Hypothesis
Null hypothesis: the EEG spectral power is not different among groups (statistical null). Biological aspect means that chronic and heavy drinking does not have any effect on the brain activities (biological null).
Alternative hypothesis: the EEG spectral power is significantly different among groups (control, case 1, and case 2) and more significant between case 2 and control than between case 1 and control. This phenomenon indicates the alteration in the brain activities in AUD with more severity in alcoholics.
Sample Size Computation
Based on the hypothesis, EEG spectral power (absolute power or relative power) is selected as the test variable for sample size calculation; see Table 5.1. Because it is the measurement variable, the test is calculated and compared based on the mean value.
The convention in most biological research is to use a significance level a = 0.05 (Z_{a/2} = 1.96) and the power value в = 80% (Zp = 0.84). This means that
^{•} If the significant difference in mean power between two groups is larger than 5%, the null hypothesis can be rejected, or type I error.
Table 5.1 Sample size calculation
Reference |
Notes |
Alcoholics («i> |
Controls П) |
Mean difference (^1 - |
Standard deviation (SD) |
Effect size (ES) |
Sample size (n) |
Ehlers and Phillips^{8} |
Alpha power in P3 |
61 |
176 |
14.9 |
4.41 |
3.39 |
2 |
Alpha power in P4 |
61 |
176 |
18.3 |
5.33 |
3.45 |
2 |
• If the significant difference in mean power between two groups is smaller than 20%, the null hypothesis can be considered again.
There is no more information for estimating so these values are chosen for the significant test.
Because two independent samples are compared with respect to continuous outcome and difference in mean variable, the sample size per group can be estimated by^{15}:
where r: ratio of controls to cases; Z_{a/2}: represents the desired level of significant level; Zp. represents the desired power; ES: effect size.
The effect size can be computed for groups with different sample size by adjusting the calculation of the pooled standard deviation with weights for the sample sizes. This adjustment is overall identical with d_{Co}h_{en} or ?_{He}d_{ges} with a correction of a positive bias in the standard deviation.
where ]л_{1}, р_{2}: mean values of case group and control group; и_{ъ} n_{2}: sample size of case group and control group; s_{b} s_{2}: standard deviation of case group and control group.
The authors found a previous study by Ehlers and Phillips^{16} who investigated the association between alcohol dependence and EEG parameters. The mean and standard deviation of EEG alpha frequency at parietal sites P3 and P4 from the previous were used for sample size calculation. The calculated sample size is too small, i.e., sample size is 2 for one group or 6 for the total (3 groups). The reason is that there are huge differences between the mean of control and alcohol users of EEG alpha activity at parietal sites. Since the number 2 is quite small and the results of three groups with such a small number of participants may not be suitable for statistical test to compare results, the investigator recruited more participants in the study to be able to statistically verify the experimental results. Hence, 15 participants were recruited in the control group, as well as 18 alcoholic participants and 12 alcohol abusers.