[Python] how to prove the significant difference between the two groups of samples (t-test hypothesis test)

Address: http://blog.csdn.net/ariesjzj/article/details/7546930

 

There are two sets of sample data. If they are based on two different methods, or tested on different devices, or from two people, how can they prove that they have or are not significantly different? Of course, you can use an Excel table to draw a chart of the data, and then find a bunch of people to vote, to see who thinks the number of votes is much lower. However, this practice is subjective and not enough explanatory power. Probability statistics provides a more objective statistical-based method. Here is a python implementation:

#!/usr/bin/python# Paired difference hypothesis testing - Student's t-test# Author:       Jin Zhuojun# History:      Create      Tue May  8 16:12:21 CST 2012import stringimport mathimport sysfrom scipy.stats import  timport matplotlib.pyplot as pltimport numpy as np############### Parameters ###############ver = 1verbose = 0alpha = 0.05def usage():    print """    usage: ./program data_file(one sample in one line)    """def main():    ##########    # Sample #    ##########    if (len(sys.argv) < 2):        usage()        sys.exit()    # f = open('./data.txt')    # f = open('./test.txt')    f = open(sys.argv[1])    try:        sample1_text = f.readline()        sample2_text = f.readline()    finally:        f.close()    if (verbose):        print("sample1 text: ", sample1_text)        print("sample2 text: ", sample2_text)    sample1_text_split = sample1_text.split()    sample2_text_split = sample2_text.split()    if (verbose):        print(sample1_text_split)        print(sample2_text_split)        print("len = ", len(sample1_text_split))    assert(len(sample1_text_split) == len(sample2_text_split))    sample_len = len(sample1_text_split)    sample1 = []    sample2 = []    for i in range(sample_len):        sample1.append(string.atof(sample1_text_split[i]))        sample2.append(string.atof(sample2_text_split[i]))    sample_diff = []    for i in range(sample_len):        sample_diff.append(sample1[i] - sample2[i])    if (verbose):        print("sample_diff = ", sample_diff)    ######################    # Hypothesis testing #    ######################    sample = sample_diff    numargs = t.numargs    [ df ] = [sample_len - 1,] * numargs    if (verbose):        print("df(degree of freedom, student's t distribution parameter) = ", df)    sample_mean = np.mean(sample)    sample_std = np.std(sample, dtype=np.float64, ddof=1)    if (verbose):        print("mean = %f, std = %f" % (sample_mean, sample_std))    abs_t = math.fabs( sample_mean / (sample_std / math.sqrt(sample_len)) )    if (verbose):        print("t = ", abs_t)    t_alpha_percentile = t.ppf(1 - alpha / 2, df)    if (verbose):        print("abs_t = ", abs_t)        print("t_alpha_percentile = ", t_alpha_percentile)    if (abs_t >= t_alpha_percentile):        print "REJECT the null hypothesis"    else:        print "ACCEPT the null hypothesis"    ########    # Plot #    ########    rv = t(df)    limit = np.minimum(rv.dist.b, 5)    x = np.linspace(-1 * limit, limit)    h = plt.plot(x, rv.pdf(x))    plt.xlabel('x')    plt.ylabel('t(x)')    plt.title('Difference significance test')    plt.grid(True)    plt.axvline(x = t_alpha_percentile, ymin = 0, ymax = 0.095,             linewidth=2, color='r')    plt.axvline(x = abs_t, ymin = 0, ymax = 0.6,             linewidth=2, color='g')    plt.annotate(r'(1 - $\alpha$ / 2) percentile', xy = (t_alpha_percentile, 0.05),            xytext=(t_alpha_percentile + 0.5, 0.09), arrowprops=dict(facecolor = 'black', shrink = 0.05),)    plt.annotate('t value', xy = (abs_t, 0.26),            xytext=(abs_t + 0.5, 0.30), arrowprops=dict(facecolor = 'black', shrink = 0.05),)    leg = plt.legend(('Student\'s t distribution', r'(1 - $\alpha$ / 2) percentile', 't value'),             'upper left', shadow = True)    frame = leg.get_frame()    frame.set_facecolor('0.80')    for i in leg.get_texts():        i.set_fontsize('small')    for l in leg.get_lines():        l.set_linewidth(1.5)    normalized_sample = [0] * sample_len     for i in range(0, sample_len):        normalized_sample[i] = (sample[i] - sample_mean) / (sample_std / math.sqrt(sample_len))    plt.plot(normalized_sample, [0] * len(normalized_sample), 'ro')    plt.show()if __name__ == "__main__":    main()

Note: When matplotlib is displayed, the ratio of coordinates is always incorrect, so the coordinates are written to death when drawing.

Save the scripts as main.py, and then use the data file data.txt (each line indicates a group of samples ):

0.26 0.30 0.40 0.49 0.43 0.84 1.18 0.25
0.18 0.33 0.57 0.32 0.58 0.29 0.98 0.17

Run:

$./Main. py data.txt

Get

Here we assume that null hypothesis has no significant difference between the two groups of data, and alternative hypothesis has a significant difference ., T value falls outside the rejection range, so we reject alternative hypothesis and accept null hypothesis, that is, there is no significant difference between the two groups of data.