ST2002 Assignment 3: One Way ANOVA

Question of Interest

the question of interest is to determine whether there is evidence of a difference in the typical flipper length of the three penguin species adelie, chinstrap and gentoo, based on data that i will provide. i will show the difference between the flipper length of three types of penguin species.

null hypothesis: the population mean flipper length is equal in the population of adelie, chinstrap and gentoo penguins

alternative hypothesis: the population mean flipper length is not equal in the population of adelie, chinstrap and gentoo penguins.

Exploratory Data Analysis

Subjective impression:

	Adelie (N=152)	Chinstrap (N=68)	Gentoo (N=124)	Overall (N=344)
flipper_length_mm
Mean (SD)	190 (6.54)	196 (7.13)	217 (6.48)	201 (14.1)
Median [Min, Max]	190 [172, 210]	196 [178, 212]	216 [203, 231]	197 [172, 231]
Missing	1 (0.7%)	0 (0%)	1 (0.8%)	2 (0.6%)

the mean of the gentoo mean flipper length is much larger than the chinstrap and adelie penguins

the adelie specie has some outliers that can affect the mean flipper length

the flipper length of adelie and chinstrap are very similar in length. ## formal analysis

One-way ANOVA

##              Df Sum Sq Mean Sq F value Pr(>F)    
## species       2  52473   26237   594.8 <2e-16 ***
## Residuals   339  14953      44                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2 observations deleted due to missingness

the p value is very small so we can reject the null hypothesis

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = flipper_length_mm ~ species, data = penguins)
## 
## $species
##                       diff       lwr       upr p adj
## Chinstrap-Adelie  5.869887  3.586583  8.153191     0
## Gentoo-Adelie    27.233349 25.334376 29.132323     0
## Gentoo-Chinstrap 21.363462 19.000841 23.726084     0

the chinstrap adelie is entirely positive. therefore we can conclude that the mean flipper length is significantly greater for adelie compared to chin strap. the chinstrap had the largest flipper length overall compared to gentoo and adelie species.

Assumptions

## # A tibble: 3 × 2
##   species   FL.sd
##   <fct>     <dbl>
## 1 Adelie     6.54
## 2 Chinstrap  7.13
## 3 Gentoo     6.48

the largest standard deviation is 7.13, which is larger than the other two standard deviations and the assumption of equality of population standard deviation is deemed reasonable. the normal distribution assumption can be checked informally using box plots by looking for symmetry in each sample seperately.

Conclusion