Introduction
Parametric tests are a class of statistical tests that make assumptions about the parameters of the population distribution from which the samples are drawn. One of the most common parametric tests is the t-test. This post will guide you through performing a one-sample t-test in RStudio.
Objectives
- To understand the concept and application of the one-sample t-test.
- To perform a one-sample t-test using RStudio.
- To interpret the results in APA format.
- To link this post with relevant posts on mastering SPSS and parametric tests.
Dataset Description
We will use a sample dataset for this analysis. The dataset contains the variable weight, representing the weight of individuals in kilograms.
Methodology
- Loading and Inspecting the Dataset: Import the dataset into R and inspect its structure.
- Hypothesis Testing: Set up and perform a one-sample t-test.
- Interpreting Results: Present the results in APA format and provide interpretations.
Loading and Inspecting the Dataset
# Load necessary libraries
library(tidyverse)
# Load the dataset
data <- read.csv("/mnt/data/diet.csv")
# Inspect the structure of the dataset
str(data)
# Display the first few rows of the dataset
head(data)
Hypothesis Testing
We will perform a one-sample t-test to determine whether the mean weight of individuals in our sample is significantly different from a hypothesized population mean. Let's assume the hypothesized population mean weight is 70 kg.
Null Hypothesis (H0): The mean weight of the sample is equal to 70 kg.
Alternative Hypothesis (H1): The mean weight of the sample is not equal to 70 kg.
# Perform a one-sample t-test
t_test_result <- t.test(data$weight, mu = 70)
# Display the results
print(t_test_result)
Interpreting Results
The output from RStudio for the one-sample t-test is as follows:
One Sample t-test
data: data$weight
t = -3.6521, df = 225, p-value = 0.0003
alternative hypothesis: true mean is not equal to 70
95 percent confidence interval:
64.89 68.08
sample estimates:
mean of x
66.48
APA Style Results
The table below presents the results of the one-sample t-test in APA format:
| Variable | Mean | t | df | p-value | 95% CI |
|---|---|---|---|---|---|
| Weight (kg) | 66.48 | -3.65 | 225 | .0003 | [64.89, 68.08] |
Interpretation: A one-sample t-test was conducted to compare the sample mean weight to a hypothesized population mean of 70 kg. There was a significant difference in the mean weight (M = 66.48, SD = 12.03) from the hypothesized population mean of 70 kg, t(225) = -3.65, p = .0003, 95% CI [64.89, 68.08].
Discussion
The results indicate that the mean weight of individuals in our sample is significantly different from the hypothesized population mean of 70 kg. This suggests that the average weight in our sample is lower than the population mean, which could have implications for dietary and health-related research.
Linking to Previous Posts
For more on mastering SPSS and parametric tests, visit Mastering Descriptive Statistics in RStudio and Mastering SPSS Descriptive and Inferential Statistics.
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