Unit 6 Flashcards
What is a matched pairs t-test?
A type of experiment where we are looking at the differences between pairs of dependent observations. We are concerned about the actual amount of the differences between, observations, not the original values themselves
What are dependent observations? What are some examples?
Observations where we have reason to believe that the differences in values between the particular pairs we have matched are meaningful (the observations are related to/dependent on each other)
- difference in performance of the same person before and after training
- reaction speed with the same person’s left and right hand
- tread on the front and back tire of the same bike
What is the null hypothesis for a test of mean difference?
(in a world where there are no significance differences) the true mean of all the differences = 0
What is the alternate hypothesis in a difference in means test?
What we might want to test if there is a real difference in between the groups. (>, <, !=)
How can we check if the real world matches our hypothesis?
Since we are observing a sample mean, with a sufficiently large number of observations we can know its sampling distribution is approximately normal by CLT. So, we can take a sample of differences and see whether our observed mean of the differences falls in the range of expected sampling variation when the true mean of all the differences = 0 is true.
What should we do if we have small sample sizes?
We may still be able to assume normality. We should test our differences first using a normal quantile plot before using the test in this case (only a concern in real life)
What are independent samples?
It does not make any sense to pair them up arbitrarily and look at individual differences. We might instead ask whether there is a difference in their overall mean
What does the sampling distribution of the difference of means look like?
the histogram of the difference in shuffled groups is normally distributed with mean 0
Why can’t we find an exact number of degrees of freedom for difference in mean for unequal variances?
Because we have a linear combination of two parameters to estimate. The equation will almost always give a decimal number, so we take the floor of the value or round down to the next lowest number found on our table
How do we know if the variances of two populations are unequal?
if the larger standard deviation divided by the smaller standard deviation is greater than two, then we will assume the variances are not equal
What are confounding factors?
Factors not included in our study that could be driving our data.
What can shuffling groups tell us about the relationship between their means?
If the means become more different after shuffling, this is a good indication that the means are similar. If they become more similar after shuffling, this is a good indication that the means are different
What is a permutation test?
We permute the groupings to test whether our model will differ under random shuffling from our hypothesized model. We can do it without making any assumptions on the parameters from our distributions
What is a parametric test?
A test where we have to make assumptions on the parameters from our distributions
What is an observational study? Why is it not always the best option?
A study where events are observed as they happen without any intervention from the researchers. It is not always the best option because intervention can control confounding factors better than observation
