## 'data.frame':    541 obs. of  2 variables:
##  $ Cholesterol: int  221 188 292 319 205 247 202 150 228 280 ...
##  $ BP_Status  : chr  "Optimal" "High" "High" "Normal" ...

Exercise 1

(a)
After conducting the ANOVA test we use the Levene Test to compare the variance between the two groups. After running the Levene test we yield a p-value = .83, which is statistically significant, so we can conclude that we do not reject the null and the equal variance assumption can be trusted.
Looking at the summary for the anova of heartbpchol we see that the sum of squares model the variation of y is quite large at 25,211. 
##              Df  Sum Sq Mean Sq F value  Pr(>F)   
## BP_Status     2   25211   12605   6.671 0.00137 **
## Residuals   538 1016631    1890                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Exercise 1

(b)

After running the Scheffe Test we examine the p-values for each group. Due to their small values we can conclude that the mean between groups ‘Normal-High’ and ‘Optimal-High’ are significantly different. Although for the groups ‘Optimal-Normal’ yielded a larger p-value telling us that the two groups mean value is equal. Changing our focus over the the differences between these values we see in our first group a negative difference which tells us that ‘High’ BP_Status has a greater mean value than ‘Normal’ and comparing this to its p-value we can assume that the difference is significant. The next group ‘Optimal-High’ has the greatest mean difference of any of the groups at -18.65 which tells us that the mean value of the ‘High’ group is much greater than the mean value of the ‘Optimal’ group, and the small p-value lets us know that the difference is significant. Lastly, group ‘Optimal-Normal’ has the smallest mean difference but the negative difference tells us that ‘Normal’ still has a slightly higher mean value. It’s larger p-value tells us that the difference is not significant.

## 
##   Posthoc multiple comparisons of means: Scheffe Test 
##     95% family-wise confidence level
## 
## $BP_Status
##                      diff    lwr.ci    upr.ci   pval    
## Normal-High    -11.543481 -21.35092 -1.736038 0.0159 *  
## Optimal-High   -18.646679 -33.46702 -3.826341 0.0089 ** 
## Optimal-Normal  -7.103198 -21.81359  7.607194 0.4958    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Exercise 2

(a)
## 'data.frame':    345 obs. of  3 variables:
##  $ mcv       : int  85 85 86 91 87 98 88 88 92 90 ...
##  $ alkphos   : int  92 64 54 78 70 55 62 67 54 60 ...
##  $ drinkgroup: int  1 1 1 1 1 1 1 1 1 1 ...

After running the Levene Test to determine the variance of the two groups we can conclude that the significance of drinkgroup is very little as 10% of the variation is explained by the independent variable. the p-value = .87 which tells us that we can trust the equal variance assumption.

## [1] 0.1077214

Exercise 2

(b)

After running the Levene Test to determine the variance of the two groups we can conclude that the significance of drinkgroup is very little as 4.2% of the variation is explained by the independent variable. the p-value = .52 which tells us that we can trust the equal variance assumption.

## [1] 0.04270721

Exercise 2

(c)

The first similarity that I notice looking at the data is that for each test group the mean values are majority equal to one another. Only 4 groups in the mcv anova set came up not equal, while only 3 groups were not equal in the alkphos group.

Still looking at mean values it appears that the alkphos group tended to have more equal variances across all groups when compared to the mcv group. Almost all of the mean values for alkphos are close to 1.

The mcv group tended to also have more positive difference opposed to the alkphos group who tended to have a more negative difference.

All groups have significantly different mean value groups within them.

## 
##   Posthoc multiple comparisons of means: Scheffe Test 
##     95% family-wise confidence level
## 
## $drinkgroup
##             diff      lwr.ci   upr.ci    pval    
## 2-1  1.241452991 -0.94020481 3.423111  0.5410    
## 3-1  0.938131313 -0.90892674 2.785189  0.6495    
## 4-1  3.744610282  1.73913894 5.750082 1.9e-06 ***
## 5-1  3.746031746  0.64379565 6.848268  0.0081 ** 
## 3-2 -0.303321678 -2.59291786 1.986275  0.9966    
## 4-2  2.503157290  0.08395442 4.922360  0.0380 *  
## 5-2  2.504578755 -0.87987039 5.889028  0.2646    
## 4-3  2.806478969  0.68408993 4.928868  0.0025 ** 
## 5-3  2.807900433 -0.37116998 5.986971  0.1151    
## 5-4  0.001421464 -3.27222796 3.275071  1.0000    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##   Posthoc multiple comparisons of means: Scheffe Test 
##     95% family-wise confidence level
## 
## $drinkgroup
##          diff      lwr.ci    upr.ci   pval    
## 2-1 -2.645299 -11.9663647  6.675766 0.9419    
## 3-1 -4.056138 -11.9476367  3.835360 0.6389    
## 4-1 -1.148743  -9.7170578  7.419571 0.9965    
## 5-1 12.572650  -0.6815582 25.826857 0.0734 .  
## 3-2 -1.410839 -11.1930681  8.371390 0.9953    
## 4-2  1.496556  -8.8394138 11.832525 0.9952    
## 5-2 15.217949   0.7579944 29.677903 0.0329 *  
## 4-3  2.907395  -6.1604467 11.975236 0.9117    
## 5-3 16.628788   3.0463078 30.211268 0.0069 ** 
## 5-4 13.721393  -0.2651729 27.707959 0.0578 .  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1