[Python] 적절한 샘플 사이즈를 찾아주는 코드

모집단이 클 경우에는 샘플링을 통해 시각화를 위해서나 통계치를 뽑아줘야 할 것이다.

 

이때 가장 적절한 샘플사이즈를 알려주는 코드가 있어서 공유한다.

 

그리고 각각에 대해서 분포별로 실험을 진행해봤다.

 

def sampleSize(
    population_size,
    margin_error=.05,
    confidence_level=.99,
    sigma=1/2
):
    """
    Calculate the minimal sample size to use to achieve a certain
    margin of error and confidence level for a sample estimate
    of the population mean.
    Inputs
    -------
    population_size: integer
        Total size of the population that the sample is to be drawn from.
    margin_error: number
        Maximum expected difference between the true population parameter,
        such as the mean, and the sample estimate.
    confidence_level: number in the interval (0, 1)
        If we were to draw a large number of equal-size samples
        from the population, the true population parameter
        should lie within this percentage
        of the intervals (sample_parameter - e, sample_parameter + e)
        where e is the margin_error.
    sigma: number
        The standard deviation of the population.  For the case
        of estimating a parameter in the interval [0, 1], sigma=1/2
        should be sufficient.
    """
    alpha = 1 - (confidence_level)
    # dictionary of confidence levels and corresponding z-scores
    # computed via norm.ppf(1 - (alpha/2)), where norm is
    # a normal distribution object in scipy.stats.
    # Here, ppf is the percentile point function.
    zdict = {
        .90: 1.645,
        .91: 1.695,
        .99: 2.576,
        .97: 2.17,
        .94: 1.881,
        .93: 1.812,
        .95: 1.96,
        .98: 2.326,
        .96: 2.054,
        .92: 1.751
    }
    if confidence_level in zdict:
        z = zdict[confidence_level]
    else:
        from scipy.stats import norm
        z = norm.ppf(1 - (alpha/2))
    N = population_size
    M = margin_error
    numerator = z**2 * sigma**2 * (N / (N-1))
    denom = M**2 + ((z**2 * sigma**2)/(N-1))
    return int(numerator/denom)

 

노말 분포

population_sizes = np.arange(100,10000,1000)
num_plots = len(population_sizes)
total_cols = 4
total_rows = num_plots//total_cols + 1
fig, axs = plt.subplots(nrows=total_rows, ncols=total_cols,
                        figsize=(7*total_cols, 7*total_rows), constrained_layout=True)
for i , population_size in enumerate(population_sizes):
    row = i//total_cols
    pos = i % total_cols
    population_ = np.random.normal(size=population_size)
    sample_ = np.random.choice(population_, sampleSize(population_size))
    sns.distplot(population_,ax=axs[row][pos])
    sns.distplot(sample_,ax=axs[row][pos])
    axs[row][pos].set_title(f"population size : {population_size}",size=30)
if total_rows * total_cols > len(population_sizes) :
    remainder_n = total_rows * total_cols - len(population_sizes)
    for i in range(remainder_n) :
        axs[row][-(i+1)].axis("off")
plt.show()

베타 분포 -1 

population_sizes = np.arange(100,10000,1000)
num_plots = len(population_sizes)
total_cols = 4
total_rows = num_plots//total_cols + 1
fig, axs = plt.subplots(nrows=total_rows, ncols=total_cols,
                        figsize=(7*total_cols, 7*total_rows), constrained_layout=True)
for i , population_size in enumerate(population_sizes):
    row = i//total_cols
    pos = i % total_cols
    population_ = np.random.beta(a=0.5,b=0.5,size=population_size)
    sample_ = np.random.choice(population_, sampleSize(population_size))
    sns.distplot(population_,ax=axs[row][pos])
    sns.distplot(sample_,ax=axs[row][pos])
    axs[row][pos].set_title(f"population size : {population_size}",size=30)
if total_rows * total_cols > len(population_sizes) :
    remainder_n = total_rows * total_cols - len(population_sizes)
    for i in range(remainder_n) :
        axs[row][-(i+1)].axis("off")
plt.show()

베타 분포 -2

population_sizes = np.arange(100,10000,1000)
num_plots = len(population_sizes)
total_cols = 4
total_rows = num_plots//total_cols + 1
fig, axs = plt.subplots(nrows=total_rows, ncols=total_cols,
                        figsize=(7*total_cols, 7*total_rows), constrained_layout=True)
for i , population_size in enumerate(population_sizes):
    row = i//total_cols
    pos = i % total_cols
    population_ = np.random.beta(a=0.9,b=0.5,size=population_size)
    sample_ = np.random.choice(population_, sampleSize(population_size))
    sns.distplot(population_,ax=axs[row][pos])
    sns.distplot(sample_,ax=axs[row][pos])
    axs[row][pos].set_title(f"population size : {population_size}",size=30)
if total_rows * total_cols > len(population_sizes) :
    remainder_n = total_rows * total_cols - len(population_sizes)
    for i in range(remainder_n) :
        axs[row][-(i+1)].axis("off")
plt.show()

mixture distribution

population_sizes = np.arange(100,10000,1000)
num_plots = len(population_sizes)
total_cols = 4
total_rows = num_plots//total_cols + 1
fig, axs = plt.subplots(nrows=total_rows, ncols=total_cols,
                        figsize=(7*total_cols, 7*total_rows), constrained_layout=True)
for i , population_size in enumerate(population_sizes):
    row = i//total_cols
    pos = i % total_cols
    mean = (-4, 2)
    cov = [[1, 0], [0, 1]]
    population_ = np.random.multivariate_normal(mean, cov, size=population_size).reshape(-1,)
    sample_ = np.random.choice(population_, sampleSize(population_size))
    sns.distplot(population_,ax=axs[row][pos])
    sns.distplot(sample_,ax=axs[row][pos])
    axs[row][pos].set_title(f"population size : {population_size}",size=30)
if total_rows * total_cols > len(population_sizes) :
    remainder_n = total_rows * total_cols - len(population_sizes)
    for i in range(remainder_n) :
        axs[row][-(i+1)].axis("off")
plt.show()