Chapter 17 Multiple DV designs

## Parsed with column specification:
## cols(
##   Verbal = col_double(),
##   Math = col_double(),
##   Sex = col_character()
## )

• Download the SPSS data set

• Download the Excel/R data set

17.1 Description

17.2 Visualization

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

17.3 Why not \(t\) tests?

## $Math
## 
##  Welch Two Sample t-test
## 
## data:  score by Sex
## t = -2, df = 158, p-value = 0.06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -59.353   0.969
## sample estimates:
## mean in group F mean in group M 
##             598             627 
## 
## 
## $Verbal
## 
##  Welch Two Sample t-test
## 
## data:  score by Sex
## t = 0.7, df = 160, p-value = 0.5
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -19.2  42.6
## sample estimates:
## mean in group F mean in group M 
##             602             590

17.4 Why not ANCOVA?

## 
## Call:
## lm(formula = Verbal ~ Sex * Math, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -254.73  -46.29   -1.98   42.55  192.55 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 579.4668     8.0852   71.67  < 2e-16 ***
## Sex         -65.5422    22.6875   -2.89   0.0044 ** 
## Math          0.7382     0.0889    8.31  4.2e-14 ***
## Sex:Math      0.0662     0.2344    0.28   0.7780    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 71.4 on 158 degrees of freedom
## Multiple R-squared:  0.495,  Adjusted R-squared:  0.486 
## F-statistic: 51.7 on 3 and 158 DF,  p-value: <2e-16

## `geom_smooth()` using formula 'y ~ x'

17.5 MANOVA

Term	d.f.	Pillai's trace	\(F\)	Num. d.f.	Denom. d.f.	Sig. \(p\)
Sex	1	0.071	6.085	2	159	0.003
Residuals	160

17.5.1 Model check

17.6 Linear Discriminant Analysis

## Call:
## lda(Sex ~ ., data = ., method = "moment")
## 
## Prior probabilities of groups:
##     F     M 
## 0.506 0.494 
## 
## Group means:
##   Verbal Math
## F    602  598
## M    590  627
## 
## Coefficients of linear discriminants:
##            LD1
## Verbal -0.0118
## Math    0.0141

## Loading required package: lattice

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  F  M
##          F 49 33
##          M 33 47
##                                         
##                Accuracy : 0.593         
##                  95% CI : (0.513, 0.669)
##     No Information Rate : 0.506         
##     P-Value [Acc > NIR] : 0.0167        
##                                         
##                   Kappa : 0.185         
##                                         
##  Mcnemar's Test P-Value : 1.0000        
##                                         
##             Sensitivity : 0.598         
##             Specificity : 0.588         
##          Pos Pred Value : 0.598         
##          Neg Pred Value : 0.588         
##              Prevalence : 0.506         
##          Detection Rate : 0.302         
##    Detection Prevalence : 0.506         
##       Balanced Accuracy : 0.593         
##                                         
##        'Positive' Class : F             
## 

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