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Chi-Square Test of Independence c2
PASW (SPSS) output for Regression Tests of Significance Normal distribution
PASW (SPSS) Instructions Exam questions More questions
Chi-Square Test of Independence c2
This question I feel is one of the easiest questions on an examination paper. It follows a set pattern each time.
Words to look for Related, Independence, Relationship, Depends Expected
Layout to look for Table with one variable across the top and one down the side. These will be the variables that replace the dots in the hypotheses.
- Write the hypotheses this way
Null Hypothesis: ............... and ............... are independent.
Alternative Hypothesis ............... and ............... are not independent.
Notice the first line has one word “are” and the second line has two words”are not”
The dots are replaced by whatever variables are in the table.
- Finding the expected values by using subtraction.
This will save some time but you can use the formula for all expected values.
What do we mean by this? The row and column totals of observed and expected values are equal. There is a formula to calculate the expected value if the two variables are indeed independent.
The formula is:
In the following tables, I have starred the values that you would calculate using the formula and the blank ones you would get by substraction.
Ok, let’s put some numbers in so we can see how it works.
The Blue numbers are the row and column totals.
The Red numbers are the expected values obtained by Formula.
The Green numbers are the expected values obtained by substraction.
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26
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15
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9
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50
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21
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10
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18
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65
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125
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So 26 is obtained by 65 x 50
125
So 18 is obtained by 65- (26 +21)
So 9 is obtained by 50 - (26 +15)
- Evaluating the chi-square statistic, c 2
c 2= (Observed Value - Expected Value) 2 = (O - E)2
Expected Value E
There is no short cut this time apart from a calculator but I still find it handy to write some values down. I tend to find it handy to write the values as the table layout. This saves time when you are checking as you can tell whether you got the same answer last time. I have shown the the actual values below, but in the examination perhaps just the answers would do as long as you put the formula somewhere.
The observed values are in Red.
The expected values are in Blue
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26 20
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15 17
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9 13
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50
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21 23
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10 13
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18
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65
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125
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c 2= (O - E) 2 = (26 - 20) 2 + (15 - 17 )2 + (9 - 13) 2
E 20 17 13
- P-value, Decision and Conclusion. Follow the usual procedure
Some silly ways of remembering when to accept and reject the Null Hypothesis. When the level of significance is 0.05 then the following applies:
If the p-value Bigger than 0.05 then Accept the Null Hypothesis
If the p-value Smaller than 0.05 then Reject the Null Hypothesis
B A British Airways or
B A and S R, these are next to each other in the alphabet.
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