the variable χ 2 Test for Used to test whether there is

# The variable χ 2 test for used to test whether there

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the variable χ 2 Test for Independence/Association Used to test whether there is an association between two classification schemes or variables Row Categories Column Categories B 1 B 2 B j Total A 1 x 11 x 12 x 1j n 1. A 2 x 21 x 22 x 2j n 2. A i x i1 x i2 x ij n i. Total n .1 n .2 n .j N H O : Row and column classifications are independent There is no association between the two classifications H A : Row and column classifications are dependent The two variables are associated Draws a single sample of subjects from a population and classifies subjects on the basis of 2 criteria of interest Expected cell frequencies are computed assuming independence of 2 criteria Misapplications of the χ 2 Tests | Sample Size Violation E ij > 0 for all cells, not more than 20% of the E ij < 5 | Proportions or percentages cannot be used — only counts or frequencies | Violation of the assumption of independence Used to determine the strength or degree of linear relationship between two or more variables Pearson Correlation Coefficient r Measures extent of linear association, estimated by r ( −1 < r < 1) If r > 0 Direct relationship r < 0 Inverse relationship r ~ 0 Weak correlation r ~ −1 or 1 Strong correlation Used to determine functional relationship between two or more variables Simple regression analysis considers only one independent variable Objectives of Regression | Explain variation of the DV in terms of its functional relationship with IVs | Write an equation of the functional relationship of the DV and IV | Estimate the value of a variable given values of other variables Characteristics of Regression | Explain variation of the DV in terms of its functional relationship with IVs Characteristics of the Regression Line b > 0 Y increases as X increases Y is directly related to X b < 0 Y decreases as X increases Y is inversely related to X b = 0 Y is constant Y is unrelated to X TAMAYO, Dominic Raphael G. Page 5 of 10
Math 101 04 - Hypothesis Testing Assumptions of Regression | DV Y is continuous and measured in interval/ratio | For a given fixed value of the IV X: Y = α + β X + ε where ε is random error with ND ~ (μ, σ 2 ) Estimated to be y = a + bx + e Subject to sampling error and can be tested for significance of regression statistics | Successive sample observations are independent Coefficient of Determination r 2 Proportion of the variance in the DV that is predictable from the IV (0 < r 2 < 1) Residual Analysis A systematic pattern in a residual plot indicates nonlinear regression relation, while absent patterns in a plot indicate linear regression should be used If the variance of the error term is constant, residual plot should show residuals falling horizontally near the center line Normality assumption of regression model can be checked by frequency histograms of residuals or χ 2 goodness of fit TAMAYO, Dominic Raphael G. Page 6 of 10
Math 101 04 - Hypothesis Testing HYPOTHESIS TESTING (BY LEVEL OF MEASUREMENT) No. of Samples (Design of Study) Level of Measurement Nominal Ordinal Interval/Ratio One Sample Case Binomial Test One Sample χ 2 Kolmogorov-Smirnov Test for One Sample One Sample Runs Test Z-Test T-Test Two Sample Cases Related Marginal χ 2

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• Fall '19
• Null hypothesis, Statistical hypothesis testing, Tamayo, Dominic Raphael G

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