setwd("~/Documents/RStudio (DATA-101)")

R ACTN3 is a gene that encodes alpha-actinin-3, a protein in fast-twitch muscle fibers, important for activities like sprinting and weightlifting. The gene has two main alleles: R (functional) and X (non-functional). The R allele is linked to better performance in strength, speed, and power sports, while the X allele is associated with endurance due to a greater reliance on slow-twitch fibers. However, athletic performance is influenced by various factors, including training, environment, and other genes, making the ACTN3 genotype just one contributing factor.

A study examines the ACTN3 genetic alleles R and X, also associated with fast-twitch muscles. Of the 436 people in this sample, 244 were classified as R, and 192 were classified as X. Does the sample provide evidence that the two options are not equally likely? Conduct the test using a chi-square goodness-of-fit test.

Hypothesis: Are the two alleles, X and R, equally likely?

observed <- c(244, 192)
observed
## [1] 244 192
chisq.test(observed)
## 
##  Chi-squared test for given probabilities
## 
## data:  observed
## X-squared = 6.2018, df = 1, p-value = 0.01276

Since the p-value is small with the observed value of 0.01276, and it’s less than 0.05, we can conclude that the two alleles are unlikely equal.

Who Is More Likely to Take Vitamins: Males or Females? The dataset NutritionStudy contains, among other things, information about vitamin use and the gender of the participants. Is there a significant association between these two variables? Use the variables VitaminUse and Gender to conduct a chi-square analysis and give the results. (Test for Association)

library(tidyverse)
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## ✔ ggplot2   4.0.2     ✔ tibble    3.3.1
## ✔ lubridate 1.9.5     ✔ tidyr     1.3.2
## ✔ purrr     1.2.1     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
df<- read_csv("NutritionStudy.csv")
## Rows: 315 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (3): Smoke, Sex, VitaminUse
## dbl (14): ID, Age, Quetelet, Vitamin, Calories, Fat, Fiber, Alcohol, Cholest...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
summary(df)
##        ID             Age           Smoke              Quetelet    
##  Min.   :  1.0   Min.   :19.00   Length:315         Min.   :16.33  
##  1st Qu.: 79.5   1st Qu.:39.00   Class :character   1st Qu.:21.80  
##  Median :158.0   Median :48.00   Mode  :character   Median :24.74  
##  Mean   :158.0   Mean   :50.15                      Mean   :26.16  
##  3rd Qu.:236.5   3rd Qu.:62.50                      3rd Qu.:28.85  
##  Max.   :315.0   Max.   :83.00                      Max.   :50.40  
##     Vitamin         Calories           Fat             Fiber      
##  Min.   :1.000   Min.   : 445.2   Min.   : 14.40   Min.   : 3.10  
##  1st Qu.:1.000   1st Qu.:1338.0   1st Qu.: 53.95   1st Qu.: 9.15  
##  Median :2.000   Median :1666.8   Median : 72.90   Median :12.10  
##  Mean   :1.965   Mean   :1796.7   Mean   : 77.03   Mean   :12.79  
##  3rd Qu.:3.000   3rd Qu.:2100.4   3rd Qu.: 95.25   3rd Qu.:15.60  
##  Max.   :3.000   Max.   :6662.2   Max.   :235.90   Max.   :36.80  
##     Alcohol         Cholesterol       BetaDiet     RetinolDiet    
##  Min.   :  0.000   Min.   : 37.7   Min.   : 214   Min.   :  30.0  
##  1st Qu.:  0.000   1st Qu.:155.0   1st Qu.:1116   1st Qu.: 480.0  
##  Median :  0.300   Median :206.3   Median :1802   Median : 707.0  
##  Mean   :  3.279   Mean   :242.5   Mean   :2186   Mean   : 832.7  
##  3rd Qu.:  3.200   3rd Qu.:308.9   3rd Qu.:2836   3rd Qu.:1037.0  
##  Max.   :203.000   Max.   :900.7   Max.   :9642   Max.   :6901.0  
##    BetaPlasma     RetinolPlasma        Sex             VitaminUse       
##  Min.   :   0.0   Min.   : 179.0   Length:315         Length:315        
##  1st Qu.:  90.0   1st Qu.: 466.0   Class :character   Class :character  
##  Median : 140.0   Median : 566.0   Mode  :character   Mode  :character  
##  Mean   : 189.9   Mean   : 602.8                                        
##  3rd Qu.: 230.0   3rd Qu.: 716.0                                        
##  Max.   :1415.0   Max.   :1727.0                                        
##    PriorSmoke   
##  Min.   :1.000  
##  1st Qu.:1.000  
##  Median :2.000  
##  Mean   :1.638  
##  3rd Qu.:2.000  
##  Max.   :3.000
observed2 <- table(df$VitaminUse, df$Sex)
observed2
##             
##              Female Male
##   No             87   24
##   Occasional     77    5
##   Regular       109   13
chisq.test(observed2)
## 
##  Pearson's Chi-squared test
## 
## data:  observed2
## X-squared = 11.071, df = 2, p-value = 0.003944

Based on our p-value results, we can prove that there is a significant difference between male and females who take vitamins.

Most fish use gills for respiration in water, and researchers can observe how fast a fish’s gill cover beats to study ventilation, much like we might observe a person’s breathing rate. Professor Brad Baldwin is interested in how water chemistry might affect gill beat rates. In one experiment, he randomly assigned fish to tanks with different calcium levels. One tank was low in calcium (0.71 mg/L), the second tank had a medium amount (5.24 mg/L), and the third tank had water with a high calcium level (18.24 mg/L). His research team counted gill rates (beats per minute) for samples of 30 fish in each tank. The results are stored in FishGills3. Perform ANOVA test to see if the mean gill rate differs depending on the calcium level of the water.

Fish <- read.csv("FishGills3.csv")
summary(Fish)
##    Calcium             GillRate    
##  Length:90          Min.   :33.00  
##  Class :character   1st Qu.:48.00  
##  Mode  :character   Median :62.50  
##                     Mean   :61.78  
##                     3rd Qu.:72.00  
##                     Max.   :98.00

Performing ANOVA

anova_results <- aov(GillRate ~ Calcium, data = Fish)
anova_results
## Call:
##    aov(formula = GillRate ~ Calcium, data = Fish)
## 
## Terms:
##                   Calcium Residuals
## Sum of Squares   2037.222 19064.333
## Deg. of Freedom         2        87
## 
## Residual standard error: 14.80305
## Estimated effects may be unbalanced
summary(anova_results)
##             Df Sum Sq Mean Sq F value Pr(>F)  
## Calcium      2   2037  1018.6   4.648 0.0121 *
## Residuals   87  19064   219.1                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(anova_results)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = GillRate ~ Calcium, data = Fish)
## 
## $Calcium
##                  diff        lwr        upr     p adj
## Low-High    10.333333   1.219540 19.4471264 0.0222533
## Medium-High  0.500000  -8.613793  9.6137931 0.9906108
## Medium-Low  -9.833333 -18.947126 -0.7195402 0.0313247

Since the p-value results to 0.0121, we can reject the null hypothesis to conclude that the mean gill rates differ among calcium groups.