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Hypothesis Testing – Two Sample

* H0 : µ1 = µ2 H1 : µ1 ≠ µ2

* Case 1 -- If you know population variances, use this and Normal table

* Case 2 -- If you know only sample variances, and samples are large, use this and Normal table

* Case 3 -- If you know only sample variances, and samples are small, and unknown population variances can be assumed identical, use this and t-table, with n1 + n2 - 2 df. (sp is called “pooled estimate of σ”)

* We use standard error of difference to compute (actual) t

Hypothesis Testing –
Means Of Dependent (Paired) Samples

tActual

* pooled estimate of population proportion

Regression and Correlation

Simple Linear Regression
(Only 1 independent variable, and linear relationship)

Regression Coefficients

Using Method Of Least Squares, we get:

Standard Error Of Estimate

Correlation:

* Variation of y around the regression line

* Variation of y around its own mean

* Coefficient of Determination

Direct Computation of r:

Chi-Square

* Make working table as follows: * List observed frequency cells, fo , in 1st column. * Compute expected frequency, fe , for each cell, and write in 2nd column. * fe = RT*CT/n where RT = row total, CT = column total, n = total no of observations in all cells of data table. * Compute (fo – fe ) for each row of working table in column 3 * Compute (fo – fe )2 for each row of working table in column 4 * Compute (fo – fe )2 / fe for each row of working table in column 5 * At the bottom of column 5, compute the sum

* It will have df = (r – 1)(c – 1) --- where r = no of rows and c = no of columns of data table

ANOVA

What A Typical ANOVA Data-set Looks Like

Working Table For...

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