HW8

library(tidyverse)

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setwd("C:/Users/sajut/OneDrive/Desktop/DATA_101")

FishGills3 <- read_csv("FishGills3.csv")

Rows: 90 Columns: 2
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (1): Calcium
dbl (1): GillRate

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.

NutritionStudy <- 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.

Problem 1: 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.

observed <- c(244, 192)
theoretical_prop <- c(0.5, 0.5)

expected_values <- theoretical_prop * sum(observed)
expected_values

[1] 218 218

Results

chisq.test(observed)

    Chi-squared test for given probabilities

data:  observed
X-squared = 6.2018, df = 1, p-value = 0.01276

Problem 2: 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)

\(H_0\): There is no association between Gender and Vitamin use \(H_0\): There is an association between Gender and Vitamin use

observed_dataset <- table(NutritionStudy$Sex, NutritionStudy$VitaminUse)
observed_dataset

        
          No Occasional Regular
  Female  87         77     109
  Male    24          5      13

chisq.test(observed_dataset)

    Pearson's Chi-squared test

data:  observed_dataset
X-squared = 11.071, df = 2, p-value = 0.003944

Problem 3: 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.

head(FishGills3)

# A tibble: 6 × 2
  Calcium GillRate
  <chr>      <dbl>
1 Low           55
2 Low           63
3 Low           78
4 Low           85
5 Low           65
6 Low           98

anova_fish <- aov(GillRate ~ Calcium, data = FishGills3)
anova_fish

Call:
   aov(formula = GillRate ~ Calcium, data = FishGills3)

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_fish)

            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_fish)

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = GillRate ~ Calcium, data = FishGills3)

$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