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Stats Formula Sheet

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Submitted By vpat
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X^2 distribution test:

X^2 distribution: not symmetric, its skewed to the right as D.F gets larger the curve looks increasingly like a normal curve. Same for t-distribution D.F = n-1
Ho: σ2= σo2
Ha: σ 2 ≠ σ02 Ha: σ 2 > σ02 Ha: σ 2 < σ02 Χ2 = [ ( n - 1 ) * s2 ] / σ2

Confidence interval for σ2 : Confidence interval for σ2 :

D.F. = n-1 D.F. = n-1

Note: sometimes L = & u =
Note: s= standard deviation

X^2 Tests:

X^2 test for dependence using a contingency table: x^2 test can be used to test dependence (a possible relationship between two systems of classification ex. Eye color & intelligence)

Difference between X^2 and test for correlation: 1. It can be used for non-numeric classifications (for qualitative rather than quantitative data) 2. Normality assumptions are not relevant 3. We are not looking for a liner relationship or positive or negative linear correlation, just some sort of relationship 4. The data consists of observed frequencies of occurrence (of various events) and is entered into a table called a contingency table. Then the expected frequencies of occurrence are computed and entered into the table. The test is based upon a comparison of these tow kinds of frequencies.

X^2 test for dependence using a contingency table:
Ho: there is no relationship between _______ and ________. E =
Ha: there is a relationship between ________ and ________.They are independent

O=observed frequency-which are the given data
E= expected frequency – must be calculated on the assumption that Ho is true
D.F.: (# of Columns - 1 )(# of rows – 1)
Note: always right tailed, compare it to X^2 of critical value

Note: all E ≥ 5, if its not you have to collapse the table until it is. Then recalculate D.F and

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