which are markedly different to variable of interest Obviously different

# Which are markedly different to variable of interest

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which are markedly different to variable of interest | Obviously different population means | Erratic performance of treatments (high or low responses) produces skewed distributions Paired Samples For two samples, wherein each observation is in a one-to-one correspondence between samples Used to make more accurate comparisons by having both members of the pair as similar as possible in factors except for treatment TAMAYO, Dominic Raphael G. Page 3 of 10
Math 101 04 - Hypothesis Testing Strategies for Pairing | Self-Pairing Each subject made to act as his own control (same exposure to two different treatments) — before and after, pre- and post-testing | By Similarity Pairs subjects who are similar w.r.t. to variables which could affect results Assumptions for Paired Samples | Randomly sampled differences from the population | Normally distributed differences with μ d and σ d 2 Analysis of Variance Compares the average effects of several treatments Assumptions for ANOVA | Populations are independent | Populations can be approximated closely with normal distribution | Populations are homoscedastic | Dependent variable should be measured in at least interval scale H O : μ 1 = μ 2 . . . = μ k H A : At least two of the means are not equal Treatments 1 2 k Replicates x 11 x 21 x k1 x 12 x 22 x k2 x 1j x 2j x kj Total T 1 T 2 T k T Mean 1 2 k Post-Hoc Tests: Duncan’s Multiple Range Test If H O is rejected, post-hoc tests are performed to determine which of the means are different The range of any subset of p treatment must exceed a R p (least significant range) before considered different Used for testing relationships between categorical variables, always right-tailed One Sample Case χ 2 Test for Goodness of Fit Used to test whether observed frequencies agree with expected frequencies under a theoretical distribution Two Sample Cases χ 2 Test for Homogeneity Used to test whether samples are homogeneous or distributed similarly w.r.t. categories of the variable Number of sample subjects for each population ( row totals ) are fixed but may be unequal Categories Samples C 1 C 2 C j Total S 1 x 11 x 12 x 1j n 1. S 2 x 21 x 22 x 2j n 2. S i x i1 x i2 x ij n i. Total n .1 n .2 n .j N Categories are assumed to be exhaustive and exclusive , are presumed to be independent H O : Samples are homogeneous The proportion of samples in each category is the same for all strata H A : Samples are not homogeneous There are differences between strata in the proportion of samples in each category Identifies 2 or more populations of interest, draws independent samples from each population, then classifies the subjects according to the categories TAMAYO, Dominic Raphael G. Page 4 of 10
Math 101 04 - Hypothesis Testing Expected frequencies are computed assuming population is homogeneous with the variable of interest If true, different samples can be treated as one large samples w.r.t.

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

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