How to Calculate Non Pooled Degrees of Freedom on Ti-84

What Are Non-Pooled Degrees of Freedom?

Degrees of freedom (DF) represent the number of independent values that can vary in a statistical calculation. In non-pooled tests, each sample has its own variance estimate, leading to separate degrees of freedom for each group.

Non-pooled degrees of freedom are used in tests like the Welch's t-test, which compares means of two independent samples with unequal variances. The formula for non-pooled degrees of freedom is:

This formula accounts for the different variances between the two samples, providing a more accurate test statistic.

When to Use Non-Pooled Degrees of Freedom

Use non-pooled degrees of freedom when:

• You're comparing two independent samples with unequal variances
• You need to perform a Welch's t-test or similar test
• You want to account for heteroscedasticity (unequal variances) in your data

Non-pooled DF is particularly useful in real-world scenarios where different groups naturally have different levels of variability, such as comparing test scores from two different teaching methods.

Calculating Non-Pooled Degrees of Freedom

To calculate non-pooled degrees of freedom manually, follow these steps:

1. Calculate the variance for each sample (s₁² and s₂²)
2. Divide each variance by its sample size (s₁²/n₁ and s₂²/n₂)
3. Square each of these results
4. Sum the squared values
5. Divide each squared value by (n-1) for its respective sample
6. Sum these divided values
7. Divide the sum from step 4 by the sum from step 6

This process gives you the non-pooled degrees of freedom, which is then used in your statistical test.

Step-by-Step TI-84 Instructions

Calculating non-pooled degrees of freedom on your TI-84 requires some manual steps since the calculator doesn't have a built-in function for this specific calculation. Here's how to do it:

1. Enter your data into the calculator using the STAT EDIT function
2. Calculate the variance for each sample:
   • Press STAT, then arrow to CALC
   • Select 1-Var Stats
   • Enter the list name (e.g., L1) and press ENTER
   • Note the variance (σ²) value
3. Calculate the sample sizes (n₁ and n₂)
4. Use the formula shown earlier to calculate non-pooled DF
5. For complex calculations, consider using the calculator's math print function to document your steps

Example Calculation

Let's calculate non-pooled degrees of freedom for two samples:

Using the formula:

The non-pooled degrees of freedom for these samples is approximately 17.22.