspects of the P value. P Value. sampling. statistic. Rule. A P value is a conditional probability considering a range of outcomes. - PowerPoint PPT Presentation
Citation preview
P Values - part 2Samples & Populations
Robin Beaumont11/02/2012
With much help from
Professor Chris Wilds material University of Auckland
Aspects of the P value
P Valuesampling
probability
statistic Rule
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
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)
One sample
Many thanks Professor Chris Wilds at the University of Auckland for the use of your material
Size matters – single samples
Many thanks Professor Chris Wilds at the University of Auckland for the use of your material
Size matters – multiple samples
Many thanks Professor Chris Wilds at the University of Auckland for the use of your material
We only have a rippled mirror
Many thanks Professor Chris Wilds at the University of Auckland for the use of your material
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
Sampling level -‘accuracy’ of estimate
From: http://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
Standard deviationsample size
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
125 126 127 128 129 130 131x
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
125 126 127 128 129 130 131x
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
Variation what have we ignored!
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
Aspects of the P value
P Valuesampling
probability
statistic Rule