# summary2way: Two-way Analysis of Variance Summary In s20x: Functions for University of Auckland Course STATS 201/208 Data Analysis

## Description

Displays summary information for a two-way anova analysis. The lm object must come from a numerical response variable and factors. The output depends on the value of page:

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```summary2way( fit, page = c("table", "means", "effects", "interaction", "nointeraction"), digit = 5, conf.level = 0.95, print.out = TRUE, new = TRUE, all = FALSE, FUN = "identity", ... ) ```

## Arguments

 `fit` an lm object, i.e. the output from 'lm()'. `page` options for output: 'table', 'means', 'effects', 'interaction', 'nointeraction' `digit` the number of decimal places in the display. `conf.level` confidence level of the intervals. `print.out` if TRUE, print out the output on the screen. `new` if `TRUE` then this will run the new version of `summary2way` which should be more robust than the old version. It does not work in the same way however. In particular, when `page = 'means'` it does not return summary statistics for each grouping of the data (pooled/by row factor/by column factor/by interaction factor). Instead it simply returns the means for each grouping. `all` Only applicable to `page = "interaction"`. If `TRUE`, pairwise comparisons for all combinations of factor levels are shown. Otherwise, comparisons are only shown between combinations that have the same level for one of the factors. `FUN` optional function to be applied to estimates and confidence intervals. Typically for backtransformation operations. `...` other arguments like inttype, pooled etc.

## Details

page = 'table' anova table page = 'means' cell means matrix, numeric summary page = 'effects' table of effects page = 'interaction' tables of contrasts page = 'nointeraction' tables of contrasts

## Value

A list with the following components:

 `Df` degrees of freedom for regression, residual and total. ```Sum of Sq``` sum squares for regression, residual and total. ```Mean Sq``` mean squares for regression and residual. ```F value``` F-statistic value. `Pr(F)` The P-value assoicated with each F-test. `Grand Mean` The overall mean of the response variable. `Row Effects` The main effects for the first (row) factor. `Col Effects` The main effects for the second (column) factor. `Interaction Effects` The interaction effects if an interaction model has been fitted, otherwise `NULL`. `results` If `new = TRUE`, then this is a list with five components: `table` - the ANOVA table, `means` the table of means from `model.tables`, `effects` - the table of effects from `model.tables`, and `comparisons` - the differences in the means with standard errors, confidence bounds, and P-values from `TukeyHSD`

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`summary1way`, `model.tables`, `TukeyHSD`
 ```1 2 3 4 5 6 7 8 9``` ```##Arousal data: data(arousal.df) arousal.fit = lm(arousal ~ gender * picture, data = arousal.df) summary2way(arousal.fit) ## Butterfat data: data("butterfat.df") fit <- lm(log(Butterfat)~Breed+Age, data=butterfat.df) summary2way(fit, page="nointeraction", FUN = exp) ```