Stats Measures of dispersion Flashcards
Range and interquartile range
75% of the data set is below Q3
50% of the data set is less than Q2
25% of the data set is below Q1
50% of the data set is between Q1 and Q3
Standard deviation
A range of one SD above and below the mean would include 68.2% of the values from the study.
A range of two SDs above and below the mean would include 95.4% of the values from the study.
A range of three SDs above and below the mean include 99.7% of the values from the study.
A few things to note about the standard deviation:
It can never be negative
The smallest value it can have is 0 (a SD of zero tells you that all the values are the same)
It is affected by outliers
It has the same units as the original data
Standard error of the mean
The standard error of the mean is an inferential statistic used to estimate the population mean.
It is a measure of the spread expected for the mean of the observations - i.e. how ‘accurate’ the calculated sample mean is from the true population mean
SEM = s / square root (n)
s = standard deviation of the sample mean n = sample size
Therefore the SEM gets smaller as the sample size (n) increases
On its own the SE is pretty meaningless, as its real use lies in calculating CIs when we are trying to estimate the precision of our estimate of the population mean.
so…
The SD quantifies scatter (how much the data varies)
The SEM quantifies how precisely you know the true mean of the population
The SEM takes into account both the value of the SD and the sample size
Both SD and SEM are in the same units (the units of the data)
The SEM, by definition, cannot be larger than the SD
The SEM gets smaller as the samples get larger
Confidence interval
A confidence interval is always quantified by a confidence level, usually expressed as a percentage (e.g. a 95% confidence interval).
Sample results such as the mean value are often presented along with a confidence interval. For example, in a study, the mean height in a sample taken from a population is 183cm. You know that the standard error (SE) (the standard deviation of the mean) is 2cm. This gives a 95% confidence interval of 179-187cm (+/- 2 SE).
This means that if the same study was repeated time and time again then the mean value would be within this interval 95% of the time. It does not mean that there is a 95% chance that the interval contains the true mean.
The ‘true value’ is the mean value that would be calulated if we had the data for the whole population (remember statistics are estimates for populations).
The confidence interval is a range that is likely to contain the true value (but it won’t always).
