Beginners statistics Assoc Prof Terry Haines

5 simple steps 1.Understand the type of measurement you are dealing with 2.Understand the type of question you are asking 3.Select a test 1.Focus today on tests of difference 4.Check assumptions where relevant 5.Run the test

Measurement Assigning numerals to variables – Nominal – Ordinal – Interval – Ratio – Count

Nominal Categories without order – Gender Male / Female – Diagnosis Orthopaedic / neurological / cardiorespiratory

Nominal Entering categorical data on a spreadsheet – Binary / dichotomous data Eg. gender One column (female=0, male=1) – Polytomous data Eg. Diagnosis Can have one column (ortho=0, neuro=1, cardio=1) – Risk that the numeric values will be misused Can have three “dummy” variables / columns – Ortho (no=0, yes=1) – Neuro (no=0, yes=1) – Cardio (no=0, yes=1)

Ordinal Categories with order, but we don’t know how much better one place is than another – Finishing order in a race 1 st, 2 nd, 3 rd – Likert scaled surveys Strongly agree, agree, undecided, disagree, strongly disagree – Entering data One column – make sure you record what numbers mean

Interval Equal intervals between numbers, but not a true zero – Eg. Degrees centigrade, IQ test scores, calendar years AD – Entering data Input the number

Ratio Equal intervals between numbers, a true zero – Eg. Distance, age, time, weight – Entering data Input the number

Count Whole, non-negative numbers indicating the frequency of an event – Eg. Number of falls, number of steps, number of therapy sessions

Manipulating data Can turn a higher level of measurement into a lower level, but not vice versa – Eg. IQ scores 0-50 below average average above average This leads to a “loss” of data and can conceal the true relationship between two variables This converts interval data to ordinal

Measurement Nominal, ordinal, interval, ratio, count Can manipulate data down this scale but not up – Be careful in doing this – Loss of data – Would need a really good reason to do so Questions on measurement scales?

What sort of question is being asked? Is A≠B? Is A>B? Is A<B? Is A=B? Is A~B? Difference Agreement / reliability / prediction Correlation

Difference AB AB AB

The confusing thing is that we test a null hypothesis. – What is the probability that there is no difference in the broader population For the one null hypothesis, there are three alternate hypotheses possible – Is A≠B? – Is A>B? – Is A<B? The magnitude of difference can also be measured

Agreement / reliability / prediction To what extent do two variables tell us exactly the same thing, or can one variable predict a later variable? AB AB

Agreement / reliability / prediction The statistical procedures of agreement / reliability / prediction test a null hypothesis – What is the probability that the amount of agreement / reliability / prediction observed occurred by chance? The magnitude of agreement can also be described

Correlation To what extent do two variables co-relate to each other – They do not have to agree in order to co-relate The statistical procedures of correlation test a null hypothesis – What is the probability that the amount of association observed occurred by chance? The magnitude of correlation can also be described

Understand the question Any questions on – Difference – Agreement / reliability / prediction – Correlation

Statistical testing Why do it? Eg. The average height of men in this room is 179 cms, the average height of women is 163 cms. I know the men in this room are taller by 16 cms – Why do a test?

Statistical testing We normally want to extrapolate the results from our sample to a broader population It is the nature of the relationship between A and B in the broader population that is of greatest interest than what is going on just inside this room

Select a test Tests will vary depending on – Measurement scale of variable A and variable B – The type of question being asked – Whether there are repeated measures or correlated samples involved

Tests of difference Variable AVariable B Tests for independent groups / repeated measures or correlated samples Nominal Nominal, 2 groupsChi 2 test (Fisher Exact test for small samples), logistic regression, relative risk, McNemar test, logistic regression with clustering Ordinal Nominal, 2 groupsMann-Whitney U, ordinal logistic regression, Wilcoxon test, ordinal logistic regression with clustering Interval / ratio Nominal, 2 groupsUnpaired t-test (equal / unequal variance), linear regression, Cox regression, paired t- test, linear regression with clustering, Cox regression with clustering Count Nominal, 2 groupsPoisson regression, Poisson regression with clustering, can use ratio tests also if normally distributed

Mock data

T-test versus regression Variable AVariable B Tests for independent groups / repeated measures or correlated samples Nominal Nominal, 2 groupsChi 2 test (Fisher Exact test for small samples), logistic regression, relative risk, McNemar test, logistic regression with clustering Ordinal Nominal, 2 groupsMann-Whitney U, ordinal logistic regression, Wilcoxon test, ordinal logistic regression with clustering Interval / ratio Nominal, 2 groupsUnpaired t-test (equal / unequal variance), linear regression, Cox regression, paired t- test, linear regression with clustering, Cox regression with clustering Count Nominal, 2 groupsPoisson regression, Poisson regression with clustering, can use ratio tests also if normally distributed

What the data says

Is there a difference? T-test

Is there a difference? Regression

Selecting a test: Correlation First check visually, then Pearson’s R Can also use linear regression for further description of the correlation

Correlation Height vs weight – Pearson’s r

Regression

Regression line is line of best fit

Y = bX + c What do these numbers mean? For each one unit increase in weight, there is a 0.87 increase in height. Height = 0.87*weight

Does this work when one variable is dichotomous? Height = 13.3*gender(0,1)

Some tricky questions Can we have: – A is different to B, but A correlates with B? – A agrees with B, and A correlates with B? – A is not different to B, and A does not correlate with B?

Some more mock data

A and B are different, but highly correlated Confidence intervals so narrow and p-value so low they can’t be calculated

A and C have a negative correlation, and are different

B and D are not different, and not correlated

But is there really no relationship here? Linear regression only looks for linear (straight line) relationships. Data transformations or other forms of regression are needed here.

Checking assumptions Many assumptions surround most statistical tests – Need to check to make sure you are doing the right thing by your data – There are specific tests to check assumptions – When in doubt, use visual examination of your data

Run the tests Can use Excel for some tests – Gives you a single number output We have been using Stata today – Lot’s more output to help you interpret your data

Any questions? Next month – 31 st March Starting small and research question development Dr Elizabeth Skinner