What is Calculate Degrees of Freedom in R?

In this article, we will learn Calculate Degrees of Freedom in R,This free achine Learning tutorial for complete beginners will help you learn achine Learning from scratch.

Calculate Degrees of Freedom in R

Understanding Degrees of Freedom

Conclusion

Here we are discuss the main methods to calculate Degrees of Freedom in R Programming Language.

Calculate Degrees of Freedom using T-Test

Conduct an independent two-sample t-test to compare the means of two groups.

# Generate sample data
data1 <- rnorm(30, mean = 10, sd = 5)
data2 <- rnorm(30, mean = 12, sd = 5)

# Perform an independent two-sample t-test
t_test_result <- t.test(data1, data2)

# Print results
print(t_test_result)

# Extract degrees of freedom
df <- t_test_result$parameter
print(paste("Degrees of Freedom:", df))

Output:

    Welch Two Sample t-test

data:  data1 and data2
t = -0.41773, df = 57.125, p-value = 0.6777
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -3.288934  2.153537
sample estimates:
mean of x mean of y 
 10.38647  10.95417 

[1] "Degrees of Freedom: 57.1245090390818"

The t-test result indicates that the t-value is -0.41773 with 57.124 degrees of freedom and a p-value of 0.6777. The degrees of freedom are not an integer due to the Welch’s correction used for unequal variances.

Calculate Degrees of Freedom using ANOVA

Perform a one-way ANOVA to compare means across three different groups.

# Generate sample data
set.seed(456) # For reproducibility
group <- factor(rep(1:3, each = 10))
response <- c(rnorm(10, mean = 10), rnorm(10, mean = 12), rnorm(10, mean = 14))

# Perform ANOVA
anova_result <- aov(response ~ group)

# Print summary
summary(anova_result)

# Extract degrees of freedom
df_between <- summary(anova_result)[[1]]["group", "Df"]
df_within <- summary(anova_result)[[1]]["Residuals", "Df"]
print(paste("Between Groups DF:", df_between))
print(paste("Within Groups DF:", df_within))

Output:

            Df Sum Sq Mean Sq F value   Pr(>F)    
group        2  76.60   38.30   33.74 4.53e-08 ***
Residuals   27  30.65    1.14                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
[1] "Between Groups DF: 2"
[1] "Within Groups DF: 27"

The ANOVA table shows the degrees of freedom between groups (2) and within groups (27). The F value is significant, indicating differences among group means.

Calculate Degrees of Freedom using Chi-Square Test

Conduct a chi-square test of independence on a 2×2 contingency table.

# Generate sample data
observed <- matrix(c(10, 20, 30, 40), nrow = 2)

# Perform chi-square test
chi_square_result <- chisq.test(observed)

# Print results
print(chi_square_result)

# Extract degrees of freedom
df <- chi_square_result$parameter
print(paste("Degrees of Freedom:", df))

Output:

Pearson's Chi-squared test with Yates' continuity correction

data:  observed
X-squared = 0.44643, df = 1, p-value = 0.504

[1] "Degrees of Freedom: 1"

The chi-square test result shows the chi-square statistic is 0.44643 with 1 degree of freedom and a p-value of 0.504, indicating no significant association between the variables.

Degrees of Freedom in R

In statistical tests, degrees of freedom are used to determine the distribution of test statistics and divert the analysis of hypothesis testing, confidence intervals, etc.