17_chi_sq_tests

17_chi_sq_tests - Summary sheet from last time: Confidence...

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Summary sheet from last time: Confidence intervals Confidence intervals take on the usual form: parameter = statistic ± t crit SE(statistic) parameter SE a s e · sqrt(1/N + m x 2 /ss xx ) b s e /sqrt(ss xx ) y’ (mean) s e · sqrt(1/N + (x o –m x ) 2 /ss xx ) y new s e · sqrt(1/N + (x new x ) 2 /ss xx + 1) (individual) • Where t crit is with N-2 degrees of freedom, and s e = sqrt( Σ (y i –y i ’) 2 /(N-2)) = sqrt((ss yy – b·ss xy )/(n-2)) Summary sheet from last time: Hypothesis testing )/SE, and crit . 0 : ρ =0: –t obt = 2 ) crit 0 : ρ = ρ o : Of course, any of the confidence intervals on the previous slide can be turned into hypothesis tests by computing t obt = (observed – expected comparing with t Testing H r·sqrt(N-2)/sqrt(1-r – Compare with t for N-2 degrees of freedom. Testing H Need to use a different test statistic for this. Chi-square tests and non- parametric statistics 9.07 4/13/2004 Statistics Descriptive – Graphs – Frequency distributions – Mean, median, & mode – Range, variance, & standard deviation Inferential – Confidence intervals – Hypothesis testing 1
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Two categories of inferential statistics Parametric statistics distributed, or at least their means are approximately normal. Parametric – What we’ve done so far Nonparametric – What we’ll talk about in this lecture Limited to quantitative sorts of dependent variables (as opposed to, e.g., categorical or ordinal variables) Require dependent variable “scores” are normally There exist some parametric statistical procedures that assume some other, non-normal distribution, but mostly a normal distribution is assumed. The general point: parametric statistics operate with some assumed form for the distribution of the data. Sometimes require that population variances are equal Parametric statistics than 0 true. Nonparametric statistics non-normal distribution or unequal population variances nd Best to design a study that allows you to use parametric procedures when possible, because parametric statistics are more powerful nonparametric. Parametric procedures are robust – they will tolerate some violation of their assumptions. But if the data severely violate these assumptions, this may lead to an increase in a Type I error, i.e. you are more likely to reject H when it is in fact Use them when: The dependent variable is quantitative, but has a very The dependent variable is categorical •M a l e o r f em a l e Democrat, Republican, or independent Or the dependent variable is ordinal Child A is most aggressive, child B is 2 most aggressive 2
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Nonparametric statistics –H 0 , H a , sampling distributions, Type I & Type II errors, Chi-square goodness-of-fit test χ 2 The design and logic of nonparametric statistics are very similar to those for parametric statistics: Would we expect to see these results by chance, if our model of the population is correct (one-sample tests)?
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This note was uploaded on 11/11/2011 for the course BIO 9.07 taught by Professor Ruthrosenholtz during the Spring '04 term at MIT.

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17_chi_sq_tests - Summary sheet from last time: Confidence...

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