Two sample unequal variance t test
![two sample unequal variance t test two sample unequal variance t test](https://sixsigmastudyguide.com/wp-content/uploads/2021/01/tt1.png)
T is the difference between treatment A 1 and treatment A 2.If we exclude random variation, the differences between these 4 means are due to a combination of the treatment effect, T, and period effect P.
#Two sample unequal variance t test how to
To understand why this is so, and how to test these results, let us rearrange these means and their differences as follows: If there were an interaction, then the lines in the last figure would no longer be parallel and we could not analyse the data as a single cross-over experiment. In other words there is probably no period × treatment interaction. These suggest a slight period effect - pain levels decrease from period 1 to period 2 - but it appears to affect both drugs similarly. Irrespective of which order the drugs are given in, the pain score is lower when patients are on treatment A 2 than when on A 1. The two top figures below follow what happens to individual subjects through the trial. We first display the results graphically. The response variable was the level of pain experienced. All subjects in sequence group (2) received treatment A 2 followed by treatment A 1. All subjects in sequence group (1) received treatment A 1 followed later by treatment A 2. A sequence group is characterized by the order in which treatments are given. Subjects were randomly allocated to two sequence groups.
#Two sample unequal variance t test trial
This example uses data gathered in a trial of two drugs used for pain relief for arthritis patients. Instead one carries out a series of two-sample t tests. If there is a period effect (say both treatments are more effective in the second period), then a simple paired t-test would give a misleading result. However, this would only be valid if there were no period effect.
![two sample unequal variance t test two sample unequal variance t test](https://www.researchgate.net/profile/Steve-Mauget/publication/258662789/figure/fig5/AS:297394462838794@1447915773973/a-Spatiotemporal-Z-series-plot-for-the-20C3M-simulation-that-was-the-closest-match-to_Q320.jpg)
One might be tempted to ignore the cross-over aspect of the design and just analyse such data with a paired t-test for all values of A 1 - A 2. It is a within units design where one group of units receives treatment A 1 followed by treatment A 2, and the other group of units receives treatment A 2 followed by treatment A 1.
![two sample unequal variance t test two sample unequal variance t test](https://i.ytimg.com/vi/ikS7itcmWZM/maxresdefault.jpg)
We looked at the cross-over design in Unit 7.