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--- chi-square_test [2024/12/08 23:15] – hkimscil
+++ chi-square_test [2025/11/30 23:11] (current) – hkimscil
@@ Line 13: / Line 13: @@
     * like to using direct mathematical concepts. There are a lot of repetition
     * here (Dr. Rice once talked about this).
-  * Pictures are taken by your TA at the RUSURE
+  * Pictures are taken by your TA at the RUSURE campaign
-    * campaign directed under Dr. Letterman and Dr. Stewart during the year, 2000.
+    * which was directed by Dr. Letterman and Dr. Stewart during the year, 2000.
-    * The study is ongoing at the SCILS department.
+    * It is an ongoing study at the SCILS department.
 Let's start with what we know first.
@@ Line 165: / Line 165: @@
 |  yes  |  5  |  32  |  13  |  50  |    |
 |  Expected value  |  (20)  |  (21)  |  (9)  |  50  |    |
-|  (O-T)2 / T  |  (-15)<sup>2</sup>/20=11.25  |  (11)<sup>2</sup>/20=5.76  |  (4)<sup>2</sup>/20=1.78  |    |  18.79  |
+|  (O-T)2 / T  |  (-15)<sup>2</sup>/20=11.25  |  (11)<sup>2</sup>/21=5.76  |  (4)<sup>2</sup>/9=1.78  |    |  18.79  |
 |  no  |  35  |  10  |  5  |  50  |    |
 |    |  (20)  |  (21)  |  (9)  |  50  |    |
-|    |  (15)<sup>2</sup>/20=11.25  |  (-11)<sup>2</sup>/20=5.76  |  (-4)<sup>2</sup>/20=1.78  |    |  18.79  |
+|    |  (15)<sup>2</sup>/20=11.25  |  (-11)<sup>2</sup>/21=5.76  |  (-4)<sup>2</sup>/9=1.78  |    |  18.79  |
 |  Total  |  40  |  42  |  18  |  100  |  37.58  |
 Chi-square value = 37.58. \\
@@ Line 182: / Line 182: @@
 .210 at 0.01 probability
 <code>
-> qchisq(0.95, 2)
+> qchisq(0.95, 2) # in R, we don't use 0.975 since we look up (the distribution table has) square values
 [1] 5.991465
-> qchisq(0.99, 2)
+> qchisq(0.99, 2) #
 [1] 9.21034
 >
@@ Line 258: / Line 258: @@
 .991 (0.05 probability)
 .210 (0.01 probability)
+OR
+<code>
+> pchisq(2.73, df=2)
+[1] 0.7446193
+</code>
 Now the rest of what you need to do is to compare the numbers (chi-square value and the critical values).