Null Hypothesis H₀: The distribution of car type preferences matches the expected equal distribution (33.3% each).

Alternate Hypothesis H₁: The distribution of car type preferences does not match the expected equal distribution.

Importing Dataset

Install required package (only once) install.packages(“readxl”) Load the package

library(readxl)

Import Excel dataset (update file path)

dataset <- read_excel(“C:/Users/Poojitha Dibbamadugu/Downloads/RQ1.xlsx”) head(dataset)

📊 Visualize the Data

We first create a frequency table (observed counts) for our categorical variable.

Replace ‘Variable’ with your dataset’s categorical variable

observed <- table(dataset$Variable)

Display observed frequencies

print(observed)

View category names

names(observed)

⚙ Define Expected Proportions

Expected proportions are based on your hypothesis or prior knowledge. They must be written as decimals and must sum to 1.

Writing Example: Equal distribution among three categories

expected <- c(0.33, 0.33, 0.34)

🔍 Conduct the Chi-Square Goodness-of-Fit Test Writing Perform test

chisq_gfit <- chisq.test(observed, p = expected)

View results

chisq_gfit

Interpretation:

If p < 0.05, reject H₀ → observed frequencies differ significantly from expected ones.

If p > 0.05, fail to reject H₀ → no significant difference.

📈 Effect Size (Cohen’s W)

Effect size quantifies how strong the difference is between observed and expected frequencies.

Writing Calculate Cohen’s W

W <- sqrt(chisq_gfit$statistic / sum(observed)) W Interpretation:

If p < 0.05, reject H₀ → observed frequencies differ significantly from expected ones.

If p > 0.05, fail to reject H₀ → no significant difference.

📈 Effect Size (Cohen’s W)

Effect size quantifies how strong the difference is between observed and expected frequencies.

Results paragraph

A Chi-Square Goodness-of-Fit Test was conducted to determine whether car type preference (Sedan, SUV, Truck) was different from an equal distribution (33.33%, 33.33%, 33.33%) among 90 participants. There was a statistically significant difference in car type preferences, χ²(2, N = 90) = 9.67, p = .008. Participants preferred SUVs more than sedans or trucks. The effect size was medium (Cohen’s W = 0.33).

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

Including Plots

You can also embed plots, for example:

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plo