139k views
1 vote
When analyzing data from experiments that involve more than two groups...

a. doing t tests on all possible pairs of means increases the probability of making a Type II error
b. doing t tests on all possible pairs of means increases the probability of making a Type I error
c. it is generally permissible to do t tests between all possible pairs of means and use student's t distribution
d. doing t tests on all possible pairs of means decrease the probability of making Type I errors

User Htellez
by
8.2k points

1 Answer

2 votes

Final answer:

Conducting t tests on all possible pairs of means when analyzing data from more than two groups increases the probability of a Type I error, not a Type II error. For multiple group comparisons, ANOVA is recommended because it corrects for the elevated risk of Type I error associated with multiple t tests.

Step-by-step explanation:

When analyzing data from experiments that involve more than two groups, doing t tests on all possible pairs of means increases the probability of making a Type I error. A Type I error occurs when we incorrectly reject a true null hypothesis. This increased risk is due to the cumulative probability of committing an error across multiple comparisons. While t tests are appropriate for comparing two means, as the number of comparisons increases, statistical methods such as Analysis of Variance (ANOVA) are recommended to control the risk of Type I errors. ANOVA compares the means across all groups simultaneously, applying a correction to account for the multiple comparisons, hence keeping the Type I error rate at the desired level.

It is important to note that failing to reject a false null hypothesis would result in a Type II error. The power of a statistical test, which is 1 - Type II error, is affected by the sample size, effect size, and variance associated with the measure used. To accurately perform a hypothesis test and minimize the Type I and Type II errors, certain distributional requirements must be met, such as using a Student's t-test for normally distributed populations or large sample sizes with an unknown population standard deviation.

User Sean Kilb
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.