Textbook Question
Explain how to determine the values of d.f.N and d.f.D when performing a two-sample F-test.
8
views
14. ANOVA
Introduction to ANOVA
1:29 minutesProblem 10.3.10
Textbook Question
"Finding a Critical F-Value for a Two-Tailed Test In Exercises 9–12, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.
α=0.10, d.f.N=24, d.f.D=28"
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the critical F-value for a two-tailed test. The level of significance (α) is 0.10, and the degrees of freedom for the numerator (d.f.N) and denominator (d.f.D) are 24 and 28, respectively.
Step 2: Recall the properties of the F-distribution. The F-distribution is used to compare variances, and the critical F-value is determined based on the level of significance (α), the degrees of freedom for the numerator (d.f.N), and the degrees of freedom for the denominator (d.f.D). For a two-tailed test, the significance level is split equally between the two tails (α/2 for each tail).
Step 3: Use an F-distribution table or statistical software to find the critical F-values. For a two-tailed test, you will need to find two critical F-values: one for the upper tail and one for the lower tail. The upper critical F-value corresponds to the right tail with α/2 = 0.05, and the lower critical F-value corresponds to the left tail with α/2 = 0.05.
Step 4: Locate the critical F-values in the F-distribution table. Find the row corresponding to d.f.N = 24 and the column corresponding to d.f.D = 28 for the upper tail (α/2 = 0.05). For the lower tail, take the reciprocal of the upper critical F-value because the F-distribution is not symmetric.
Step 5: Verify your results. Ensure that the critical F-values you found are consistent with the level of significance (α = 0.10) and the degrees of freedom provided. If using statistical software, double-check the input values for accuracy.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Critical F-Value
The critical F-value is a threshold used in hypothesis testing to determine whether to reject the null hypothesis. It is derived from the F-distribution, which is used when comparing variances between two or more groups. In a two-tailed test, the critical F-value is found at both ends of the distribution, corresponding to the specified level of significance (α).
Recommended video:
05:50
Critical Values: t-Distribution
Degrees of Freedom
Degrees of freedom (d.f.) refer to the number of independent values that can vary in an analysis without violating any constraints. In the context of an F-test, there are two types of degrees of freedom: d.f.N (numerator) and d.f.D (denominator), which correspond to the number of groups being compared and the total number of observations, respectively. These values are crucial for determining the critical F-value.
Recommended video:
05:50Critical Values: t-Distribution
Level of Significance (α)
The level of significance (α) is the probability of rejecting the null hypothesis when it is actually true, commonly set at values like 0.05 or 0.10. It defines the threshold for determining whether the observed data is statistically significant. In a two-tailed test, this significance level is split between both tails of the distribution, affecting the critical values used in hypothesis testing.
Recommended video:
03:33Finding Binomial Probabilities Using TI-84 Example 1
6:46mWatch next
Master Introduction to ANOVA with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice