Yes! This is a homework question, but I don't want the numerical answer, I want the understanding of how to work the problem so that I can explain it to someone.
Here is the question:
A researcher conducts a T test for dependent means in which it is predicted that there will be a decrease in unemployment from before to after a particular job-skills training program. The cutoff "t" needed is -1.8333. The standard deviation of the distribution of means of change scores is 2.0 and the mean change score for the sample studied is an increase of 5.2.
What is the t score?
here is where I am leaning on this problem (so far).
First, let's look at the definition for T.
T = [
(Average of Sample) - (Presumed Average of larger Population)] / [((Standard Deviation of Sample) / (Square Root of the Sample Size))]
Let's break up the terms so that we can pick this apart.
I will start with the devisor in the equation.
My best guess is that ((Standard Deviation of Sample) / (Square Root of the Sample Size)) is the same thing as The standard deviation of the distribution of means of change scores = 2.0.
I am having a very hard time getting a definition of change scores, but when I do I may modify my thoughts here.
My best guess for the numerator above ((Average of Sample) - (Presumed Average of larger Population)) the divisor is the mean change score for the sample studied is an increase = 5.2.
If we plug these two terms into the equation we get:
T = 5.2/2.0 = 2.60
Now here is the disclaimer! My understanding of statistics is very shaky at best, so I want to ask you some questions in hope that you might know where to look to answer them.
First, the denominator. What does the ((Standard Deviation of Sample) / (Square Root of the Sample Size)) mean? My tendency was to assign that term to the standard deviation of the means of the change scores. I can't substantiate that yet, so I will keep looking.
Second, the numerator. The quiz question stated the the mean change score for the sample studied is an increase of 5.2. What did that increase from? That implies a "difference" in my mind, so I looked at the (Average of Sample) - (Presumed Average of larger Population) as being a difference of means and if change scores is defined as a difference of means, it seemed like a good fit. Again, I am guessing by 80-90% here because I don't have a good definition for change scores and the increase cited in the quiz.
What disturbs me is the cutoff T needed is cited as –1.8333. I don't see how this relates to the problem and it implies something opposite of where I am going. So what is the relationship between the cutoff T and the T score?
Can anyone help plug up the holes in my understanding? I know, they are big holes, but I have to start somewhere.
Thanks in advance!
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