Lab Report 2

Gabrielle Coelho

2022-04-01

Chi-squared test

Chi-square test examines whether rows and columns of a contingency table are statistically significantly associated.

#>            
#>             good poor
#>   placebo    127  158
#>   treatment  172   98
#>            
#>             good poor
#>   placebo   TRUE TRUE
#>   treatment TRUE TRUE
#> 
#>  Pearson's Chi-squared test with Yates' continuity correction
#> 
#> data:  tab
#> X-squared = 19.682, df = 1, p-value = 9.148e-06

If the calculated Chi-square statistic is greater than the critical value, then we must conclude that the row and the column variables are not independent of each other. This implies that they are significantly associated.

The chi-squared statistic (x-squared) is significantly higher than that of the critical value (p). The expected value for all variables was tested to be greater than 5 which is displayed as TRUE. We can therefore reject the null hypothesis with confidence there is significance. This evidence indicates a high level of dependence of patient status on treatment.

The mosaic plot graphically represents the Chi-squared test

Figure 1. Patients under the treatment category have a higher proportion of recorded good status than that of patients under the placebo category

Risk and Odd ratio

A relative risk or odds ratio greater than one indicates an event to be harmful, while a value less than one indicates a protective effect.

  • Risk ratio
#> $data
#>            
#>             good poor Total
#>   placebo    127  158   285
#>   treatment  172   98   270
#>   Total      299  256   555
#> 
#> $measure
#>            risk ratio with 95% C.I.
#>              estimate     lower     upper
#>   placebo   1.0000000        NA        NA
#>   treatment 0.6547117 0.5418409 0.7910945
#> 
#> $p.value
#>            two-sided
#>               midp.exact fisher.exact   chi.square
#>   placebo             NA           NA           NA
#>   treatment 6.178541e-06 6.334767e-06 6.138238e-06
#> 
#> $correction
#> [1] FALSE
#> 
#> attr(,"method")
#> [1] "Unconditional MLE & normal approximation (Wald) CI"
  • Odds ratio
#> $data
#>            
#>             good poor Total
#>   placebo    127  158   285
#>   treatment  172   98   270
#>   Total      299  256   555
#> 
#> $measure
#>            odds ratio with 95% C.I.
#>              estimate     lower     upper
#>   placebo   1.0000000        NA        NA
#>   treatment 0.4588706 0.3255106 0.6443252
#> 
#> $p.value
#>            two-sided
#>               midp.exact fisher.exact   chi.square
#>   placebo             NA           NA           NA
#>   treatment 6.178541e-06 6.334767e-06 6.138238e-06
#> 
#> $correction
#> [1] FALSE
#> 
#> attr(,"method")
#> [1] "median-unbiased estimate & mid-p exact CI"

Both indicate a ratio greater than one for the placebo groups and reports a ratio less than one for treatment groups. This indicates that the treatment had a “protective” effect on the patients.

Clustering

Two Way Anova Model

ggplot(respiratory, aes(y = subject, x = treatment, colour = factor(status))) + geom_boxplot() + theme_classic() + 
    xlab("Treatment") + ylab("subject") + labs(colour = "Status")

Regression model