In the last video we calculated a one variable chi square on learning styles
we wondered if there was a dominant learning style, but now you're interested
in whether there is a difference in how men and women learn now you have two
variables so you need to calculate a two variable chi square although the
underpinnings of the same there is one critical difference in the setup which is how you
calculate the expected values. For this video we will calculate a two variable chi square paying particular
attention to how to calculate the expected values, for this example we'll look at the relationship between two
variables learning styles, and sex let's do the easy part for calculating degrees
of freedom in a one variable chi square degrees of freedom was the number of
categories or K minus one, if we weren't looking at males and females there would only be one row
across three categories so degrees of freedom for a one variable to Chi Square
would be 3-1 or two but since we now have two rows of data we have a different formula.
Now we take the number of rows we have two so 2-1 is one then we turned to the number of columns which
is three as we have columns for visual, auditory, and kinesthetic and we subtract one ending up with two,
then we multiply these two numbers together two times one equals two or two degrees of freedom, the
next part is to calculate the expected values the underlying concept is the
same as the one variable chi square but the calculation is a bit trickier here
you take the rows sum and multiply it by the column sum and then divide that product by the grand total.
Now we have all the data to calculate our expected values let's start with the first cell males who are visual
learners we take the row sum for the males one hundred and multiply it by the column sum
for visual which is 72, 100 times 72 is 7210 then we divide that by the grand total
of 200 we come up with 36 for expected, go to the next cell the male
auditory learners cell row sum is 100 times the column sum up 46 equals 4600 divide that by the grand total and
you get 23 you would do exactly the same for each cell for the females only this time you're using the row
total for the females. Stop some of you have already figured out that in this case the numbers are the same
for males and for females caution however this only works if you have exactly the same
number for each row total in this case there are 100 males and 100 females if
for example you had 72 males and a 128 females you're likely come out with some very different numbers so
unfortunately you'll have to do this calculation for each cell in the table.
You're ready to move on now you have your observed data and you've now calculated your expected data now
you just have to do the same thing you did for the 1 variable chi square following the same formula in
each cell starting with the male visual learners observed 30-3 expected which you calculated earlier at 36 is
-6, square that and you'll get 36 take that number 36, and divided by the
expected 36 and you'll get 1 do the same for the next cell male auditory
learners observed 22 minus the expected which you calculated at 23 is -1 square that and you get 1 take that
number 1 and divided by the expected 23 and you'll get 0.04. And for male kinesthetic learners observed at 48
minus the expected 41 is 7, 7 square is 49 and 49 divided by the 41 the expected is 1.2 do exactly the same
calculations for each of the cells for females again don't get excited because the resulting numbers are mirror
images of each other the last step to calculate the chi square is to add all those numbers together which will equal 4.48.
From here on the steps are the same as one variable chi square we already calculated the degrees of freedom
using the formula of the number of rows minus 1, times the number of columns minus 1, giving us 2
degrees of freedom assume that we have established our alpha at .05 now go to the
critical value table and find where two degrees of freedom intersect with .05 alpha level and it
is 5.991 is our chi square of 4.48 higher than the critical value if yes then we reject the null, but 4.48 it is less than
the critical value of 5.991 meaning we must accept the null and conclude that our data do not support that there
are differences between males and females on the variable of learning styles.
Processing time How do you calculate the expected values for a cell in a two variable chi square?
remember for each cell you multiply the row sum by the column sum and divide that product by the grand total.
How are degrees of freedom calculated for a two variable chi square? the formula is to multiply the
number of rows minus one by the number of columns minus one and What would you do if your calculated chi
square is lower than the critical value chi square? you should be accepting the null hypothesis and rejecting the
alternative chi square hypothesis concluding that there are no significant differences between what you
observed and what you would have expected to see if the data were evenly distributed.
Hopefully you can calculate chi square when given data like we have practice
with here if you understand one variable chi square just remember how to
calculate the expected values for the two variable chi square and you should be all set.