Question

In: Statistics and Probability

Determine whether the conclusion is true or false, and explain why. 1. In a one-way (between-subjects)...

Determine whether the conclusion is true or false, and explain why.

1. In a one-way (between-subjects) ANOVA, if the observed group means in the sample differ entirely due to random variations (i.e., sampling errors), the critical value for testing the ratio of between-group mean squares to within-group mean squares will depend on the total sample size (among other aspects).

2. A significant result (i.e., p<.05) from a one-way (between-subjects) ANOVA implies that the means of the groups are all different from one another in the population.

3. A researcher conducted an independent-samples t-test to test his research hypothesis, and obtained a very small p-value which is less than .001. This implies that the probability of type 1 error is less than .1%, assuming no flaws in data collection and analysis.

Solutions

Expert Solution

(1)

Correct option:

True

Explanation:

The Degrees of Freedom for testing the ratio of between-group mean squares to within-group mean squares :

The Degrees of Freedom for numerator = k - 1

where k is the number of groups.

The Degrees of Freedom for denominator = N - k,

where N is the total sample size.

So, we understand that the critical value for testing the ratio of between-group mean squares to within-group mean squares will depend on the total sample size (among other aspects).

(2)

Correct option:

False

Explanation:

A significant result (i.e., p<.05) from a one-way (between-subjects) ANOVA implies that the difference is significant. Reject null hypothesis.

Conclusion:

At least the mean of one group is different from other groups.

(3)

Correct option:

False

Explanation:

Low value of p - value does not imply that = the probability of type 1 error is less than .1%, assuming no flaws in data collection and analysis.

orchestra answered 1 year ago
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