====== 描述与假设检验 ======
>在线运行R:[[https://rdrr.io/snippets/]] [[https://learningstatisticswithr.com/|R入门教程]]
>[[https://repl.it/languages/rlang]]
>R 基础[[stat:3descntests:rsnipp]]
>[[https://rstudio.cloud/projects]]

>Scipy.stats:[[https://docs.scipy.org/doc/scipy/reference/stats.html]]
>statsmodels:[[http://www.statsmodels.org/stable/py-modindex.html]]
>DataFrame:[[http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.html#pandas.DataFrame]]
>sklearn:[[http://scikit-learn.org/stable/modules/classes.html#module-sklearn.linear_model]]
>Matplotlib subplot ax: [[https://matplotlib.org/api/axes_api.html]]
>Seaborn [[https://seaborn.pydata.org/api.html]]
>py-Bokeh作图包:[[http://bokeh.pydata.org/en/latest/docs/user_guide.html]]

>CheatSheet：[[https://github.com/pandas-dev/pandas/blob/master/doc/cheatsheet/Pandas_Cheat_Sheet.pdf]]

====CSV操作====
[[http://pandas.pydata.org/pandas-docs/stable/generated/pandas.read_csv.html|Pandas.read_csv]] [[http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.to_csv.html|pandas.to_csv]]
<code>
df = pd.read_csv('data.csv', encoding='utf-8')
df.to_csv('data.csv')
</code>
R
<code>
df<-read.table("save.dat")
df<-read.csv("file.csv")
write.table
</code>
====groupby操作====
[[http://blog.csdn.net/shenshaoqiu/article/details/78888602]]
=====数据初始处理=====
^ Name                    ^ Python                                                                                                                              ^ R                                                               ^ 备注  ^
^ 统计描述·describe           | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.describe.html#scipy.stats.describe|stats.describe]]              | summary() misc包describe() psych包describe() pastecs包stat.desc()  |     |
^ 算数均数·tmean              | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tmean.html#scipy.stats.tmean|stats.tmean]]                       |                                                                 |     |
^ 方差·variance             | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tvar.html#scipy.stats.tvar|stats.tvar]]                          |                                                                 |     |
^ 标准差·standard deviation  | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tstd.html#scipy.stats.tstd|stats.tstd]]                          |                                                                 |     |
^ 标准误·sem                 | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tsem.html#scipy.stats.tsem|stats.tsem]]                          |                                                                 |     |
^ 变异系数·variation          | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.variation.html#scipy.stats.variation|stats.variation]]           |                                                                 |     |
^ 几何均数·gmean              | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gmean.html#scipy.stats.gmean|stats.gmean]]                       |                                                                 |     |
^ 贝叶斯均数                   | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bayes_mvs.html#scipy.stats.bayes_mvs|stats.bayes_mvs]]           |                                                                 |     |
^ 调和平均数·hmean             | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.hmean.html#scipy.stats.hmean|stats.hmean]]                       |                                                                 |     |
^ 减尾后均数·trim_mean         | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.trim_mean.html#scipy.stats.trim_mean|stats.trim_mean]]           |                                                                 |     |
^ 峰度·kurtosis             | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kurtosis.html#scipy.stats.kurtosis|stats.kurtosis]]              |                                                                 |     |
^ 偏度·skewness             | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skew.html#scipy.stats.skew|stats.skew]]                          |                                                                 |     |
^ 查找重复值                   | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.find_repeats.html#scipy.stats.find_repeats|stats.find_repeats]]  |                                                                 |     |
^ 双减尾                     | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.trimboth.html#scipy.stats.trimboth|stats.trimboth]]              |                                                                 |     |
^ 单减尾                     | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.trim1.html#scipy.stats.trim1|stats.trim1]]                       |                                                                 |     |
===分布检验===
^ Name                                           ^ Python                                                                                                                                       ^ R  ^ 备注             ^
^ normaltest                                     | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html#scipy.stats.normaltest|stats.normaltest]]                 |    |                |
^ Shapiro-Wilk test for normality                | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html#scipy.stats.shapiro|stats.shapiro]]                          |    | 正态性            |
^ Kolmogorov-Smirnov test·KS检验                   | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html#scipy.stats.kstest|stats.kstest]]                             |    | 分布检验 需要连续分布资料  |
| :::                                            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ks_2samp.html#scipy.stats.ks_2samp|stats.ks_2samp]]                       |    | 比较分布           |
^ Anderson-Darling test                          | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html#scipy.stats.anderson|stats.anderson]]                       |    | 修改版的KS检验       |
| :::                                            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson_ksamp.html#scipy.stats.anderson_ksamp|stats.anderson_ksamp]]     |    |                |
^ kurtosistest                                   | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kurtosistest.html#scipy.stats.kurtosistest|stats.kurtosistest]]           |    |                |
^ skewtest                                       | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skewtest.html#scipy.stats.skewtest|stats.skewtest]]                       |    |                |
|                                                                                                                                                                                                                  ||||
^ O’Brien transform 方差齐性                         | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.obrientransform.html#scipy.stats.obrientransform|stats.obrientransform]]  |    |                |
^ Bartlett’s test for equal variances            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bartlett.html#scipy.stats.bartlett|stats.bartlett]]                       |    |                |
^ Levene test for equal variances                | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.levene.html#scipy.stats.levene|stats.levene]]                             |    | 显著非正态时         |
^ Jarque-Bera                                    | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.jarque_bera.html#scipy.stats.jarque_bera|stats.jarque_bera]]              |    |                |
^ Fligner-Killeen test for equality of variance  | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.fligner.html#scipy.stats.fligner|stats.fligner]]                          |    |                |

=====假设检验=====
^ Name                                    ^ 名称         ^ Python                                                                                                                                                                                                                             ^ R  ^ 备注          ^
^ Student's t-test                        | t检验        | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_1samp.html#scipy.stats.ttest_1samp|stats.ttest_1samp]]                                                                                                    |    |             |
| :::                                     | :::        | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html#scipy.stats.ttest_ind|stats.ttest_ind]]                                                                                                          |    |             |
| :::                                     | :::        | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind_from_stats.html#scipy.stats.ttest_ind_from_stats|stats.ttest_ind_from_stats]]                                                                         |    |             |
| :::                                     | :::        | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_rel.html#scipy.stats.ttest_rel|stats.ttest_rel]]                                                                                                          |    |             |
^ ANOVA                                   | 方差分析       | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f_oneway.html#scipy.stats.f_oneway|stats.f_oneway]]                                                                                                             |    | 独立、正态、方差齐性  |
|                                         | 方差不齐的多组比较  | [[https://stats.stackexchange.com/questions/91872/alternatives-to-one-way-anova-for-heteroskedastic-data|heteroskedastic]][[https://stats.stackexchange.com/questions/56971/alternative-to-one-way-anova-unequal-variance|alter]]  |    |             |
^ chisquare                               | 卡方检验       | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chisquare.html#scipy.stats.chisquare|stats.chisquare]]                                                                                                          |    |             |
^ chi2_contingency                        | 列联表        | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2_contingency.html#scipy.stats.chi2_contingency|stats.chi2_contingency]]                                                                                     |    |             |
^ Fisher exact test 2x2                   |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.fisher_exact.html#scipy.stats.fisher_exact|stats.fisher_exact]]                                                                                                 |    |             |
^ friedmanchisquare                       |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.friedmanchisquare.html#scipy.stats.friedmanchisquare|stats.friedmanchisquare]]                                                                                  |    |             |
^ combine_pvalues                         | 合并p值       | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.combine_pvalues.html#scipy.stats.combine_pvalues|stats.combine_pvalues]]                                                                                        |    |             |
^ pearsonr                                | 皮尔逊相关系数    | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html#scipy.stats.pearsonr|stats.pearsonr]]                                                                                                             |    |             |
^ pointbiserialr                          |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pointbiserialr.html#scipy.stats.pointbiserialr|stats.pointbiserialr]]                                                                                           |    |             |
^ linregress                              | 线性最小二乘回归   | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html#scipy.stats.linregress|stats.linregress]]                                                                                                       |    |             |
|                                                                                                                                                                                                                                                                                                          |||||
^ rankdata                                |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rankdata.html#scipy.stats.rankdata|stats.rankdata]]                                                                                                             |    |             |
^ Wilcoxon signed-rank test               |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wilcoxon.html#scipy.stats.wilcoxon|stats.wilcoxon]]                                                                                                             |    |             |
^ Wilcoxon  two samples                   |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ranksums.html#scipy.stats.ranksums|stats.ranksums]]                                                                                                             |    | 连续分布        |
^ mannwhitneyu                            |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html#scipy.stats.mannwhitneyu|stats.mannwhitneyu]]                                                                                                 |    | 连续分布        |
^ spearmanr                               | 斯皮尔曼等级相关   | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html#scipy.stats.spearmanr|stats.spearmanr]]                                                                                                          |    |             |
^ kendalltau                              |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kendalltau.html#scipy.stats.kendalltau|stats.kendalltau]]                                                                                                       |    |             |
^ weightedtau                             |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weightedtau.html#scipy.stats.weightedtau|stats.weightedtau]]                                                                                                    |    |             |
^ tiecorrect                              | U/KW检验校正   | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tiecorrect.html#scipy.stats.tiecorrect|stats.tiecorrect]]                                                                                                       |    |             |
^ Kruskal-Wallis H-test                   |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kruskal.html#scipy.stats.kruskal|stats.kruskal]]                                                                                                                |    | 非参版方差分析     |
^ Bernoulli experiment                    | 伯努利试验      | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom_test.html#scipy.stats.binom_test|stats.binom_test]]                                                                                                       |    |             |
^ Mood’s median test                      | 中位数检验      | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.median_test.html#scipy.stats.median_test|stats.median_test]]                                                                                                    |    |             |
^ Mood’s test for equal scale parameters  |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mood.html#scipy.stats.mood|stats.mood]]                                                                                                                         |    |             |
|                                                                                                                                                                                                                                                                                                          |||||
^ Box-Cox                                 |            |                                                                                                                                                                                                                                    |    |             |
^ Wasserstein distance                    |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wasserstein_distance.html#scipy.stats.wasserstein_distance|stats.wasserstein_distance]]                                                                         |    |             |
^ energy distance                         |            | [[https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.energy_distance.html#scipy.stats.energy_distance|stats.energy_distance]]                                                                                        |    |             |

====多重比较====
[[http://www.statsmodels.org/stable/stats.html#module-statsmodels.stats.multitest]]\\
[[http://www.statsmodels.org/stable/generated/statsmodels.sandbox.stats.multicomp.multipletests.html#statsmodels.sandbox.stats.multicomp.multipletests|statsmodels.sandbox.stats.multicomp.multipletests]]\\
[[http://www.statsmodels.org/stable/generated/statsmodels.sandbox.stats.multicomp.MultiComparison.html#statsmodels.sandbox.stats.multicomp.MultiComparison|statsmodels.sandbox.stats.multicomp.MultiComparison]]\\

方法比较[[http://www.medsci.cn/article/show_article.do?id=73743429933]]\\
Python post hoc包：[[https://github.com/maximtrp/scikit-posthocs]]\\

<code>|两两比较|LSD检验，Bonferroni法，tukey法，Scheffe法，SNK法|</code>

====方法选择====
<code>
1.连续数据，正态分布，线性关系，用pearson相关系数是最恰当，当然用spearman相关系数也可以，
  就是效率没有pearson相关系数高。
2.上述任一条件不满足，就用spearman相关系数，不能用pearson相关系数。
3.两个定序测量数据之间也用spearman相关系数，不能用pearson相关系数。
用pearson处理的数据，必须满足一下条件：成对数据、连续、整体是正态分布的。

其实, Spearman 和Pearson相关系数在算法上完全相同. 只是PEARSON相关系数是用原来的数值计算积差相关系数, 而SPEARMAN是用原来数值的秩次计算积差相关系数.
</code>
====方法选用标准====
|数据是否线性| |
|方差齐不齐|Satterthwate Wilcoxon|
|分布正态否|Bonferroni法校正P值 Wilcoxon检验 Fridman|
|多组完全随机|Kruscal－Wallis|

<code>
Fisher最小显著差异法（Fisher's Least Significant Difference test ）
学生t检验(Student's t-test)
曼-惠特尼 U 检定（Mann-Whitney U）
回归分析（regression analysis）
相关性（correlation）
皮尔森积矩相关系数(Pearson product-moment correlation coefficient)
史匹曼等级相关系数（Spearman's rank correlation coefficient ）
卡方分布（chi-square ）
</code>

====写作====
[[stat:tests:chiq]]