Ciccarelli: Psychology_5 (5th Edition)
Ciccarelli: Psychology_5 (5th Edition)
5th Edition
ISBN: 9780134477961
Author: Saundra K. Ciccarelli, J. Noland White
Publisher: PEARSON
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#8- need help show full work psyc stats
**Problem 8:** A researcher uses an ANOVA to compare six treatment conditions with a sample of \( n = 12 \) in each treatment. For this analysis, find \( df_{\text{total}} \), \( df_{\text{between}} \), and \( df_{\text{within}} \). --- **Explanation:** In ANOVA, the degrees of freedom are calculated to understand how many values in the final calculation are free to vary: - **Total Degrees of Freedom (\( df_{\text{total}} \)):** - Formula: \( N - 1 \) - Where \( N \) is the total number of observations. Here, \( N = \text{Number of Treatments} \times \text{Sample Size per Treatment} = 6 \times 12 = 72 \). - Thus, \( df_{\text{total}} = 72 - 1 = 71 \). - **Between-Groups Degrees of Freedom (\( df_{\text{between}} \)):** - Formula: \( k - 1 \) - Where \( k \) is the number of treatment groups. Here, \( k = 6 \). - Thus, \( df_{\text{between}} = 6 - 1 = 5 \). - **Within-Groups Degrees of Freedom (\( df_{\text{within}} \)):** - Formula: \( N - k \) - Given \( N = 72 \) and \( k = 6 \), - Thus, \( df_{\text{within}} = 72 - 6 = 66 \). These calculations help determine the variance within treatments and between treatments to assess any significant differences using ANOVA.
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Transcribed Image Text:**Problem 8:** A researcher uses an ANOVA to compare six treatment conditions with a sample of \( n = 12 \) in each treatment. For this analysis, find \( df_{\text{total}} \), \( df_{\text{between}} \), and \( df_{\text{within}} \). --- **Explanation:** In ANOVA, the degrees of freedom are calculated to understand how many values in the final calculation are free to vary: - **Total Degrees of Freedom (\( df_{\text{total}} \)):** - Formula: \( N - 1 \) - Where \( N \) is the total number of observations. Here, \( N = \text{Number of Treatments} \times \text{Sample Size per Treatment} = 6 \times 12 = 72 \). - Thus, \( df_{\text{total}} = 72 - 1 = 71 \). - **Between-Groups Degrees of Freedom (\( df_{\text{between}} \)):** - Formula: \( k - 1 \) - Where \( k \) is the number of treatment groups. Here, \( k = 6 \). - Thus, \( df_{\text{between}} = 6 - 1 = 5 \). - **Within-Groups Degrees of Freedom (\( df_{\text{within}} \)):** - Formula: \( N - k \) - Given \( N = 72 \) and \( k = 6 \), - Thus, \( df_{\text{within}} = 72 - 6 = 66 \). These calculations help determine the variance within treatments and between treatments to assess any significant differences using ANOVA.
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Step 1: 1. Total Degrees of Freedom (df total):
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Step 2: 2. Between-Group Degrees of Freedom (dfbetween):
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Step 3: 3. Within-Group Degrees of Freedom (dfwithin)
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