Analysing and comparing continuously measured data (7/12) Flashcards
Define the difference between Paired data and two independent groups
Paired data - the response of one group under different conditions as in a cross-over trial, or of matched pairs of subjects.
Two independent groups within one study, e.g. groups of patients given different treatments. Male & female or randomised for different interventions
What are the two types of statistical tests?
Parametric or Non-parametric
Properties of Parametric methods
- Assume data are distributed according to a particular distribution e.g. Normal distribution.
- More powerful than non-parametric tests, when the assumptions about the distribution of the data are true.
Give 3 Examples of parametric tests:
t-test, analysis of variance, linear regression techniques.
Properties of Non-parametric methods
• Nonparametric methods provide alternative data analysis techniques without assuming anything about the shape (distribution) of the data. i.e.
So, on-parametric methods often referred to as ‘distribution free’.
○ e.g. data may be skewed, ranked or ordinal
• Nonparametric techniques are usually based on ranks or signs.
• Not affected by potential outliers
• Nonparametric methods should not be considered as an alternative way to find significant P-values!
• Nonparametric methods are based on ranks of the data and not the actual data.
• Nonparametric methods are used when the assumptions underlying a parametric test are not met
Assumptions for the parametric approach for Independent two-sample t-test for comparing means
- Two ‘independent’ groups;
- Continuous outcome variable;
- Outcome data in both groups is Normally distributed ;
- Outcome data in both groups have similar standard deviations.
How to check conditions are met when making assumptions for the parametric approach for Independent two-sample t-test for comparing means
- Plotting two histograms, one for each group to assess Normality; it doesn’t have to be perfect, just roughly symmetric;
- Calculating standard deviations – as a rough estimate, one should be no more than twice the other;
- However the t-test is very robust to violations of the assumptions of Normality and equal variances, particularly for moderate to large sample sizes.
Steps for calculating the two step :
- First calculate the mean difference between groups.
- Combine the data to Calculate the pooled standard deviation.
- Then calculate the standard error of the difference between two means.
- Calculate the test statistic t.
- Compare the test statistic with the t distribution with
n1 + n2 - 2 degrees of freedom. - This gives us the probability of the observing the test statistic t or more extreme under the null hypothesis.
The non-parametric equivalent of the 2 independent samples t-test is…
the Mann-Whitney U test.
Steps: to calculate hypothesis test
- First arrange all the data in increasing order (smallest observation to the largest).
- Choosing one group; for each observation in that group count how many observations in the other group lie below it.
- Add all of these numbers up to get the U-statistic.
- Compare the U test statistic with it’s theoretical distribution under the null hypothesis (that the samples come from the same population).
From this we can find out the probability of the observing the test statistic U or a value more extreme under the null hypothesis
What tests are used when there are > 2 independent groups?
• The Analysis of variance technique (ANOVA)
○ Parametric test
○ Similar to the t-test but extended for more than two groups
• Kruskal-Wallis Test
○ Non-parametric equivalent of analysis of variance
○ Similar to Mann-Whitney U test but extended for more than two groups
Can data be non-parametric?
No
only the TESTS are (non)parametric
Assumptions for carryiung out a paired t-test
- continuous outcome
- the paired differences are independent of each other
- the paired differences are plausibly normally distributed
- paired observations
