Measures of variation

Question	Answer
When you see 'repeatability' and 'precision', which test should you be thinking of?	Standard error of the mean.
What is the calculation for standard error of the mean?	σ/√n standard deviation / √ no. of samples or measurements
Why is standard error a more precise measure of variability than standard deviation?	Because it takes into account the number of observations/samples that make up a mean rather than just the standard deviation about that mean.
How are standard deviations about a mean commonly represented? How could this representation be misinterpreted?	Mean ± standard error This does NOT mean that we are sure that the true mean figure lies between these limits - at best, assuming normality, there is a ~68% change that the true mean is between these limits. It also does NOT mean that all the observations lie between these limits. If these limits were being represented on a graph, they could be misinterpreted for confidence intervals.
What is replicability/repeatability?	It is a measure of short term variation. It involves repeat measurements on the same items under the conditions e.g. same time, same experiment, same location, using same experimenter/observer. If the same biomedical scientist measured the pH of 6 samples of the same blood taken at the same time with the same equipment, one would expect the data to display repeatability.
What is reproducibility?	A longer-term measure of variation relating to whether or not the experiment can be replicated. It is how consistent a set of data is between occasions, on a larger scale, or using different experimenters/observers. If two different biomedical scientists tested the pH of the same sample of blood taken at the same time using the same equipment and got consistent values, the data/experiment could be said to be reproducible.
What test should you be thinking of when you see key words: repeatability/reproducibility?	Standard deviation.
What is the calculation for standard deviation?	σ = √(Σni = 1 (xi - x-bar)-squared ) / n-1 Minus the mean from each individual value to find the deviations. Square these. Total the squared values. Divide by the sample number -1. Square root the whole thing. This is your standard deviation.
Define coefficient of variation.	The ratio of the standard deviation to the mean expressed as a percentage: (σ / x-bar) x 100. (Standard deviation/mean) x100
When is it more appropriate to use coefficient of variation rather than standard deviation alone?	Coefficient of variation makes variation 'unit-less' so it is very useful for comparing data with different means and standard deviations e.g. comparing the variability of count data and percentage data simultaneously.
What are the two common ways in which standard error may be expressed graphically?	In a bar chart, standard error bars will usually be added positively (i.e. mean + 1x standard error) to each bar as opposed to ±. In a scatter plot, ±standard error bars will usually be added to each point.
What should you do if you want to be fairly sure that your error bar includes in the true value on a graph?	The error bars should be at least: mean ± 2x standard error.
What is the calculation for a 95% confidence interval?	95% C.I. = μ ± 1.96 (σ/n) = true mean ± 1.96 x (standard error)
What is the calculation for a 99% confidence interval?	μ ± 2.576 (σ/n) true mean ± 2.576 (standard error)
If you have a 95% confidence interval, what does that mean?	It means that you are 95% confident that the true mean lies in this range.
If you want to be more confident that your value falls within a given range, you will increase your interval. However, what are you sacrificing in order to do this?	Precision.
When can 1.96 (95%) and 2.576 (99%) not be used for calculating confidence intervals?	When confidence intervals are being calculated for small samples i.e. <30.
How do you find the correct value to use if you cannot use 1.96 (95%) or 2.576 (99%) to calculate confidence intervals?	You look up a t value in the t table according to the proportion of 2.5% (0.025; for 95% C.I.) or 1% (0.005; for 99% C.I.) and n-1 degrees of freedom.
Why can z values (i.e. 1.96 for 95% C.I.) not be used for confidence intervals for samples <30?	Because the values are not likely to be normally distributed with a sample size this small, so adjusted values must be used which take into account the sample size (degrees of freedom).

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	Created by sophietevans almost 10 years ago