Data Types

population

entire collection of units or measurements of those units in which we are interested

sample

subset of the population selected for the study as it is generally impractical to measure the variable of interest on all individuals in a population

dependent variables

measure the outcome / effect

independent variables e

measures the causes / predictors

categorical (qualitative data)

nominal

ordinal

nominal data

no intrinsic order

ie. blood group, marital status

any values assigned to nominal variables are labels or categories without true numerical properties

ordinal data

ie. pain - none, mild, moderate, severe

any values that can be ranked, but do not have true numerical properties

distances between levels may not be the same (ie. cancer stage 2 is not the same as cancer stage 1)

binary / dichotomus or binomial variables

data that only has 2 possible categories

multinominal if there are more than 2 categories

numerical (quantitative data)

discrete

continuous

discrete data

uses whole numbers

typically a count

ie. number of laps, days of sickness

continuous data

on a scale

intervals - ie. temperature, distance run

ratio - ie. speed in m/min, BMI

interval vs ratio

interval

• zero is arbitrary (does not have absolute minimum)

• distances between points matter and makes sense (ie. 30 deg - 15 deg = 15 deg) but their ratio does make sense (30 deg is not twice as hot as 15 deg)

ratio

• zero point is not arbitrary (zero is absolute)

• ratio between points of equal distance is the same and must make sense (ie. 40km/h is 2x as fast as 20km/h)

likert scale

primarily ordinal like a 5p scale for responses to a questionnaire and responses are deemed equal

probability

can take only numerical values from 0 - 1

with values in between levels of uncertainty

p-value

measures the probability of obtaining the result we observed or more extreme, ie. a difference or a relationship between variables (alternative hypothesis), when there is no effect (null). It answers the question: what is the probability that we got our result when it is actually a false alarm and the null is true?

small p-value

the smaller the p-value, the less likely our result was purely due to chance and the stronger the evidence against the null hypothesis, with a cut-off point of 0.05 often being used to define a statistically significant result

p-value = <0.05

result is said to be statistically significant

CI

range of values, derived from sample data, that is likely to contain the true value of an unknown population parameter

what does a 95% CI mean

If we repeat the same experiment a large number of times, the confidence interval is expected to cover the true value 95% of the time

CI

 Whilst the p-value is reported to give an indication of the statistical significance or how valid our results are likely to be, the actual result of an experiment or trial are reported in the form of a point estimate. A point estimate can be a mean (average), or a proportion, for example.  

 The point estimate is often accompanied by a confidence interval enclosed in brackets to express how reliable the result is, in the form of the estimated range of values that is likely to include the true population value.  A % value is also given to express how confident we are that the true value lies within that range.

clinical significance

clinically meaningful change

implies a difference that is important enough to make a clinician, patient or investigator change their decision

statistical significance

measures the strength of evidence against the hypothesis or no difference by assessing likelihood that results are not due to chance

may not be clinically important

effect size

the result of a study may sometimes be accompanied by the effect size, which is standardised measures of the magnitude of an effect, generally interpreted from Cohen (1988) - known as Cohen’s d.

since it is standardised it is useful in comparing outcomes on the same scale

standard deviation

descriptive statistic

relates to individual differences around the mean in a sample

measures sample variability

is reliable if the distribution is normal

standard error

inferential statistic that estimates population characteristic

used to estimate

estimates how far the sample mean is likely to be from the population mean and is used to calculate the CI

always smaller than the SD, and gets smaller with larger sample size

error bars

show the extent of uncertainty and useful when comparing data on graphs

risk calculation

number of people with the outcome / the total number of people