Question

24. A study compared union activity of employees in 10 plants during two different decades. The researchers reported “a significant increase in union activity, t ( 9 ) = 3.28 , p < .01. t ( 9 ) = 3.28 , p < .01. ” Explain this result to a person who has never had a course in statistics. Be sure to use sketches of the distributions in your answer.

Answer 1

TO A LEYMANN: Let say you want to check whether the flow of employees have been increasing or decreasing in 10 firms in your town area over last 2 decades. How are you going to check? We fortunately have a science of data and probability called statistics which furnishes us with some small and large sample test for processing the similar problems as above.Here, you can see that your study wants comparison of 2 different decades and you have a sample of size 10 only(which is small). So the study is going to take one of the small sample tests.

If your study is going to make the following assumptions-

1) samples are independent to each other.

2) The two different decades are independent of each other.

3) The variances for the two different decades are equal and unknown.

4) The population from which you have sampled your 10 sample (i.e parent population) is Normal (bell shaped)

Then the 2 sample t test is best suited for your study.

you can make the following hypothesis.( according to your objective of study)

now, what is t(9)=3.28? and p?

9=degree of freedom of t dist.(9 values in t statistics are free to vary)

3.28=tabulated value of t dist. at 9 degree of freedom

0.01= level of significance(that much error we can tolerate) i.e we want 99% confidence in our results.(called alpha)

p= it helps us determine the significance of our result. Used mostly as a rejection/acceptance criteria of H0 when we do the calculations in software like excel etc.