Calculating P-Value with N 18 R 0.5 and 0.01

What is a p-value?

A p-value is a statistical measure that helps determine the significance of your results in a hypothesis test. It represents the probability of observing your data (or something more extreme) if the null hypothesis is true.

In simple terms, the p-value tells you whether your results are statistically significant. If the p-value is less than your chosen significance level (α), you can reject the null hypothesis. Common significance levels are 0.05, 0.01, and 0.001.

How to use this calculator

Our calculator makes it easy to compute the p-value for your specific scenario. Here's how to use it:

1. Enter your sample size (n) in the first field. For this example, we're using n = 18.
2. Enter your correlation coefficient (r) in the second field. In this case, r = 0.5.
3. Enter your significance level (α) in the third field. We're using α = 0.01.
4. Click the "Calculate" button to compute the p-value.
5. Review the results and interpretation provided.

The calculator will display the computed p-value and provide guidance on how to interpret it.

The formula for p-value

The p-value for a correlation coefficient is calculated using the t-distribution. The formula is:

Where:

• t is the t-statistic
• r is the correlation coefficient
• n is the sample size

Once you have the t-statistic, you can look up the p-value in a t-distribution table or use statistical software to find the probability associated with that t-value.

Interpreting the results

When you calculate a p-value, you need to compare it to your chosen significance level (α) to determine whether your results are statistically significant.

• If p-value < α: Reject the null hypothesis (there is a statistically significant relationship)
• If p-value ≥ α: Fail to reject the null hypothesis (there is no statistically significant relationship)

For our example with α = 0.01, if the calculated p-value is less than 0.01, we can conclude that there is a statistically significant correlation at the 1% level.

Worked example

Let's walk through an example calculation with n = 18, r = 0.5, and α = 0.01:

1. First, calculate the t-statistic using the formula:
   t = 0.5 × √((18 - 2) / (1 - 0.5²)) = 0.5 × √(16 / 0.75) ≈ 0.5 × 5.2915 ≈ 2.6458
2. Next, find the p-value for t = 2.6458 with degrees of freedom (df) = n - 2 = 16.
3. Using statistical tables or software, we find that the two-tailed p-value for t = 2.6458 with df = 16 is approximately 0.015.
4. Compare the p-value (0.015) to α (0.01). Since 0.015 > 0.01, we fail to reject the null hypothesis.

This means that with a sample size of 18 and a correlation coefficient of 0.5, we do not have statistically significant evidence to reject the null hypothesis of no correlation at the 1% significance level.