Question 1: An Independent Measures T Test Produced A T Stat
Question 1an Independent Measures T Test Produced A T Statistic Withdf
Question 1 An independent-measures t test produced a t statistic with df = 20. If the same data had been evaluated with an analysis of variance, what would be the df values for the F-ratio? Answer a. 1, 20 b. 2, 20 c. 1, 19 d. 2, 19
Paper For Above instruction
The question concerns the relationship between degrees of freedom (df) in an independent-measures t test and those in an analysis of variance (ANOVA). Specifically, when an independent-measures t test yields a t statistic with df=20, what are the corresponding df values for the F-ratio in an ANOVA? To answer this, we need to understand the connection between t and F distributions in the context of two-group comparisons.
The independent-measures t test is used to determine whether there are significant differences between the means of two independent groups. The degrees of freedom for the t test in this case are calculated as df = n1 + n2 - 2, where n1 and n2 are the sample sizes for each group. Since the question indicates df = 20, this suggests that the total sample size (n1 + n2) is 22 (because df = 22 - 2 = 20).
In the context of ANOVA, the F-ratio for two groups is mathematically related to the t-statistic, with the relationship F = t^2. The degrees of freedom for the numerator (between-groups variability) in this case are typically 1 because there are two groups (k = 2). The denominator degrees of freedom (within-groups variability) equal the total sample size minus the number of groups, which is (n1 + n2) - 2, or 22 - 2 = 20.
Therefore, the F-ratio for this situation would have df between = 1 and df within = 20. The value of 1 in the numerator indicates one numerator degree of freedom, aligning with the two-group comparison, and 20 as the denominator degrees of freedom aligns with the within-group variability degrees of freedom.
Given the options: a. 1, 20; b. 2, 20; c. 1, 19; d. 2, 19, the correct choice is a, which matches the degrees of freedom calculations derived above.
In summary, the degrees of freedom for the F-ratio when evaluating the same data with ANOVA and the original t test are 1 for between-groups and 20 for within-groups, consistent with the relationship between t and F for two groups.
Paper For Above instruction
Question 1an Independent Measures T Test Produced A T Statistic Withdf
The question concerns the relationship between degrees of freedom (df) in an independent-measures t test and those in an analysis of variance (ANOVA). Specifically, when an independent-measures t test yields a t statistic with df=20, what are the corresponding df values for the F-ratio in an ANOVA? To answer this, we need to understand the connection between t and F distributions in the context of two-group comparisons.
The independent-measures t test is used to determine whether there are significant differences between the means of two independent groups. The degrees of freedom for the t test in this case are calculated as df = n1 + n2 - 2, where n1 and n2 are the sample sizes for each group. Since the question indicates df = 20, this suggests that the total sample size (n1 + n2) is 22 (because df = 22 - 2 = 20).
In the context of ANOVA, the F-ratio for two groups is mathematically related to the t-statistic, with the relationship F = t^2. The degrees of freedom for the numerator (between-groups variability) in this case are typically 1 because there are two groups (k = 2). The denominator degrees of freedom (within-groups variability) equal the total sample size minus the number of groups, which is (n1 + n2) - 2, or 22 - 2 = 20.
Therefore, the F-ratio for this situation would have df between = 1 and df within = 20. The value of 1 in the numerator indicates one numerator degree of freedom, aligning with the two-group comparison, and 20 as the denominator degrees of freedom aligns with the within-group variability degrees of freedom.
Given the options: a. 1, 20; b. 2, 20; c. 1, 19; d. 2, 19, the correct choice is a, which matches the degrees of freedom calculations derived above.
In summary, the degrees of freedom for the F-ratio when evaluating the same data with ANOVA and the original t test are 1 for between-groups and 20 for within-groups, consistent with the relationship between t and F for two groups.
References
- Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.