Probably the most popular inferential statistic - especially for beginning
statistics students - is the t-test. The t-test is wonderful because it allows us
to compare two samples and it opens up a world of possibility for our research.
Instead of comparing a sample to a population, researchers often want to
compare two or more sets of data, such as comparing two different methods of
teaching, or how to competing therapy techniques effect depression, or if
changes in scores occur after a treatment. There are two ways to
structure these tests: as separate samples ,or by using the same sample.
Let's begin by reviewing single sample techniques, and then we can talk about
two sample tests. Single sample techniques compare a sample mean to a
population mean. The Z test and the t-test statistics that we have used so
far are called "single sample techniques". They are calculated based on one sample
drawn from a population. Any time you have a sample of scores, you can calculate
their mean and standard deviation. The sample is assumed to have been drawn
from a population of scores which also has a mean and standard deviation. If the
population standard deviation is known (which is really rare) we would use a
z-test, but if the population standard deviation is unknown (which is very
common), then we use a t-test. But what if we want to compare an experimental group
to a control group? In other words, compare two samples? For that we need
some new kinds of T tests; ones that work with two samples. Two sample techniques
compare two measurements of samples. Very commonly, we want to compare two samples,
such as comparing a control group to an experimental group. The mean of the
control group is assumed to be the same as the experimental group, unless the
experimental intervention made a difference. Then the means would be
different. These two groups are separate samples. Separate sample t-tests compare
scores for two groups that are measured at about the same time. For instance,
we sample a group of individuals on their attitudes about a political
candidate, and then we compare the responses from men to those from women.
Or we group them into people who do have a college education and those who did
not finish high school. The groups are independent of one another. For instance,
the political preferences of uneducated voters do not influence the preferences
of the college educated voters. And because we are comparing scores between
two groups, this is called an "independent measures test" or a "between subjects
design". Specifically, the type of test we use is an "independent samples t-test".
On the other hand, sometimes instead of comparing two different groups, we want
to see what happens to a single group of people before and after an intervention.
We want to compare scores for the same group measured across time. For example,
we have a sample of people who have signed up for a health improvement
course. They want to improve their health and lose weight. So we begin with their
weight before starting the program, then we get them enrolled in the program, wait
for them to complete it, and then we weigh the same group of people after
they complete the program. We compare their beginning and ending weights to
see if the weight score changed. A slightly different - but related - research
design would be if we were measuring the effectiveness of giving junior high
school students a laptop computer to use in the classroom. We would
probably not get a lot of buy-in if we proposed giving free laptops to a
randomly selected half of the students in the classroom, and then seeing how
they performed compared to students sitting next to them who were scribbling
with a pen and paper. So instead, we measure students at the beginning of the
school year, then we provide laptops to everybody, and then we measure them again
at the end of the school year. And this is called a "repeated-measures test" or a
"within-subjects design". When we are comparing within the same group,
pre-treatment versus post-treatment, or when we have deliberately matched
individuals in one condition (say, heart patients) with individuals in another
group (say, hip replacement) patients, we use a paired samples t-test. We are going
to learn how to set up and conduct both the independent samples t-test, and a
paired samples t-test in this set of videos.