PUBH2007 Lecture Notes - Lecture 5: Statistical Parameter, Null Hypothesis, Blood Pressure
PUBH2007 LECTURE FIVE
Revision of Normal probabilities and sampling distributions
‘eferece or oral rage for idividual easureets
Definition of statistical inference
Reasoning of statistical estimation
Calculation of a confidence interval
Interpretation of a confidence level
How confidence intervals behave
Writing hand: lurking variable therefore eliminated all left handed participants
Greater spread among men (as per SD)
Distributions for grip strength:
Women:
68% between 25.1 and 34.9 kg
(mean ± 1 std dev = 30.012 ± 4.864)
95% between 20.3 and 39.7 kg
99.7% between 15.4 and 44.6 kg
Men
68% between 40.7 and 54.0 kg
95% between 34.0 and 60.7 kg
99.7% between 27.4 and 67.4 kg
Reference or 'normal' range: values corresponding to 95% limits are sometimes called the reference
range.
E.g. Right grip strength females: 95% between 20.3 and 39.7 kg
Chance of a female in this age group having right grip strength outside this range (i.e., <20.3 or > 39.7)
is less than 5% or probability (P)< 0.05, (or P<0.025 for each tail separately).
Where an individual is expected to sit, used in diagnostics.
Doesn't necessarily mean that those with a grip strength outside normal range are unwell.
• Note: 1, 2 and 3 standard deviations are approximations.
• Exact values can be obtained from tables, calculators or using statistical software.
find more resources at oneclass.com
find more resources at oneclass.com
R COMMANDER: MEAN 0, SD 1 and values 0.025 and 0.975 for 95%
If probability = 0.95, exact values are mean +/- 1.96 SD
If probability = 0.99, exact values are mean +/- 2.576 SD
NOTE: Probabilities usually written as fractions, not percentages.
Make inferences about population based on data from sample.
The purpose of a sample is to give us information about a larger population . The process of drawing
conclusions about a population on the basis of sample data is called statistical inference.
Different samples from same population will vary. Statistics calculated from different samples will vary.
Question: is it different from the population or is it just due to chance?
Sampling distribution:
• Is you selected many samples from the same population, you could calculate the mean for each
sample.
• Could draw a histogram of the sample means - an idealised model of the histogram is called
the sampling distribution of the mean.
Central Limit Theorem: when n is large, the sampling distribution of the sample mean x-bar is
approximately Normal: x-bar is approximately N (μ, σ / √ n)
Therefore smaller n = smaller standard error
Standard error of the mean
In theory, you can calculate:
• The mean of the sample means - should be a good estimate of population mean
• The standard deviation of sample means - summarises variation between samples - called the
standard error of the mean, SE(mean)
In practice you have just one sample, you can calculate:
• Sample mean and SE (mean) from the sample data
If s is the sample standard deviation and n is the sample size, then
Sample statistic –numerical characteristic of a sample, e.g. sample mean – calculated from sample data
Population parameter – numerical characteristic of a population, e.g. population mean – usually
unknown
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Writing hand: lurking variable therefore eliminated all left handed participants. 68% between 25. 1 and 34. 9 kg (mean 1 std dev = 30. 012 4. 864) Reference or "normal" range: values corresponding to 95% limits are sometimes called the reference range. Right grip strength females: 95% between 20. 3 and 39. 7 kg. Chance of a female in this age group having right grip strength outside this range (i. e. , <20. 3 or > 39. 7) is less than 5% or probability (p)< 0. 05, (or p<0. 025 for each tail separately). Where an individual is expected to sit, used in diagnostics. Doesn"t necessarily mean that those with a grip strength outside normal range are unwell: note: 1, 2 and 3 standard deviations are approximations, exact values can be obtained from tables, calculators or using statistical software. R commander: mean 0, sd 1 and values 0. 025 and 0. 975 for 95% If probability = 0. 95, exact values are mean +/- 1. 96 sd.
