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python进行方差分析_使用Python进行重复测量的双向方差分析
阅读量:2517 次
发布时间:2019-05-11

本文共 15751 字,大约阅读时间需要 52 分钟。

python进行方差分析

Previously I have shown how to analyze data collected using (i.e., R from within Python) and . In this post I will extend it into a factorial ANOVA using Python (i.e., ). In fact, we are going to carry out a Two-way ANOVA but the same method will enable you to analyze any factorial design. I start with importing the Python libraries that  are going to be use.

之前,我已经展示了如何 (即Python中的R)和分析使用收集的数据。 在本文中,我将使用Python(即 )将其扩展为阶乘方差分析。 实际上,我们将进行双向方差分析,但相同的方法将使您能够分析任何因子设计。 我首先导入将要使用的Python库。

import numpy as npimport pyvttbl as ptfrom collections import namedtupleimport numpy as npimport pyvttbl as ptfrom collections import namedtuple

Numpy is be used in simulating the data. I create a data set in which we have one factor of two levels (P) and a second factor of 3 levels (Q). As in many of my examples the dependent variable is going to be response time (rt) and we create a list of lists for the different population means we are going to assume (i.e., the variable ‘values’). I was a bit lazy when coming up with the data so I named the independent variables ‘iv1’ and ‘iv2’. However, you could think of iv1 as two different memory tasks; verbal and spatial memory. Iv2 could be different levels of distractions (no distraction, synthetic sounds, and speech, for instance).

Numpy用于模拟数据。 我创建了一个数据集,其中我们有一个因子为两个级别(P),第二个因子为3个级别(Q)。 正如在我的许多示例中一样,因变量将是响应时间(rt),并且我们将为不同的人口创建一个列表列表,这意味着我们要假设(即变量“值”)。 当我想出数据时我有点懒,所以我将自变量命名为“ iv1”和“ iv2”。 但是,您可以将iv1视为两个不同的内存任务; 语言和空间记忆。 Iv2可能是不同程度的干扰(例如,没有干扰,合成声音和语音)。

模拟数据 (Simulate data)

I start with a boxplot using the method boxplot from Pyvttbl. As far as I can see there is not much room for changing the plot around. We get this plot and it is really not that beautiful.

我首先使用Pyvttbl的boxplot方法创建一个boxplot。 据我所知,没有多少空间可以改变周围的情节。 我们得到了这个情节,它确实不是那么美丽。

df.box_plot('rt', factors=['iv1', 'iv2'])df.box_plot('rt', factors=['iv1', 'iv2'])
在进行Python双向ANOVA之前的箱线图
Boxplot Pyvttbl
箱线图

Python中对象内部设计的双向ANOVA (Two-way ANOVA for within-subjects design in Python)

To run the Two-Way ANOVA is simple; the first argument is the dependent variable, the second the subject identifier, and than the within-subject factors. In two previous posts I showed how to carry out and ANOVA for independent measures. One could, of course combine these techniques, to do a split-plot/mixed ANOVA by adding an argument ‘bfactors’ for the between-subject factor(s).

运行双向方差分析很简单; 第一个参数是因变量,第二个参数是主题标识符,而不是主题内因素。 在前两篇文章中,我展示了如何对独立措施进行和方差分析。 当然,可以通过为对象间因素添加自变量“ bfactors”来组合这些技术,以进行分割图/混合方差分析。

The output one get from this is an ANOVA table. In this table all metrics needed plus some more can be found; F-statistic, p-value, mean square errors, confidence intervals, effect size (i.e., eta-squared) for all factors and the interaction. Also, some corrected degree of freedom and mean square error can be found (e.g., Grenhouse-Geisser corrected). The output is in the end of the post. It is a bit hard to read.  If you know any other way to do a repeated measures ANOVA using Python please let me know. Also, if you happen to know that you can create nicer plots with Pyvttbl I would also like to know how! Please leave a comment.

从中得到的输出是ANOVA表。 在此表中,可以找到所有需要的指标以及更多指标。 所有因素的F统计量,p值,均方误差,置信区间,效应大小(即eta平方)和相互作用。 同样,可以找到某种校正后的自由度和均方误差(例如,Grenhouse-Geisser校正)。 输出在帖子末尾。 有点难读。 如果您知道使用Python执行重复测量方差分析的其他方法,请告诉我。 另外,如果您碰巧知道可以使用Pyvttbl创建更好的图,我也想知道如何! 请发表评论。

输出方差分析表 (Output ANOVA table)

rt ~ iv1 * iv2TESTS OF WITHIN SUBJECTS EFFECTSMeasure: rt  Source                            Type III      eps      df         MS           F        Sig.      et2_G   Obs.     SE     95% CI    lambda    Obs.                                         SS                                                                                                         Power =======================================================================================================================================================iv1           Sphericity Assumed   4419957.211       -        1   4419957.211   324.248   2.128e-13   3.295     60   16.096   31.548   1023.941       1               Greenhouse-Geisser   4419957.211       1        1   4419957.211   324.248   2.128e-13   3.295     60   16.096   31.548   1023.941       1               Huynh-Feldt          4419957.211       1        1   4419957.211   324.248   2.128e-13   3.295     60   16.096   31.548   1023.941       1               Box                  4419957.211       1        1   4419957.211   324.248   2.128e-13   3.295     60   16.096   31.548   1023.941       1 -------------------------------------------------------------------------------------------------------------------------------------------------------Error(iv1)    Sphericity Assumed    258996.722       -       19     13631.406                                                                                         Greenhouse-Geisser    258996.722       1       19     13631.406                                                                                         Huynh-Feldt           258996.722       1       19     13631.406                                                                                         Box                   258996.722       1       19     13631.406                                                                           -------------------------------------------------------------------------------------------------------------------------------------------------------iv2           Sphericity Assumed   5257766.564       -        2   2628883.282   206.008   4.023e-21   3.920     40   18.448   36.158    433.701       1               Greenhouse-Geisser   5257766.564   0.550    1.101   4777252.692   206.008   1.320e-12   3.920     40   18.448   36.158    433.701       1               Huynh-Feldt          5257766.564   0.550    1.101   4777252.692   206.008   1.320e-12   3.920     40   18.448   36.158    433.701       1               Box                  5257766.564   0.500        1   5257766.564   206.008   1.192e-11   3.920     40   18.448   36.158    433.701       1 -------------------------------------------------------------------------------------------------------------------------------------------------------Error(iv2)    Sphericity Assumed    484921.251       -       38     12761.086                                                                                         Greenhouse-Geisser    484921.251   0.550   20.911     23189.668                                                                                         Huynh-Feldt           484921.251   0.550   20.911     23189.668                                                                                         Box                   484921.251   0.500       19     25522.171                                                                           -------------------------------------------------------------------------------------------------------------------------------------------------------iv1 *         Sphericity Assumed   1622027.598       -        2    811013.799    83.220   1.304e-14   1.209     20   22.799   44.687     87.600   1.000 iv2           Greenhouse-Geisser   1622027.598   0.545    1.091   1486817.582    83.220   6.085e-09   1.209     20   22.799   44.687     87.600   1.000               Huynh-Feldt          1622027.598   0.545    1.091   1486817.582    83.220   6.085e-09   1.209     20   22.799   44.687     87.600   1.000               Box                  1622027.598   0.500        1   1622027.598    83.220   2.262e-08   1.209     20   22.799   44.687     87.600   1.000 -------------------------------------------------------------------------------------------------------------------------------------------------------Error(iv1 *   Sphericity Assumed    370327.311       -       38      9745.456                                                                           iv2)          Greenhouse-Geisser    370327.311   0.545   20.728     17866.175                                                                                         Huynh-Feldt           370327.311   0.545   20.728     17866.175                                                                                         Box                   370327.311   0.500       19     19490.911                                                                           TABLES OF ESTIMATED MARGINAL MEANSEstimated Marginal Means for iv1iv1    Mean     Std. Error   95% Lower Bound   95% Upper Bound ==============================================================1     983.755       43.162           899.157          1068.354 2     599.917       21.432           557.909           641.925 Estimated Marginal Means for iv2iv2     Mean     Std. Error   95% Lower Bound   95% Upper Bound ===============================================================1      525.025       19.324           487.150           562.899 2      814.197       49.416           717.342           911.053 3     1036.286       43.789           950.459          1122.114 Estimated Marginal Means for iv1 * iv2iv1   iv2     Mean     Std. Error   95% Lower Bound   95% Upper Bound =====================================================================1     1      553.522       24.212           506.066           600.978 1     2     1103.488       28.411          1047.804          1159.173 1     3     1294.256       19.773          1255.501          1333.011 2     1      496.528       29.346           439.009           554.047 2     2      524.906       20.207           485.301           564.512 2     3      778.317       21.815           735.560           821.073 rt ~ iv1 * iv2TESTS OF WITHIN SUBJECTS EFFECTSMeasure: rt  Source                            Type III      eps      df         MS           F        Sig.      et2_G   Obs.     SE     95% CI    lambda    Obs.                                         SS                                                                                                         Power =======================================================================================================================================================iv1           Sphericity Assumed   4419957.211       -        1   4419957.211   324.248   2.128e-13   3.295     60   16.096   31.548   1023.941       1               Greenhouse-Geisser   4419957.211       1        1   4419957.211   324.248   2.128e-13   3.295     60   16.096   31.548   1023.941       1               Huynh-Feldt          4419957.211       1        1   4419957.211   324.248   2.128e-13   3.295     60   16.096   31.548   1023.941       1               Box                  4419957.211       1        1   4419957.211   324.248   2.128e-13   3.295     60   16.096   31.548   1023.941       1 -------------------------------------------------------------------------------------------------------------------------------------------------------Error(iv1)    Sphericity Assumed    258996.722       -       19     13631.406                                                                                         Greenhouse-Geisser    258996.722       1       19     13631.406                                                                                         Huynh-Feldt           258996.722       1       19     13631.406                                                                                         Box                   258996.722       1       19     13631.406                                                                           -------------------------------------------------------------------------------------------------------------------------------------------------------iv2           Sphericity Assumed   5257766.564       -        2   2628883.282   206.008   4.023e-21   3.920     40   18.448   36.158    433.701       1               Greenhouse-Geisser   5257766.564   0.550    1.101   4777252.692   206.008   1.320e-12   3.920     40   18.448   36.158    433.701       1               Huynh-Feldt          5257766.564   0.550    1.101   4777252.692   206.008   1.320e-12   3.920     40   18.448   36.158    433.701       1               Box                  5257766.564   0.500        1   5257766.564   206.008   1.192e-11   3.920     40   18.448   36.158    433.701       1 -------------------------------------------------------------------------------------------------------------------------------------------------------Error(iv2)    Sphericity Assumed    484921.251       -       38     12761.086                                                                                         Greenhouse-Geisser    484921.251   0.550   20.911     23189.668                                                                                         Huynh-Feldt           484921.251   0.550   20.911     23189.668                                                                                         Box                   484921.251   0.500       19     25522.171                                                                           -------------------------------------------------------------------------------------------------------------------------------------------------------iv1 *         Sphericity Assumed   1622027.598       -        2    811013.799    83.220   1.304e-14   1.209     20   22.799   44.687     87.600   1.000 iv2           Greenhouse-Geisser   1622027.598   0.545    1.091   1486817.582    83.220   6.085e-09   1.209     20   22.799   44.687     87.600   1.000               Huynh-Feldt          1622027.598   0.545    1.091   1486817.582    83.220   6.085e-09   1.209     20   22.799   44.687     87.600   1.000               Box                  1622027.598   0.500        1   1622027.598    83.220   2.262e-08   1.209     20   22.799   44.687     87.600   1.000 -------------------------------------------------------------------------------------------------------------------------------------------------------Error(iv1 *   Sphericity Assumed    370327.311       -       38      9745.456                                                                           iv2)          Greenhouse-Geisser    370327.311   0.545   20.728     17866.175                                                                                         Huynh-Feldt           370327.311   0.545   20.728     17866.175                                                                                         Box                   370327.311   0.500       19     19490.911                                                                           TABLES OF ESTIMATED MARGINAL MEANSEstimated Marginal Means for iv1iv1    Mean     Std. Error   95% Lower Bound   95% Upper Bound ==============================================================1     983.755       43.162           899.157          1068.354 2     599.917       21.432           557.909           641.925 Estimated Marginal Means for iv2iv2     Mean     Std. Error   95% Lower Bound   95% Upper Bound ===============================================================1      525.025       19.324           487.150           562.899 2      814.197       49.416           717.342           911.053 3     1036.286       43.789           950.459          1122.114 Estimated Marginal Means for iv1 * iv2iv1   iv2     Mean     Std. Error   95% Lower Bound   95% Upper Bound =====================================================================1     1      553.522       24.212           506.066           600.978 1     2     1103.488       28.411          1047.804          1159.173 1     3     1294.256       19.773          1255.501          1333.011 2     1      496.528       29.346           439.009           554.047 2     2      524.906       20.207           485.301           564.512 2     3      778.317       21.815           735.560           821.073

翻译自:

python进行方差分析

转载地址:http://fhqwd.baihongyu.com/

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