Evidence Based Medicine
Statistics
Regarding confidence intervals for the sample mean, which of the following statements is CORRECT:
Answer:
The 95% confidence interval for the mean is the mean +/- 1.96 SEM. This is the range in which we can be 95% confident that the true population mean lies. The width of the confidence interval will decrease with a smaller SEM, which in turn will decrease with increasing sample size or decreasing variability. A narrow confidence interval shows a more precise estimate.Inferring Population Results from Samples
Evidence Based Medicine / Statistics
Last Updated: 21st April 2019
Even if we ensure that every member of the population has a known and equal chance of being included in a sample, it does not follow that a series of samples drawn from one population will be identical. They will show chance variations from one to another, and the variation may be slight or considerable. For example, a series of samples of the body temperature of healthy people would show very little variation from one another, but the variation between samples of systolic blood pressure would be considerable. Thus the variation between samples depends partly on the amount of variation in the population from which they are drawn. The variation between samples also depends partly on the size of the sample. If a series of samples are drawn from the population, the larger the sample size, the more chance of the sample accurately representing the population.
To generalise the result from a random sample to the target population two concepts need to be understood:
- Standard Error
- Confidence Intervals
Standard Error of the Mean
The standard error of the mean (SEM) is a measure of the expected spread of sample means (i.e. how much the mean varies on repeated sampling) and gives us a measure of the precision of the sample mean as an estimate of the true population mean.
The SEM for a data sample = σ/√n, where σ = standard deviation and n = sample size.
A large SEM indicates the estimate is imprecise and small SEM indicates that the estimate is precise. The SEM is reduced if the size of the sample is increased or the data is less variable.
N.B. Standard deviation is a measure of variation between individual observations in a sample whereas standard error is a measure of precision of an estimate of the population parameter in that sample. Standard deviation is therefore unaffected by sample size, whereas standard error will decrease as sample size increases.
Confidence Intervals
The SEM is not, by itself, particularly useful, but it is used to calculate confidence intervals for the sample mean.
The 95% confidence interval for the mean is the mean +/- 1.96 SEM.
This is the range in which we can be 95% confident that the true population mean lies.
Changing the multiplier from 1.96 to 2.58 includes exactly 99% of the distribution.
The width of the confidence interval depends on the size of the SEM, which in turn depends on the sample size and the variability of the data; a narrow confidence interval shows a more precise estimate. The upper and lower limits of the confidence intervals provide a way of assessing whether results are clinically important.
When quoted alongside a difference between two groups (e.g. mean difference), a confidence interval that includes 0 is statistically non-significant.
When quoted alongside a ratio (e.g. relative risk, odds ratio), a confidence interval that includes 1 is statistically non-significant.
N.B. Confidence intervals can also be calculated for single observations in a normally distributed sample. A 95% confidence interval is the mean +/- 1.96 σ, and this is the range within which we can be 95% confident that any given value from our sample will fall.
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- Biochemistry
- Blood Gases
- Haematology
| Biochemistry | Normal Value |
|---|---|
| Sodium | 135 – 145 mmol/l |
| Potassium | 3.0 – 4.5 mmol/l |
| Urea | 2.5 – 7.5 mmol/l |
| Glucose | 3.5 – 5.0 mmol/l |
| Creatinine | 35 – 135 μmol/l |
| Alanine Aminotransferase (ALT) | 5 – 35 U/l |
| Gamma-glutamyl Transferase (GGT) | < 65 U/l |
| Alkaline Phosphatase (ALP) | 30 – 135 U/l |
| Aspartate Aminotransferase (AST) | < 40 U/l |
| Total Protein | 60 – 80 g/l |
| Albumin | 35 – 50 g/l |
| Globulin | 2.4 – 3.5 g/dl |
| Amylase | < 70 U/l |
| Total Bilirubin | 3 – 17 μmol/l |
| Calcium | 2.1 – 2.5 mmol/l |
| Chloride | 95 – 105 mmol/l |
| Phosphate | 0.8 – 1.4 mmol/l |
| Haematology | Normal Value |
|---|---|
| Haemoglobin | 11.5 – 16.6 g/dl |
| White Blood Cells | 4.0 – 11.0 x 109/l |
| Platelets | 150 – 450 x 109/l |
| MCV | 80 – 96 fl |
| MCHC | 32 – 36 g/dl |
| Neutrophils | 2.0 – 7.5 x 109/l |
| Lymphocytes | 1.5 – 4.0 x 109/l |
| Monocytes | 0.3 – 1.0 x 109/l |
| Eosinophils | 0.1 – 0.5 x 109/l |
| Basophils | < 0.2 x 109/l |
| Reticulocytes | < 2% |
| Haematocrit | 0.35 – 0.49 |
| Red Cell Distribution Width | 11 – 15% |
| Blood Gases | Normal Value |
|---|---|
| pH | 7.35 – 7.45 |
| pO2 | 11 – 14 kPa |
| pCO2 | 4.5 – 6.0 kPa |
| Base Excess | -2 – +2 mmol/l |
| Bicarbonate | 24 – 30 mmol/l |
| Lactate | < 2 mmol/l |
