A friend gives you the following Fs and decision made. Does the decision appear to be correct? Explain.Do NOT provide critical or table values as explanations.
F(2, 63) = .10, not significant
F(3, 85) = -1.70, not significant
F(1, 120) = 64.32, not significant
F(5, 70) = 1.00, significant
To determine whether the decision appears to be correct, we need to understand the significance of the F-statistic within the context of the data analysis.
In hypothesis testing for the analysis of variance (ANOVA), the F-statistic measures the variation between group means relative to the variation within the groups. It is used to compare the observed variability between groups with the expected variability if there were no differences between the groups.
The F-statistic is associated with a p-value, which represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. A p-value less than a chosen significance level (commonly 0.05) typically leads to the rejection of the null hypothesis and suggests that there is a significant difference between the groups.
Now let's analyze each F-statistic provided:
1. F(2, 63) = 0.10, not significant:
In this case, since the p-value is not provided, we cannot determine its significance. However, if the p-value is above the significance level (e.g., 0.05), the decision to reject the null hypothesis (not significant) would be correct.
2. F(3, 85) = -1.70, not significant:
Similarly, without the p-value, we cannot determine the significance of this F-statistic. However, if the p-value is greater than the significance level, rejecting the null hypothesis would be correct.
3. F(1, 120) = 64.32, not significant:
Similar to the previous cases, the p-value is missing, and we cannot determine its significance directly. However, if the p-value is more than the chosen significance level, the decision to not reject the null hypothesis (not significant) would be correct.
4. F(5, 70) = 1.00, significant:
The p-value is not provided here either, but unlike the previous cases, it is stated that the result is significant. Therefore, if the p-value is less than the significance level, the decision to reject the null hypothesis (significant) would be correct.
To conclusively determine if the decisions are correct, it is necessary to calculate the p-values associated with each F-statistic and compare them to the chosen significance level.