Samples amp Populations Robin Beaumont 11022012 With much help from Professor Chris Wilds material University of Auckland Aspects of the P value P Value sampling probability statistic ID: 443737
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Slide1
P Values - part 2Samples & Populations
Robin Beaumont11/02/2012With much help fromProfessor Chris Wilds material University of AucklandSlide2
Aspects of the P value
P Value
sampling
probability
statistic
RuleSlide3
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 valueSlide4
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)Slide5
One sample
Many thanks Professor Chris Wilds at the University of Auckland for the use of your materialSlide6
Size matters – single samples
Many thanks Professor Chris Wilds at the University of Auckland for the use of your materialSlide7
Size matters – multiple samples
Many thanks Professor Chris Wilds at the University of Auckland for the use of your materialSlide8
We only have a rippled mirror
Many thanks Professor Chris Wilds at the University of Auckland for the use of your materialSlide9
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 tutorialSlide10
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 hereSlide11
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
131
xSlide12
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
131
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) = 0.047Slide13
Variation what have we ignored!Slide14
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 sampleAssumes we have a Random sampleSlide15
Aspects of the P value
P Value
sampling
probability
statistic
Rule