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Field
Planned Number of Observations
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Before
Main analysis
The main analysis will be a Poisson regression in which the main coefficient of interest is an interaction. For Poisson regressions, GPower provides power analysis only for a single non-interacted variable. Accordingly, we calculated the required sample size as follows:
(a) OLS regression with three explanatory variables, focusing on the interaction, belief in the gambler's fallacy x previous booking cancelled: 658;
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(b) OLS regression limited to believers in the gambler's fallacy with one explanatory variable, focusing on the previous booking cancelled: 102;
(c) Poisson regression limited to believers in the gambler's fallacy with one explanatory variable, focusing on the previous booking cancelled: 114.
Poisson inflation factor = (c)/(b) = 114/102. Poisson with interaction = OLS with interaction x Poisson inflation factor = (a) x (c)/(b) = 658 x 114/102 = 736.
Secondary analysis
The secondary analysis will be a Poisson regression in which the main coefficient of interest is an interaction. For Poisson regressions, GPower provides power analysis only for a single non-interacted variable. Accordingly, we calculated the required sample size as follows:
(a) OLS regression with three explanatory variables, focusing on the interaction, tutorial x previous booking cancelled: 69;
(b) OLS regression limited to previous booking cancelled with one explanatory variable, focusing on tutorial: 59;
(c) Poisson regression limited to previous booking cancelled with one explanatory variable, focusing on tutorial: 90.
Poisson inflation factor = (c)/(b) = 90/59. Poisson with interaction = OLS with interaction x Poisson inflation factor = (a) x (c)/(b) = 69 * 90/59 = 106.
Based on the previous study, 0.34 of subjects believe in the gambler's fallacy. Accordingly, the required sample for the secondary analysis is 106/0.34 = 312.
Considering both the main and secondary analyses, the required sample size is the larger of the required sample size for the two analyses, i.e., 736. In addition, we must allow for subjects not completing the survey . Based on the previous study, 0.2 of subjects did not complete the survey. Accordingly, the required sample (Planned Number of Observations) is 736/0.80 = 920.
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After
Main analysis
The main analysis will be a Poisson regression in which the main coefficient of interest is an interaction. For Poisson regressions, GPower provides power analysis only for a single non-interacted variable. Accordingly, we calculated the required sample size as follows:
(a) OLS regression with three explanatory variables, focusing on the interaction, belief in the gambler's fallacy x previous booking cancelled: 658;
(b) OLS regression limited to believers in the gambler's fallacy with one explanatory variable, focusing on the previous booking cancelled: 102;
(c) Poisson regression limited to believers in the gambler's fallacy with one explanatory variable, focusing on the previous booking cancelled: 114.
Poisson inflation factor = (c)/(b) = 114/102. Poisson with interaction = OLS with interaction x Poisson inflation factor = (a) x (c)/(b) = 658 x 114/102 = 736.
Secondary analysis
The secondary analysis will be a Poisson regression in which the main coefficient of interest is an interaction. For Poisson regressions, GPower provides power analysis only for a single non-interacted variable. Accordingly, we calculated the required sample size as follows:
(a) OLS regression with three explanatory variables, focusing on the interaction, tutorial x previous booking cancelled: 69;
(b) OLS regression limited to previous booking cancelled with one explanatory variable, focusing on tutorial: 59;
(c) Poisson regression limited to previous booking cancelled with one explanatory variable, focusing on tutorial: 90.
Poisson inflation factor = (c)/(b) = 90/59. Poisson with interaction = OLS with interaction x Poisson inflation factor = (a) x (c)/(b) = 69 * 90/59 = 106.
Based on the previous study, 0.34 of subjects believe in the gambler's fallacy. Accordingly, the required sample for the secondary analysis is 106/0.34 = 312.
Considering both the main and secondary analyses, the required sample size is the larger of the required sample size for the two analyses, i.e., 736. In addition, we must allow for subjects not completing the survey . Based on the previous study, 0.2 of subjects did not complete the survey. Accordingly, the required sample (Planned Number of Observations) is 736/0.80 = 920.
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