Differences

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--- chi-square_test [2016/05/16 07:49] – hkimscil
+++ chi-square_test [2016/05/16 08:21] (current) – hkimscil
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 {{keywords>"Chi-square test" statistics "research methods"}}
 ====== Short Explanation ======
+To be filled...
 ====== Chi-square test, explanation ======
 This is rather a redudent, long description of chi-square test.
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 Let's start with what we know first.
-Two variables:: Let's say you are interested in the relationships between the types of religions and opinions about abortion.
+Two variables: Let's say you are interested in the relationships between the types of religions and opinions about abortion.
 You have a hunch that people who have a different religion will have a different opinion about abortion. This actually reveals that you think having a particular religion will affect what to think about abortion. Therefore, particular religions will be the __IndependentVariable__ (IV). And the opinions abut abortion will be the __DependentVariable__ (DV).
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 <WRAP clear />
 {{ 11-419460-rusure.jpg?202|Dr Mokros at RuSure Campaign SCILS Rutgers 2000}}
-Chi-square test:: This is how the Chi-square method was involved in ... Anyway, now let's think about the chi-square test. Previously, you wanted to know if there are differences in the abortion opinions among religious groups; and you got the frequency table. Now think about what the table would look like if there is no differences in the abortion opinion among religious groups?
+Chi-square test: This is how the Chi-square method was involved in ... Anyway, now let's think about the chi-square test. Previously, you wanted to know if there are differences in the abortion opinions among religious groups; and you got the frequency table. Now think about what the table would look like if there is no differences in the abortion opinion among religious groups?
 We already know from the first contingency, frequency, or bivariate analysis table that there were 50 people who were for legal abortion and 50 people who were against legal abortion -- the ratio of each category was (YES --&gt; 50 out of 100; NO --&gt; 50 out of 100). And there were 40 Catholics; 42 Protestant; and 18 others.
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 I do not know exactly why the degree of freedom is important in a conceptual way -- so, having a difficulty explaining it. But, the idea behind it is that if you know totals of column and row, and the values of two cells (as a minimum requirement; called degree of freedom), you would be able to obtain the values of the other four cells without consulting the actual observed values.
-{{07-419434-a-tshirt-camp-scils-rutgers.jpg?202 |RUSURE campaign SCILS Rutgers 2000}} Anyway, you just obtained the chi-square value (37.58) and the degrees of freedom (2). You can look up the text book (for chi-square test): (1) find your degrees of freedom (2), that is, the second row of the table; (2) decide the probability you want to employ (usually .05 or .01); (3) write down the numbers; and (4) compare them to your chi-square value.
+{{07-419434-a-tshirt-camp-scils-rutgers.jpg?202 |RUSURE campaign SCILS Rutgers 2000}} Anyway, you just obtained the chi-square value (37.58) and the degrees of freedom (2). You can look up the text book (for chi-square test): (1) find your degrees of freedom (2), that is, the second row of the table; (2) decide the probability you want to employ (usually .05 or .01); (3) write down the numbers; and (4) compare them to your chi-square value. (see [[:chi-square distribution table]])
 The numbers you obtain from the book are 5.991 for the 0.05 probability and 9.210 for the 0.01 probability. They are called critical values. So the critical values are:
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 {{ princeton-nassau-inn-1.jpg?202|Naussau Inn near Princeton University}}
-Chi-square test, example:: Let's have an exercise for the chi-square thing. I hope you remember the below part which is from the last essay I wrote. Let's go through it, first. Let's look at another table. I will show the percentage in the table -- the ratio between the opinions in a religious group.
+Chi-square test, example: Let's have an exercise for the chi-square thing. I hope you remember the below part which is from the last essay I wrote. Let's go through it, first. Let's look at another table. I will show the percentage in the table -- the ratio between the opinions in a religious group.
 |  Abortion opinion and Religeon   |||||
 |    | Catholic  | Protestant  | other  | Total  |
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 | yes  | 18  | 25  | 12  | 55  |    |
 | Expected Value  | (22)  | (22)  | (11)  | (55)  |    |
-| (O-T)2 / T  | (-4)2/22=0.73  | (3)2/22=0.41  | (1)2/11=0.09  |    | 1.23  |
+| (O-T)<sup>2</sup> / T  | (-4)<sup>2</sup>/22=0.73  | (3)<sup>2</sup>/22=0.41  | (1)<sup>2</sup>/11=0.09  |    | 1.23  |
 | no  | 22  | 15  | 8  | 45  |    |
 | Expected Value  | (18)  | (18)  | (9)  | (45)  |    |
-| (O-T)2 / T  | (4)2/18=0.89  | (-3)2/18=0.5  | (-1)2/9=0.11  |    | 1.5  |
+| (O-T)<sup>2</sup> / T  | (4)<sup>2</sup>/18=0.89  | (-3)<sup>2</sup>/18=0.5  | (-1)<sup>2</sup>/9=0.11  |    | 1.5  |
 | Total  | 40  | 40  | 20  | 100  | 2.73  |
-Chi-square value = The sum of the entire 6 yellow cells = 2.73.
+**Chi-square value = The sum of the entire 6 yellow cells = 2.73.**  \\
-Degrees of Freedom (df) = (the # of columns-1) x (the # of rows-1)= (3-1) x (2-1) = 2 x 1 = 2.
+**Degrees of Freedom (df) = (the # of columns-1) x (the # of rows-1)= (3-1) x (2-1) = 2 x 1 = 2.** \\
+\\
 Look up the values in your textbook -- which is called "critical values."
+\\
 They are:
 .991 (0.05 probability)
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 In the first place, you assumed that there would be no differences in the abortion issue among the religious groups to get the expected values. And you compared the expected values to the observed values. In other words, you tested your survey result (the observed values) against the idea of "no difference." Your plans were: If the some of the comparison (chi-square) is big enough, you'd say that the idea of "no difference" was not likely true. If the some of the comparison (chi-square) is small enough, you'd say that there seems to be no reason to reject the idea of "no difference." In other words, in the first place, you assumed that there would be no difference, and you tested your survey result against this idea. What you conclude from this testing was you failed to disapprove the idea -- the idea of no differences.
-{{raritan-river-01.jpg?132|Princeton Park river}} __Why null?__ -- Someone in the class cleverly asked why we should use null hypothesis in the first place. As you see the above, it would be harder to test whether the researcher is right. Most statistic methods (chi-square, t-test, ANOVA, and others) test against the idea of 0 (zero -- no difference).
+{{raritan-river-01.jpg?132 |Princeton Park river}} __Why null?__ -- Someone in the class cleverly asked why we should use null hypothesis in the first place. As you see the above, it would be harder to test whether the researcher is right. Most statistic methods (chi-square, t-test, ANOVA, and others) test against the idea of 0 (zero -- no difference). Therefore, it would not have been safe, had you ever said, "Sure 45% and 62.5% are different."
-Therefore, it would not have been safe, had you ever said, "Sure 45% and 62.5% are different."
 __Another note:__ You might have a question... Hey, wait a minute... If I pick up some other numbers from the chi-square distribution table, the result would be totally different!
+<WRAP clear />
-*** For your information, the table looks as follows. And the chi-square value you got from your data was 2.73.
+For your information, the table looks as follows. And the chi-square value you got from your data was 2.73 (see [[:Chi-square distribution table]]).
 | df  | .30  | .20  | .10  | .05  | .02  | .01  | .001  |
 | 1  | 1.074  | 1.642  | 2.706  | 3.841  | 5.412  | 6.635  | 10.827  |
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 Yes, choosing the probability means that you decide the certainty of your decision. The chances of your being wrong in your statement -- there is differences in the abortion issue among the religious groups -- was 3 out 10. And unlike the probability of 0.05 or 0.01, this risk is too big to take. In other words, it is a bit meaningless. This is why professor White said that social scientists usually take 0.05 as a criterion of his or her statistical tests.