建设银行上海黄浦支行网站,网站建设搭建环境,学网站建设要多长时间,做it行业招标网站经典例题
某校高二年级共有四个班#xff0c;采用四种不同的教学方法进行数学教学#xff0c;为了比较这四种教学法的效果是否存在明显的差异#xff0c;期末统考后#xff0c;从这四个班中各抽取 5 名考生的成绩#xff0c;如下所示。 班级 一班 二班 三班 四班 …经典例题
某校高二年级共有四个班采用四种不同的教学方法进行数学教学为了比较这四种教学法的效果是否存在明显的差异期末统考后从这四个班中各抽取 5 名考生的成绩如下所示。 班级 一班 二班 三班 四班 1 75 93 65 72 2 77 80 67 70 3 70 85 77 71 4 88 90 68 65 5 72 84 65 81 6 80 86 64 72 7 79 85 62 68 8 81 81 68 74
问这四种教学法的效果是否存在显著性差异α 0.05
1.计算F值
import numpy as np
from scipy.stats import f_oneway# Data for the four classes
class1 [75, 77, 70, 88, 72, 80, 79, 81]
class2 [93, 80, 85, 90, 84, 86, 85, 81]
class3 [65, 67, 77, 68, 65, 64, 62, 68]
class4 [72, 70, 71, 65, 81, 72, 68, 74]# Perform one-way ANOVA
f_statistic, p_value f_oneway(class1, class2, class3, class4)# Output the results
print(F-statistic:, f_statistic)
print(P-value:, p_value)# Interpret the results
alpha 0.05
if p_value alpha:print(There is a significant difference in the effectiveness of the teaching methods.)
else:print(There is no significant difference in the effectiveness of the teaching methods.)F-statistic: 22.045992451864645
P-value: 1.5622062333927252e-07
There is a significant difference in the effectiveness of the teaching methods.
2.计算SS、df和F值
import numpy as np
import pandas as pd
from scipy.stats import f_oneway, f# Data for the four classes
class1 [75, 77, 70, 88, 72, 80, 79, 81]
class2 [93, 80, 85, 90, 84, 86, 85, 81]
class3 [65, 67, 77, 68, 65, 64, 62, 68]
class4 [72, 70, 71, 65, 81, 72, 68, 74]# Perform one-way ANOVA
f_statistic, p_value f_oneway(class1, class2, class3, class4)# Degrees of freedom
num_groups 4
num_samples len(class1) len(class2) len(class3) len(class4)
df_between num_groups - 1
df_within num_samples - num_groups# Calculate sum of squares (SS)
mean_total np.mean([np.mean(class1), np.mean(class2), np.mean(class3), np.mean(class4)])
ss_total np.sum((np.concatenate([class1, class2, class3, class4]) - mean_total) ** 2)
ss_between np.sum([len(class1) * (np.mean(class1) - mean_total) ** 2,len(class2) * (np.mean(class2) - mean_total) ** 2,len(class3) * (np.mean(class3) - mean_total) ** 2,len(class4) * (np.mean(class4) - mean_total) ** 2])
ss_within np.sum((class1 - np.mean(class1)) ** 2) \np.sum((class2 - np.mean(class2)) ** 2) \np.sum((class3 - np.mean(class3)) ** 2) \np.sum((class4 - np.mean(class4)) ** 2)# Calculate mean squares (MS)
ms_between ss_between / df_between
ms_within ss_within / df_within# Calculate F-statistic
f_statistic_manual ms_between / ms_within# Critical F-value
alpha 0.05
f_crit f.ppf(1 - alpha, df_between, df_within)# Create a DataFrame for better tabular representation
data {Class 1: class1,Class 2: class2,Class 3: class3,Class 4: class4,
}df pd.DataFrame(data)# Output the ANOVA results
print(Analysis of Variance (ANOVA):)
print(F-statistic (from scipy.stats):, f_statistic)
print(P-value (from scipy.stats):, p_value)
print(\nManual Calculation:)
print(SS Between:, ss_between)
print(SS Within:, ss_within)
print(DF Between:, df_between)
print(DF Within:, df_within)
print(MS Between:, ms_between)
print(MS Within:, ms_within)
print(F-statistic (manual calculation):, f_statistic_manual)
print(Critical F-value:, f_crit)# Interpret the results
if p_value alpha:print(\nThere is a significant difference in the effectiveness of the teaching methods.)
else:print(\nThere is no significant difference in the effectiveness of the teaching methods.)Manual Calculation:
SS Between: 1538.59375
SS Within: 651.375
DF Between: 3
DF Within: 28
MS Between: 512.8645833333334
MS Within: 23.263392857142858
F-statistic (manual calculation): 22.045992451864645
Critical F-value: 2.9466852660172655
