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Answer :
Final answer:
To find the total number of scores, add the degrees of freedom for the effect, the degrees of freedom for error, and 1, then multiply by the number of measurements. The total number of scores is 63, which is not listed in the provided options, suggesting an error in the question or its options.
Explanation:
The study involves assessing participants' attitudes at three different points in time. The statistical result presented indicates an F-ratio of F (2, 18) = 12.27. The F-ratio has two numbers representing degrees of freedom: one for the effect (across time points) and one for the error.
The first number, 2, represents the degrees of freedom for the effect (numerator), which comes from the number of time points minus one (3 - 1 = 2). The second number, 18, is the degrees of freedom for error (denominator) and reflects the degrees of freedom associated with the subjects.
To calculate the total number of individual scores, we need to account for the degrees of freedom plus the number of groups (which is the number of measurements).
The formula to calculate the total number of scores is total = between + within + 1, where total represents total degrees of freedom (sum of both plus 1 because degrees of freedom are always one less than the actual number), between is for the number of conditions, and within is for the number of subjects.
Using the given total = 29, we can calculate the total number of scores as follows:
Total scores = between + within + 1 = 2 + 18 + 1 = 21
However, because there are three measures for each subject, we then need to multiply the number of subjects by three: Total scores = Number of subjects × Number of measurements = 21 × 3 = 63
This isn’t one of the options provided in the original question, which suggests a possible error in the provided options or misinterpretation of the question's data.
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