lecture 6 - comparing groups: continuous variables Flashcards
(18 cards)
what is the t-test?
Developed William Sealy Gosset
Very common statistical procedure
T-test is used to compare means between groups
Easy to use and can be misused
what is independent data?
Data comes from different (independent) groups of people
Eg. classic experiment (eg. Group 1 receives intervention A, Group 2 receives intervention B).
Study participant is in one group only
Compare differences between groups (mean or median) if outcome is ratio/interval
what is paired data?
Data comes from one group of individuals
Data collected from an individual at different points in time or under different conditions
Compare differences in outcome between time 1 and time 2 or condition 1 and 2 (mean or median)
Other terms: repeated measures, before and after study, crossover trial
what are the assumptions for independent sample t-test?
Dependent variable is ratio/interval: SCALE in SPSS
If either group is small (30 or less), distribution of Dependent Variable for each group should not be badly skewed
The variance of the Dependent Variable for the two groups should not be very different: Levene’s test.
what should you do before conducting analysis?
- good practice to graphically explore data before conducting analysis
- check for outliers
- check variance
what is a problematic difference in variances indicated by?
significant Levene’s Test
If significant, interpret the p value associated with ‘equal variances not assumed’
If non‐significant, interpret p value associated with ‘equal variances assumed’
what are the assumptions of the paired t-test?
Pair-wise differences between matching data points.
Assumptions:
Samples randomly selected
Samples are paired
Distribution of differences is normally distributed
Basically, testing if the mean differences equal to zero or not.
what are non-parametric equivalents to t-tests?
If we have an ordinal scale Dependent Variable, or a ratio/ interval Dependent Variable that does not meet parametric assumptions we use non‐parametric equivalents
These compare medians (ranks) rather than means
They are usually less powerful (need larger sample)
when should you use non-parametric tests?
Non‐parametric tests are used when assumptions of parametric tests are not met (i.e. breached) such as the level of measurement (e.g., interval or ratio data), normal distribution, and homogeneity of variances across groups
They make fewer assumptions about the type of data on which they can be used
Many of these tests use “ranked” data
what is the independent but non-parametric test?
Mann-Whitney U test
what is the Mann-Whitney U test used for?
It is used to test the null hypothesis that two samples come from the same population (i.e. have the same median) or, alternatively, whether observations in one sample tend to be larger than observations in the other
what are the assumptions for the Mann-Whitney U test?
Data must meet the requirement that the two samples are independent
The Mann‐Whitney procedure uses ranks instead of the raw data values
Data values are assigned ranks relative to both samples combined
when is it appropriate to use the Mann-Whitney U test?
The data are ratio, interval or ordinal
The sample sizes are small, and normality is questionable.
The data contain outliers or extreme values that, because of their magnitude, distort the mean values and affect the outcome of the comparison.
Assumes distributions of two groups being compared are the same shape
Assumes not too many ties in ranks of data
what is the test used for non-parametric data?
Wilcoxon signed-rank test
what data is used by Wilcoxon Signed-rank test?
interval, ratio or ordinal data that is paired
what is the Wilcoxon Signed-rank test used for?
to compare paired data as nonparametric alternatives to the paired t‐test
when is the Wilcoxon Signed-rank test used?
when you cannot justify a normality assumption for the differences
what is involved in the Wilcoxon Signed-rank test?
The sign test is very simple in that it counts the number of differences that are positive (+) and those that are negative (‐) and makes a decision based on these counts
