A chi-squared test, also referred to as chi-square test or 
test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Also considered a chi-squared test is a test in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chi-squared distribution as closely as desired by making the sample size large enough.
test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Also considered a chi-squared test is a test in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chi-squared distribution as closely as desired by making the sample size large enough.
Chitest Interpretation of result:
Let’s say
you want to know if there is a difference in the proportion of men and women
who are left handed and let’s say in your sample 10% of men and 5% of women
were left-handed.
How it’s Calculated (Without the gory details)
1. You
collect the data. For example, you ask
120 men and 140 women which hand they use and get this:
ACTUAL
DATA
|
Left-handed
|
Right-handed
|
Men
|
12
|
108
|
Women
|
7
|
133
|
2. Calculate what numbers of left and
right-handers we would expect IF men and women were the same.
In this case, IF men and women were
equally left and right handed, we would have expected these numbers in
our sample of 260 people (Ask if you want to know how this is done):
EXPECTED
IF NO DIFFERENCE
|
Left-handed
|
Right-handed
|
Men
|
8.77
|
111.23
|
Women
|
10.23
|
129.77
|
3. The computer calculates a
Chi-square (pronounced Ki-square) value.
The Chi-square value is a single number that adds up all the differences
between our actual data and the data expected if there is no difference. If the actual data and expected data (if no
difference) are identical, the Chi-square value is 0. A bigger difference will give a bigger
Chi-square value.
4. Look up the Chi-square value
in a table to see if it is big enough to indicate a significant difference
in handedness of males and females.
Interpretation
Greater
differences between expected and actual data produce a larger Chi-square
value. The larger the Chi-square value,
the greater the probability that there really is a significant difference.
With a 2
by 2 table like this (If you have more than 4 cells of data in your table, see
your instructor):
If
the Chi-square value is greater than or equal to the critical value
There is a
significant difference between the groups we are studying. That is, the difference between actual data
and the expected data (that assumes the groups aren’t different) is probably
too great to be attributed to chance. So
we conclude that our sample supports the hypothesis of a difference.
If
the Chi-square value is less than the critical value
There is no
significant difference. The amount
of difference between expected and actual data is likely just due to
chance. Thus, we conclude that our sample
does not support the hypothesis of a difference.
In this
example, the critical value is 3.8. The
Chi-square value was 2.383, which is less than 3.8. Thus, there is no significant difference in
handedness between men and women in our sample.
We conclude that based on this sample, men and women in general
seem equally likely to be left or right handed.
Sources:
www.wikipedia.com
www.radford.edu/~biol-web/stats/chi-sq_explanation.doc
