4. A power analysis for a one-sample t test A Aa Neck injuries can be very painful and prevent patients from working for a significant time period. Suppose an alternative medicine center decides to do a research project on how meditation affedts recovery time. The hypothesis of this study is that the mean rate of recovery with meditation is different than with the standard treatment, or Ho Hereditation - Putandard treatment Hs: meditation utandard trent. You know from previous studies that the rate of recovery for people with neck injuries who receive the standard treatment has a mean - 4.14 and a standard deviation a 1.12. Prior empirical evidence suggests that the meditation treatment effect is 0.40 weeks shorter than the standard treatment, with a standard deviation equivalent to that of the standard treatment. You want to determine whether a sample size of 81 will have sufficient power to detect the suggested difference between the mean number of weeks to recovery for patients receiving meditation treatment and the mean number of weeks to recovery for those receiving the standard treatment. The alternative medicine center requires the power of the test (given the proposed treatment effect has occurred) to be 0.9500 or greater in order to conduct its study without first increasing the sample size You intend to use a one-sample t test to test the null hypothesis. Based on the prior evidence, the estimated effect Size, a, that you can use to calculate the power before you begin the study is To use the power table that uses delta (6) and the significance level (o) to compute the power, you first need to calculate 8 delta), the measure that combines a and the sample size. The value of 8 for this one-sample t test when you're contemplating a sample size of Bis To see the entire power table that follows, click on the downward-pointing arrow to the right of the box that says Table: Power. The significance level you intend to use for your two-tailed test is a = 01. With a sample size of 81, the estimated power of your test is Table Power Your study with a sample size of 81 satisfy the power requirements of the alternative medicine center Suppose the alternative medicine center requires the power of the test to be 0.8. The minimum sample size needed to meet this requirement with a = .01 is Alpha (a) for a Two-Tailed Hypothesis Test 0.10 0.05 0.02 0.01 Delta (8) 1.00 0.26 0.17 0.09 0.06 1.10 0.29 0.19 0.11 0.07 1.20 0.33 0.22 0.08 0.13 0.15 1.30 0.37 0.25 0.10 1.40 0.40 0.29 0.18 0.12 1.50 0.44 0.32 0.20 0.14 1.60 0.48 0.36 0.23 0.16 1.70 0.52 0.40 0.27 0.19 1.80 0.56 0.44 0.30 0.22 1.90 0.60 0.48 0.33 0.25 2.00 0.64 0.52 0.37 0.28 0.68 0.56 0.41 0.32 2.10 2.20 0.71 0.59 0.45 0.35 2.30 0.74 0.63 0.49 0.39 2.40 0.77 0.67 0.53 0.43 2.50 0.80 0.71 0.57 0.47 2.60 0.83 0.74 0.61 0.51 0.85 2.70 0.77 0.65 0.55 0.88 2.80 0.80 0.68 0.59 0.90 0.83 0.72 2.90 0.63 3.00 0.85 0.75 0.91 0.66 3.10 0.93 0.87 0.78 0.70 0.81 3.20 0.89 0.73 0.94 TINDTAP oblem Set 3.20 0.94 0.89 0.81 0.73 3.30 0.95 0.91 0.83 0.77 3.40 0.96 0.93 0.86 0.80 3.50 0.97 0.94 0.88 0.82 3.60 0.97 0.95 0.90 0.85 3.70 0.98 0.96 0.92 0.87 3.80 0.98 0.97 0.93 0.89 3.90 0.99 0.97 0.94 0.91 4.00 0.99 0.98 0.95 0.92 4.10 0.99 0.98 0.96 0.94 4.20 0.99 0.99 0.97 0.95 4.30 1.00 0.99 0.98 0.96 4.40 1.00 0.99 0.98 0.97 4.50 1.00 0.99 0.99 0.97 4.60 1.00 1.00 0.99 0.98 4.70 1.00 1.00 0.99 0.98 4.80 1.00 1.00 0.99 0.99 4.90 1.00 1.00 0.99 0.99 5.00 1.00 1.00 1.00 0.99 4. A power analysis for a one-sample t test A Aa Neck injuries can be very painful and prevent patients from working for a significant time period. Suppose an alternative medicine center decides to do a research project on how meditation affedts recovery time. The hypothesis of this study is that the mean rate of recovery with meditation is different than with the standard treatment, or Ho Hereditation - Putandard treatment Hs: meditation utandard trent. You know from previous studies that the rate of recovery for people with neck injuries who receive the standard treatment has a mean - 4.14 and a standard deviation a 1.12. Prior empirical evidence suggests that the meditation treatment effect is 0.40 weeks shorter than the standard treatment, with a standard deviation equivalent to that of the standard treatment. You want to determine whether a sample size of 81 will have sufficient power to detect the suggested difference between the mean number of weeks to recovery for patients receiving meditation treatment and the mean number of weeks to recovery for those receiving the standard treatment. The alternative medicine center requires the power of the test (given the proposed treatment effect has occurred) to be 0.9500 or greater in order to conduct its study without first increasing the sample size You intend to use a one-sample t test to test the null hypothesis. Based on the prior evidence, the estimated effect Size, a, that you can use to calculate the power before you begin the study is To use the power table that uses delta (6) and the significance level (o) to compute the power, you first need to calculate 8 delta), the measure that combines a and the sample size. The value of 8 for this one-sample t test when you're contemplating a sample size of Bis To see the entire power table that follows, click on the downward-pointing arrow to the right of the box that says Table: Power. The significance level you intend to use for your two-tailed test is a = 01. With a sample size of 81, the estimated power of your test is Table Power Your study with a sample size of 81 satisfy the power requirements of the alternative medicine center Suppose the alternative medicine center requires the power of the test to be 0.8. The minimum sample size needed to meet this requirement with a = .01 is Alpha (a) for a Two-Tailed Hypothesis Test 0.10 0.05 0.02 0.01 Delta (8) 1.00 0.26 0.17 0.09 0.06 1.10 0.29 0.19 0.11 0.07 1.20 0.33 0.22 0.08 0.13 0.15 1.30 0.37 0.25 0.10 1.40 0.40 0.29 0.18 0.12 1.50 0.44 0.32 0.20 0.14 1.60 0.48 0.36 0.23 0.16 1.70 0.52 0.40 0.27 0.19 1.80 0.56 0.44 0.30 0.22 1.90 0.60 0.48 0.33 0.25 2.00 0.64 0.52 0.37 0.28 0.68 0.56 0.41 0.32 2.10 2.20 0.71 0.59 0.45 0.35 2.30 0.74 0.63 0.49 0.39 2.40 0.77 0.67 0.53 0.43 2.50 0.80 0.71 0.57 0.47 2.60 0.83 0.74 0.61 0.51 0.85 2.70 0.77 0.65 0.55 0.88 2.80 0.80 0.68 0.59 0.90 0.83 0.72 2.90 0.63 3.00 0.85 0.75 0.91 0.66 3.10 0.93 0.87 0.78 0.70 0.81 3.20 0.89 0.73 0.94 TINDTAP oblem Set 3.20 0.94 0.89 0.81 0.73 3.30 0.95 0.91 0.83 0.77 3.40 0.96 0.93 0.86 0.80 3.50 0.97 0.94 0.88 0.82 3.60 0.97 0.95 0.90 0.85 3.70 0.98 0.96 0.92 0.87 3.80 0.98 0.97 0.93 0.89 3.90 0.99 0.97 0.94 0.91 4.00 0.99 0.98 0.95 0.92 4.10 0.99 0.98 0.96 0.94 4.20 0.99 0.99 0.97 0.95 4.30 1.00 0.99 0.98 0.96 4.40 1.00 0.99 0.98 0.97 4.50 1.00 0.99 0.99 0.97 4.60 1.00 1.00 0.99 0.98 4.70 1.00 1.00 0.99 0.98 4.80 1.00 1.00 0.99 0.99 4.90 1.00 1.00 0.99 0.99 5.00 1.00 1.00 1.00 0.99