如何计算 python 中的（统计）幂函数与样本量？

Question

如何在 python 中完成？

计算给定功效和 alpha 的样本量？
计算给定样本大小和 alpha 的功效？

注：我对 python 给出的（统计）幂函数计算函数感到非常困惑 :(

有人可以帮我在这里下单吗？

statsmodels下有两个函数：

from statsmodels.stats.power import ttest_power, tt_ind_solve_power()

我们有：

tt_ind_solve_power(effect_size=effect_size, alpha=alpha, power=0.8, ratio=1, alternative='two-sided')

我们还有：

ttest_power(0.2, nobs=sampleSize, alpha=alpha, alternative='two-sided')

还有这段代码：

import statsmodels.stats.api as sms
es = sms.proportion_effectsize(prop1, prop2, method='normal')
n = sms.NormalIndPower().solve_power(es, power=0.9, alpha=0.05, ratio=2)

我在某处找到了这个例子，但它没有解释什么是 prop1 和 prop2！

每一个都给我不同的价值观。

谢谢

Answer 1

作为对上述问题的回答，我编写了这个计算功效与样本大小的函数。

调用tt_ind_solve_power时需要留一个参数None，以便计算。在下面的示例中，我将电源保持为 None.

我希望有人会觉得它有用，欢迎任何改进。

from statsmodels.stats.power import  tt_ind_solve_power
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt

def test_ttest_power_diff(mean, std, sample1_size=None, alpha=0.05, desired_power=0.8, mean_diff_percentages=[0.1, 0.05]):
    '''
    calculates the power function for a given mean and std. the function plots a graph showing the comparison between desired mean differences
    :param mean: the desired mean
    :param std: the std value
    :param sample1_size: if None, it is assumed that both samples (first and second) will have same size. The function then will
    walk through possible sample sizes (up to 100, hardcoded).
    If this value is not None, the function will check different alternatives for sample 2 sizes up to sample 1 size.
    :param alpha: alpha default value is 0.05
    :param desired_power: will use this value in order to mark on the graph
    :param mean_diff_percentages: iterable list of percentages. A line per value will be calculated and plotted.
    :return: None
    '''
    fig, ax = plt.subplots()
    for mean_diff_percent in mean_diff_percentages:
        mean_diff = mean_diff_percent * mean
        effect_size = mean_diff / std

        print('Mean diff: ', mean_diff)
        print('Effect size: ', effect_size)

        powers = []

        max_size  = sample1_size
        if sample1_size is None:
            max_size = 100

        sizes = np.arange(1, max_size, 2)
        for sample2_size in sizes:
            if(sample1_size is None):
                n = tt_ind_solve_power(effect_size=effect_size, nobs1=sample2_size, alpha=alpha, ratio=1.0, alternative='two-sided')
                print('tt_ind_solve_power(alpha=', alpha, 'sample2_size=', sample2_size, '): sample size in *second* group: {:.5f}'.format(n))
            else:
                n = tt_ind_solve_power(effect_size=effect_size, nobs1=sample1_size, alpha=alpha, ratio=(1.0*sample2_size/sample1_size), alternative='two-sided')
                print('tt_ind_solve_power(alpha=', alpha, 'sample2_size=', sample2_size, '): sample size *each* group: {:.5f}'.format(n))

            powers.append(n)

        try: # mark the desired power on the graph
            z1 = interp1d(powers, sizes)
            results = z1(desired_power)

            plt.plot([results], [desired_power], 'gD')
        except Exception as e:
            print("Error: ", e)
            #ignore

        plt.title('Power vs. Sample Size')
        plt.xlabel('Sample Size')
        plt.ylabel('Power')

        plt.plot(sizes, powers, label='diff={:2.0f}%'.format(100*mean_diff_percent)) #, '-gD')

    plt.legend()
    plt.show()

例如，如果您使用 mean=10 和 std=2 调用此函数，您将得到此图：

如何计算 python 中的（统计）幂函数与样本量？

How to calculate (statistical) power function vs. sample size in python?

python

statistics

t-test

sample-size