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Chi Square, Significantly Different, One Variable, Chance Difference, Observed Frequency, Expected Frequency, Different Categories, Two Variables Independent, Contingency Table, Career Choice. These are the important points of Data Analysis in Psychology.
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2 Classifying yourself as studious or not. Yes No Total 58 42 100 Are they significantly different? 12 18 30 46 24 70 58 42 100 Yes No Total Read ahead Yes No Total
Studious
One variable Choice of PSYA01 Section L01 L02 L03 L30 Total 25 40 15 36 116 Is this more than a chance difference?
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O = the observed frequency in a category E = the expected frequency in that category We may expect different categories to have the same frequency if chance alone is at work. = −
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( 25 29 ) ( ) ( ) ( − ) 29 40 29 29 15 29 29 36 29 29 2 2 2 2 = .55 + 4.17 + 6.79 + 1. = 13. Is this significant? Go to the table. df = k - 1
Two Variables – Expected Frequencies Testing the null hypothesis that the variables are independent We know that the probability of the joint occurrence of two independent events is the product of their separate probabilities. 37 16 53 47 62 109 84 78 162 e.g., (84/162) X (53/162) = .1696 or 16.96% of the observations are expected in the upper left hand cell. But, N (162) times = 27.48 (expected frequency) 27.48 25. 56.52 52. Expected Frequencies Now we can use…..
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Expected Frequencies and Alternative Calculations
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R = the row total C = the column total E 11 53 162 = =27 48 (84) . E 12 53 78 162 = = 2552 ( )
. E 22 109 78 162 = =52 48 ( ) E 21. 109 162 = =56 52 (84) .
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(. ) − . (. ) . (. ) . (. ) . 37 27 48 27 48 16 2552 2552 47 56 52 56 52 62 52 48 52 48 2 2 2 2 = 3.30 + 3.55 + 1.60 + 1. = 10. Is the probability of this Chi-Square value (or larger) less than .05?
2 Will establish (at the .05 alpha level) whether two variables are related. A significant Chi-Square means we reject the null hypothesis (which assumes that the two variable are independent. We feel we have evidence That the two variable are related.
Gives the numerical value to the relation. The value can range from zero to one. Zero meaning no relation at all (independence) and one indicating a prefect relations. If you know one variable’s value you, you can perfectly predict the value of the other variable.
