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Hi Everyone, Lloyd Rieber here again with our next example
of using Excel to compute some statistics. In this video, we compute the second of three
inferential statistics covered in this course, namely the t test for an independent-samples
design. This is a short video that builds on what we learned in the previous video tutorial
on computing the t test for a correlated-samples design.
So, if you have successfully completed that previous video tutorial, then you will find
this video tutorial to be a snap. But, if you have decided to take a look at this video
without having first completed the previous one, then be warned that what you will find
here will be very confusing. I recommend you stop, turn around, and go back. As I've said
all along, understanding statistics requires us to build upon our previous work, and this
video is a very good example of that. So, this video tutorial will be a short and sweet
ride for those who are ready, or a very frustrating experience for those who are not.
OK, let's begin with a very short recap of the t tests formulas and a quick explanation
of what we will be doing once we get to Excel.
Here again are the two formulas for the two t tests. And remember that in both cases a
t test is a difference between means divided by the standard error of a difference and
with a t test you always only have two means so last time we computed the t test for a
correlated samples design and this time we're going to be computing the t test for an independent
samples designed to in a few minutes we'll consider the conceptual difference between
the two designs and they really are quite dramatic but for now let's just consider the
mathematical differences between these two formulas and I need to point out a small correction
that I've made in this particular slide that probably some of you who are quite astute
have already noticed. In the formula for t test between independent samples I only have
Xs, I've taken out the Ys. Because really in an independent sample design you have two
separate groups and those are better represented by X bar one minus X bar two. The mathematics
remain the same but you'll see that I've updated many the formula on this slide in place of
the Y bar. So mathematically what I need to update is the denominator, the standard in
place of the Y bar. So mathematically what I need to update is the denominator, the standard
error of a difference for an independent samples design. So you see it there, and if we jump
down to the bottom you see it there, and that is equal to the square root of the standard
error the mean of the first group squared plus the standard error of the mean subXbar
one and subXbar two and we will be squaring both of those which is really represented
in the final part of the formula here where you recall we calculated all that based on
the two standard deviations and the two Ns where N1 is the total number of people in
the first group and N2 is the total number of people in the second group when we move
to Excel in a few minutes we'll start by opening the Excel spreadsheet that we ended with in
the previous video and of course there we computed the standard error of a difference
between correlated means or s subDbar but of course the first part of that formula mathematically
is going to be exactly equal to the formula for an independent samples design except that
we are not going to be subtracting that last part that contains the Pearson r. So by taking
out that last part of the formula, the formula magically transforms from the standard error
of a difference between correlated means into the standard error of a difference between
means so when we get to Excel all we'll need to do is delete that last part of the formula
although the mathematics requires just a little tweaking conceptually we are making a dramatic
change to the design of this particular experiment recall that with a correlated samples design
we are using only one group of people and we give that one group of people two observations
that we were calling a pretest and a posttest now with an independent samples we are going
to have two groups and it is going to be very important that all the people chosen have
a 50-50 chance of being in either group one or in group two. So the principle of random
assignment is critical here So this is called a posttest only control group design so we
have two groups we are then going to give only the experimental group the treatment
or activity or training program whatever it might be that is group one group two is the
control group and that the people in group two do not receive the treatment then we will
give both groups an observation which we'll call the posttest and then we will compute
the means of the posttest of those two groups which we will then compare. Recall that the
null hypothesis is that there is no difference between the two group means. After we compute
a t value we will need to look up the critical value, based on degrees of freedom, to see
if it is equal to or greater than the critical value and if it is then we will reject the
null hypothesis and if the mean of the experimental group, group one is greater than the mean
of the control group, group two, then we'll conclude that the treatment did have an impact
or we might say made a difference in the learning of the people in group one finally we will
need to make one more mathematical tweak in our Excel spreadsheet related to the degrees
of freedom recall that in the t test between correlated samples the degrees of freedom
is N-1 where n is the total number of people in group one, or the total number of pairs
of scores however for the t test between independent samples we have a degrees of freedom equal
to N1 plus N2 minus two, or the total number of people in group one plus the total number
of people in group two, minus 2. Well, this makes sense because we have two groups and
we have different people and each of the two groups. We have in essence two "N-1s" that
we are combining.
Okay I think we're ready to go to Excel to quickly make these changes. Let's go! Let's
start by opening the Excel file we created and saved last time. Recall that the file
title was our "last name-correlated_t_tests" and I use underscores for the spaces. So let's
now go and save this with a different name. So I choose "save as" I'm again saving it
to the inferential statistics folder that's located in our course folder and all we're
going to do is change the word correlated to independent making sure we are saving to
the right place. Click save. Once again a reminder that I'm using the Macintosh Excel
2011 version, so if you are not remember you'll have to translate my actions to whatever version
you are using. Let's start by dealing with that conceptual change where we go from having
one group of people being given a pretest and a posttest to two separate groups of people
each being given a posttest so let's start with some labeling I'm going to go up to where
it says pretest and I'm going to change that to group one press return I'll go and click
on posttest and I will type group 2 and I could change the label "scores" to posttest
but I really don't see a reason to do that, so I'm just going to leave that alone but
it is very important conceptually to re-label how the students are identified so in group
1, I have them identified as students a through j, but in group 2 they are a completely new
or different set of students. So I'm going to go to change the labels there starting
with K, L, M, N, and so on. All the way down to T. So do stop and reflect on how those
very small changes in labeling equate to a very dramatic or big change, conceptually,
in the overall experimental design. Okay let's finally make the mathematical changes that
are needed I'm going to go and click on the t denom value, the denominator for t and I
am going to go up and edit the formula taking out the minus and everything after it but
leaving one parenthesis So take a moment, make sure yours looks like mine, and then
press return so the value of the denominator is now 2.83 and notice that the t value has
now been updated to -2.29 okay just one more thing to do and that is to update the degrees
of freedom so click on degrees of freedom then click up in the formula to edit it, and
I think it's going to be easier just to delete everything except the equal sign and now we
need to enter N1, the value, so I click on the 10, N2, minus two. press return so the
degrees of freedom are now 18 well, according to my watch it took just over a minute to
make all those mathematical updates we have one more step now that we're equipped with
the t value of -2.29 and degrees of freedom of 18 we need to go to a table of the t distribution
to look up the critical value in order to see if the group two mean of 34.40 is significantly
different than the group one mean of 27.9 let's go and do it here's the table of the
t distribution and this is exactly the same table that we used in the previous video Let
me start by putting in our two values here we have the t value of -2.29 and we have a
degrees of freedom equal to 18 okay and a reminder that we are again using a two tailed
test with a alpha level, or significance level, of .05 so we now need to come down to degrees
of freedom of 18 and we go and look at the intersection and see a critical value of 2.101
so the absolute value of our t value of 2.29 is clearly equal to or greater than the critical
value of 2.101 therefore yes this is a statistically significant difference between the two means
of course we better check our work so let's compare the results of our Excel spreadsheet
with those calculated with SPSS here's the output from SPSS and of course there is a
lot of data here, but let's just check out some of the key elements so for example here
is our t value it shows -2.293 so yes that checks out degrees of freedom 18 that checks
out and finally we have a p value or probability value of .034 which is equal to or less than
the alpha or significance level of .05 so this also checks that this is a statistically
significant difference. Well, that concludes this video tutorial on how to calculate a
t test of an independent samples design I hope you are now feeling a great sense of
accomplishment and satisfaction in knowing how to calculate different types of t tests
and how to use them in the evaluation of instruction and training. Until next time!