Assignment 5 Question 1 - Is there a difference between the current distribution of ice cream purchases versus the expected ice cream flavor distribution?

corrections in total surround the idea of the concepts learned in assignment 4 corrections after lectures were updated.

library(ggpubr)
## Loading required package: ggplot2
library(readxl)
A5Q1_1 <- read_excel("A5Q1-1.xlsx")

create observed table

observed <- table(A5Q1_1$flavor) 
observed
## 
##  Chocolate      Mango Strawberry    Vanilla 
##         87         32         57         74

Create the barchat of the observed data above corrections made to the main title from distribution of flavors to ice cream purchases

barplot(observed,
        main = "Ice Cream Purchases",
        xlab = "Flavor",
        ylab = "Count",
        col = rainbow(length (observed)))

Create expected scores below

expected <- c(.20, .20, .20, .40)

conduct the chi-square goodness of fit test

chi_result <-chisq.test(x = observed, p = expected)
chi_result
## 
##  Chi-squared test for given probabilities
## 
## data:  observed
## X-squared = 41.6, df = 3, p-value = 4.878e-09

conduct the calculations effect size

w <- sqrt(as.numeric(chi_result$statistic) / sum(observed))
w
## [1] 0.4079216

Data Interpretation

A Chi-Square Goodness of Fit test was conducted to determine if there was a difference between the observed [flavors] frequencies and the expected frequencies. The results showed that there [was] a difference between the observed and expected frequencies, χ²(3) = 41.6, p <.001. The difference was [moderate], (Cohen’s W = .41).

one correction was for the second decimal place for the Cohen’s W = .41 when I had .4 originally.