Download Statistical Analysis, Chapter 4

Statistical Analysis, Chapter 4
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Preparing data for sta2s2cal analysis Descrip2ve sta2s2cs Comparing means T tests Analysis of variance (ANOVA) Assump2ons of t tests and F tests Iden2fying rela2onships Regression Nonparametric sta2s2cal tests Preparing data for analysis •  Cleaning up data –  Detect errors –  FormaCng •  Coding –  Types of data that need to be coded –  Be consistent •  Organizing the data –  Accommodate to the requirements of sta2s2cal soIware Descrip2ve sta2s2cs •  Measures of central tendency –  Mean –  Median –  Mode •  Measures of spread –  Range –  Variance –  Standard devia2ons Videos http://www.khanacademy.org/math/statistics/v/small-sample-hypothesis-test
http://www.youtube.com/watch?v=leHOBf_-9kM
Comparing means •  Summary of methods Comparing 2 means: T tests •  Independent-­‐samples t test: between-­‐group design Comparing 2 means: T tests •  Paired-­‐sample t test: within-­‐group design Comparing 2 or more means: Analysis of variance (ANOVA) •  Also called F tests •  One-­‐way ANOVA: for between-­‐group design •  Data layout: Table 4.6 •  Results summary: Factorial ANOVA •  For between-­‐group design •  2 or more independent variables involved •  Data layout: table 4.9 Factorial ANOVA •  Summary results Repeated measures ANOVA •  For within-­‐group design •  Can inves2gate one or more variables •  One-­‐way ANOVA Repeated measures ANOVA •  One way ANOVA summary report: Repeated measures ANOVA •  Two way ANOVA experiment design: Repeated measures ANOVA Two way ANOVA data layout Repeated measures ANOVA •  Two way ANOVA summary report: Split-­‐plot ANOVA •  Involves both between-­‐group and within-­‐group factors •  Experiment design Split-­‐plot ANOVA data layout Split-­‐plot ANOVA summary report Interpre2ng test sta2s2cs, p-­‐values 1) The null hypothesis here is that the means are equal, and the alternative
hypothesis is that they are not. A big t, with a small p-value, means that the
null hypothesis is discredited, and we would assert that the means are
significantly different (while a small t, with a big p-value indicates that they are
not significantly different).
2) The null hypothesis here is that one mean is greater than the other, and the
alternative hypothesis is that it isn't. A big t, with a small p-value, means that
the null hypothesis is discredited, and we would assert that the means are
significantly different in the way specified by the null hypothesis (and a small t,
with a big p-value means they are not significantly different in the way
specified by the null hypothesis).
3) The null hypothsis here is that the group means are all equal, and the
alternative hypothesis is that they are not. A big F, with a small p-value,
means that the null hypothesis is discredited, and we would assert that the
means are significantly different (while a small F, with a big p-value indicates
that they are not significantly different).
4) The null hypothsis here is that the group variances are all equal, and the
alternative hypothesis is that they are not. A big K2, with a small p-value, means that
the null hypothesis is discredited, and we would assert that the group variances are
significantly different (while a small K2, with a big p-value indicates that they are not
significantly different).
5) The null hypothesis here is that there is not a general relationship between the
response (dependent) variable and one or more of the predictor (independent)
variables, and the alternative hypothesis is that there is one. A big F, with a small pvalue, means that the null hypothesis is discredited, and we would assert that there is
a general relationship between the response and predictors (while a small F, with a
big p-value indicates that there is no relationship).
6) The null hypothesis is that the value of the p-th regression coefficient is 0, and the
alternative hypothesis is that it isn't. A big t, with a small p-value, means that the null
hypothesis is discredited, and we would assert that the regression coefficient is not 0
(and a small t, with a big p-value indicates that it is not significantly different from 0).
Iden2fy rela2onships •  Correla2on: Two factors are correlated if there is a rela2onship between them •  Most commonly used test for correla2on is the Pearson’s product moment correla2on coefficient test •  Pearson’s r: ranges between -­‐1 to 1 •  Pearson’s r square represents the propor2on of the variance shared by the two variables Iden2fy rela2onships •  Correla2on does not imply causal rela2onship Iden2fy rela2onships •  Regression: can inves2gate the rela2onship between one DV and mul2ple IVs •  Regression is used for 2 purposes: –  Model construc2on –  Predic2on •  Different regression procedures –  Simultaneous –  Hierarchical Non-­‐parametric tests •  Non-­‐parametric tests are used when: –  The error is not normally distributed –  The distances between any two data units are not equal –  The variance of error is not equal Non-­‐parametric tests •  CHI-­‐square test –  Used to analyze categorical data –  Table of counts (con2ngency table) –  Assump2ons of the test •  Data points need to be independent •  The sample size should not be too small Non-­‐parametric tests •  Two groups of data –  For between-­‐group design: Mann–Whitney U test or the Wald–Wolfowitz runs test –  For within-­‐group design: Wilcoxon signed ranks test •  Three or more groups of data –  For between-­‐group design: Kruskal–Wallis one-­‐
way analysis of variance by ranks –  For within-­‐group design: Friedman’s two-­‐way analysis of variance test