Function Reference¶

Hypothesize exposes the following top-level functions for comparing groups and measuring associations. The function names, code, and descriptions are kept generally consistent with Wilcox's WRS package. If you want to learn more about the theory and research behind any given function here, see Wilcox's books, especially Introduction to Robust Estimation and Hypothesis Testing.

Jump to:

Comparing groups with a single factor

Comparing groups with two factors

Measuring associations

Other important functions

Comparing groups with a single factor¶

Statistical tests analogous to a 1-way ANOVA or T-tests. That is, group tests that have a single factor.

Independent groups¶

l2drmci¶

hypothesize.compare_groups_with_single_factor.l2drmci(x, y, est, *args, pairwise_drop_na=True, alpha=.05, nboot=2000, seed=False)

Compute a bootstrap confidence interval for a measure of location associated with the distribution of x-y. That is, compare x and y by looking at all possible difference scores in random samples of x and y. x and y are possibly dependent.

Note that arguments up to and including args are positional arguments

Parameters:

x: Pandas Series

Data for group one

y: Pandas Series

Data for group two

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

pairwise_drop_na: bool

If True, treat data as dependent and remove any row with missing data. If False, remove missing data for each group seperately (cannot deal with unequal sample sizes)

alpha: float

Alpha level (default is .05)

nboot: int

Number of bootstrap samples (default is 2000)

seed: bool

Random seed for reproducible results (default is False)

Returns:

Dictionary of results

ci: list

Confidence interval

p_value: float

p-value

linconb¶

hypothesize.compare_groups_with_single_factor.linconb(x, con, tr=.2, alpha=.05, nboot=599, seed=False)

Compute a 1-alpha confidence interval for a set of d linear contrasts involving trimmed means using the bootstrap-t bootstrap method. Independent groups are assumed. CIs are adjusted to control FWE (p values are not adjusted).

Parameters:

x: DataFrame

Each column represents a group of data

con: array

con is a J (number of columns) by d (number of contrasts) matrix containing the contrast coefficents of interest. All linear constrasts can be created automatically by using the function con1way (the result of which can be used for con).

tr: float

Proportion to trim (default is .2)

alpha: float

Alpha level (default is .05)

nboot: int

Number of bootstrap samples (default is 2000)

seed: bool

Random seed for reproducible results. Default is False.

Return:

Dictionary of results

con: array

Contrast matrix

crit: float

Critical value

n: list

Number of observations for each group

psihat: DataFrame

Difference score and CI for each contrast

test: DataFrame

Test statistic, standard error, and p-value for each contrast

pb2gen¶

hypothesize.compare_groups_with_single_factor.pb2gen(x, y, est, *args, alpha=.05, nboot=2000, seed=False)

Compute a bootstrap confidence interval for the the difference between any two parameters corresponding to two independent groups.

Note that arguments up to and including args are positional arguments

Parameters:

x: Pandas Series

Data for group one

y: Pandas Series

Data for group two

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

alpha: float

Alpha level (default is .05)

nboot: int

Number of bootstrap samples (default is 2000)

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

ci: list

Confidence interval

est_1: float

Estimated value (based on est) for group one

est_2: float

Estimated value (based on est) for group two

est_dif: float

Estimated difference between group one and two

n1: int

Number of observations in group one

n2: int

Number of observations in group two

p_value: float

p-value

variance: float

Variance of group one and two

tmcppb¶

hypothesize.compare_groups_with_single_factor.tmcppb(x, est, *args, con=None, bhop=False, alpha=.05, nboot=None, seed=False)

Multiple comparisons for J independent groups using trimmed means and the percentile bootstrap method. Rom’s method is used to control the probability of one or more type I errors. For C > 10 hypotheses, or when the goal is to test at some level other than .05 and .01, Hochberg’s method is used. Setting the argument bhop to True uses the Benjamini–Hochberg method instead.

Note that arguments up to and including args are positional arguments

Parameters:

x: Pandas DataFrame

Each column represents a group of data

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

con: array

con is a J (number of columns) by d (number of contrasts) matrix containing the contrast coefficents of interest. All linear constrasts can be created automatically by using the function con1way (the result of which can be used for con). The default is None and in this case all linear contrasts are created automatically.

bhop: bool

If True, the Benjamini–Hochberg method is used to control FWE

alpha: float

Alpha level. Default is .05.

nboot: int

Number of bootstrap samples (default is 2000)

seed: bool

Random seed for reproducible results. Default is False.

Return:

Dictionary of results

con: array

Contrast matrix

num_sig: int

Number of statistically significant results

output: DataFrame

Difference score, p-value, critical value, and CI for each contrast

yuenbt¶

hypothesize.compare_groups_with_single_factor.yuenbt(x, y, tr=.2, alpha=.05, nboot=599, seed=False)

Compute a 1-alpha confidence interval for the difference between the trimmed means corresponding to two independent groups. The bootstrap-t method is used. During the bootstrapping, the absolute value of the test statistic is used (the "two-sided method").

Parameters:

x: Pandas Series

Data for group one

y: Pandas Series

Data for group two

tr: float

Proportion to trim (default is .2)

alpha: float

Alpha level (default is .05)

nboot: int

Number of bootstrap samples (default is 599)

seed: bool

Random seed for reproducible results. Default is False.

Return:

Dictionary of results

ci: list

Confidence interval

est_dif: float

Estimated difference between group one and two

est_1: float

Estimated value (based on est) for group one

est_2: float

Estimated value (based on est) for group two

p_value: float

p-value

test_stat: float

Test statistic

Dependent groups¶

bootdpci¶

hypothesize.compare_groups_with_single_factor.bootdpci(x, est, *args, nboot=None, alpha=.05, dif=True, BA=False, SR=False)

Use percentile bootstrap method, compute a .95 confidence interval for the difference between a measure of location or scale when comparing two dependent groups.

Note that arguments up to and including args are positional arguments

The argument dif defaults to True indicating that difference scores will be used, in which case Hochberg’s method is used to control FWE. If dif is False, measures of location associated with the marginal distributions are used instead.

If dif is False and BA is True, the bias adjusted estimate of the generalized p-value is recommended. Using BA=True (when dif=False) is recommended when comparing groups with M-estimators and MOM, but it is not necessary when comparing 20% trimmed means (Wilcox & Keselman, 2002).

The so-called the SR method, which is a slight modification of Hochberg's (1988) "sequentially rejective" method can be applied to control FWE, especially when comparing one-step M-estimators or M-estimators.

Parameters:

x: Pandas DataFrame

Each column represents a group of data

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

alpha: float

Alpha level. Default is .05.

nboot: int

Number of bootstrap samples. Default is None in which case nboot will be chosen for you based on the number of contrasts.

dif: bool

When True, use difference scores, otherwise use marginal distributions

BA: bool

When True, use the bias adjusted estimate of the generalized p-value is applied (e.g., when dif is False)

SR: bool

When True, use the modified "sequentially rejective", especially when comparing one-step M-estimators or M-estimators

Return:

Dictionary of results

con: array

Contrast matrix

num_sig: int

Number of statistically significant results

output: DataFrame

Difference score, p-value, critical value, and CI for each contrast

rmmcppb¶

hypothesize.compare_groups_with_single_factor.rmmcppb(x, est, *args, alpha=.05, con=None, dif=True, nboot=None, BA=False,hoch=False, SR=False, seed=False)

Use a percentile bootstrap method to compare dependent groups. By default, compute a .95 confidence interval for all linear contrasts specified by con, a J-by-C matrix, where C is the number of contrasts to be tested, and the columns of con are the contrast coefficients. If con is not specified, all pairwise comparisons are done.

If est is the function onestep or mom (these are not implemeted yet), method SR can be used to control the probability of at least one Type I error. Otherwise, Hochberg's method is used.

If dif is False and BA is True, the bias adjusted estimate of the generalized p-value is recommended. Using BA=True (when dif=False) is recommended when comparing groups with M-estimators and MOM, but it is not necessary when comparing 20% trimmed means (Wilcox & Keselman, 2002).

Hochberg's sequentially rejective method can be used and is used if n>=80.

Note that arguments up to and including args are positional arguments

Parameters:

x: Pandas DataFrame

Each column represents a group of data

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

alpha: float

Alpha level (default is .05)

con: array

con is a J (number of columns) by d (number of contrasts) matrix containing the contrast coefficents of interest. All linear constrasts can be created automatically by using the function con1way (the result of which can be used for con). The default is None and in this case all linear contrasts are created automatically.

dif: bool

When True, use difference scores, otherwise use marginal distributions

nboot: int

Number of bootstrap samples. Default is None in which case nboot will be chosen for you based on the number of contrasts.

BA: bool

When True, use the bias adjusted estimate of the generalized p-value is applied (e.g., when dif is False)

hoch: bool

When True, Hochberg's sequentially rejective method can be used and is used if n>=80.

SR: bool

When True, use the modified "sequentially rejective", especially when comparing one-step M-estimators or M-estimators.

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

con: array

Contrast matrix

num_sig: int

Number of statistically significant results

output: DataFrame

Difference score, p-value, critical value, and CI for each contrast

lindepbt¶

hypothesize.compare_groups_with_single_factor.lindepbt(x, tr=.2, con=None, alpha=.05, nboot=599, dif=True, seed=False)

Multiple comparisons on trimmed means with FWE controlled with Rom's method Using a bootstrap-t method.

Parameters:

x: Pandas DataFrame

Each column in the data represents a different group

tr: float

Proportion to trim (default is .2)

con: array

con is a J (number of groups) by d (number of contrasts) matrix containing the contrast coefficents of interest. All linear constrasts can be created automatically by using the function con1way (the result of which can be used for con). The default is None and in this case all linear contrasts are created automatically.

alpha: float

Alpha level. Default is .05.

nboot: int

Number of bootstrap samples (default is 2000)

dif: bool

When True, use difference scores, otherwise use marginal distributions

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

con: array

Contrast matrix

num_sig: int

Number of observations for each group

psihat: DataFrame

Difference score and CI for each contrast

test: DataFrame

Test statistic, p-value, critical value, and standard error for each contrast

ydbt¶

hypothesize.compare_groups_with_single_factor.ydbt(x, y, tr=.2, alpha=.05, nboot=599, side=True, seed=False)

Using the bootstrap-t method, compute a .95 confidence interval for the difference between the marginal trimmed means of paired data. By default, 20% trimming is used with 599 bootstrap samples.

Parameters:

x: Pandas Series

Data for group one

y: Pandas Series

Data for group two

tr: float

Proportion to trim (default is .2)

alpha: float

Alpha level. Default is .05.

nboot: int

Number of bootstrap samples (default is 2000)

side: bool When True the function returns a symmetric CI and a p value, otherwise the function returns equal-tailed CI (no p value)

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

ci: list

Confidence interval

dif: float

Difference between group one and two

p_value: float

p-value

Comparing groups with two factors¶

Statistical tests analogous to a 2-way ANOVA. That is, group tests that have a two factors.

Dependent groups¶

wwmcppb¶

hypothesize.compare_groups_with_two_factors.wwmcppb(J, K, x, est, *args, alpha=.05, dif=True,nboot=None, BA=True, hoch=True, seed=False)

Do all multiple comparisons for a within-by-within design using a percentile bootstrap method.A sequentially rejective method is used to control alpha. Hochberg's method can be used and is if n>=80.

Note that arguments up to and including args are positional arguments

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Each column represents a cell in the factorial design. For example, a 2x3 design would correspond to a DataFrame with 6 columns (levels of Factor A x levels of Factor B).

Order your columns according to the following pattern (traversing each row in a matrix):

the first column contains data for level 1 of Factor A and level 1 of Factor B
the second column contains data for level 1 of Factor A and level 2 of Factor B
column K contains the data for level 1 of Factor A and level K of Factor B
column K + 1 contains the data for level 2 of Factor A and level 1 of Factor B
and so on ...

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

alpha: float

Alpha level (default is .05)

dif: bool

When True, use difference scores, otherwise use marginal distributions

nboot: int

Number of bootstrap samples (default is 599)

BA: bool

When True, use the bias adjusted estimate of the generalized p-value is applied (e.g., when dif is False)

hoch: bool

When True, Hochberg's sequentially rejective method can be used to control FWE

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

The following results are returned for factor A, factor B, and the interaction. See the keys 'factor_A', 'factor_A', and 'factor_AB', respectively.

con: array

Contrast matrix

num_sig: int

Number of statistically significant results

output: DataFrame

Difference score, p-value, critical value, and CI for each contrast

wwmcpbt¶

hypothesize.compare_groups_with_two_factors.wwmcpbt(J, K, x, tr=.2, alpha=.05, nboot=599, seed=False)

Do multiple comparisons for a within-by-within design. using a bootstrap-t method and trimmed means. All linear contrasts relevant to main effects and interactions are tested. With trimmed means FWE is controlled with Rom's method.

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Each column represents a cell in the factorial design. For example, a 2x3 design would correspond to a DataFrame with 6 columns (levels of Factor A x levels of Factor B).

Order your columns according to the following pattern (traversing each row in a matrix):

the first column contains data for level 1 of Factor A and level 1 of Factor B
the second column contains data for level 1 of Factor A and level 2 of Factor B
column K contains the data for level 1 of Factor A and level K of Factor B
column K + 1 contains the data for level 2 of Factor A and level 1 of Factor B
and so on ...

tr: float

Proportion to trim (default is .2)

alpha: float

Alpha level (default is .05)

nboot: int

Number of bootstrap samples (default is 599)

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

The following results are returned for factor A, factor B, and the interaction. See the keys 'factor_A', 'factor_A', and 'factor_AB', respectively.

con: array

Contrast matrix

num_sig: int

Number of statistically significant results

psihat: DataFrame

Difference score and CI for each contrast

test: DataFrame

Test statistic, p-value, critical value, and standard error for each contrast

Mixed designs¶

These designs are also known as "split-plot" or "between-within" desgins. Hypothesize follws the common convention that assumes that the between-subjects factor is factor A and the within-subjects conditions are Factor B. For example, in a 2x3 mixed design, factor A has two levels. For each of these levels, there are 3 within-subjects conditions.

Make sure your DataFrame corresponds to a between-within design, not the other way around

For example, in a 2x3 mixed design, the first 3 columns correspond to the first level of Factor A. The last 3 columns correspond to the second level of factor A.

bwamcp¶

hypothesize.compare_groups_with_two_factors.bwamcp(J, K, x, tr=.2, alpha=.05, pool=False)

All pairwise comparisons among levels of Factor A in a mixed design using trimmed means. The pool option allows you to pool dependent groups across Factor A for each level of Factor B.

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Each column represents a cell in the factorial design. For example, a 2x3 design would correspond to a DataFrame with 6 columns (levels of Factor A x levels of Factor B).

Order your columns according to the following pattern (traversing each row in a matrix):

the first column contains data for level 1 of Factor A and level 1 of Factor B
the second column contains data for level 1 of Factor A and level 2 of Factor B
column K contains the data for level 1 of Factor A and level K of Factor B
column K + 1 contains the data for level 2 of Factor A and level 1 of Factor B
and so on ...

tr: float

Proportion to trim (default is .2)

alpha: float

Alpha level (default is .05)

pool: bool

If True, pool dependent groups together (default is False). Otherwise generate pairwise contrasts across factor A for each level of factor B.

Return:

Dictionary of results

n: list

Number of observations for each group

psihat: DataFrame

Difference score and CI, amd p-value for each contrast

test: DataFrame

Test statistic, critical value, standard error, and degrees of freedom for each contrast

bwbmcp¶

hypothesize.compare_groups_with_two_factors.bwbmcp(J, K, x, tr=.2, con=None, alpha=.05,dif=True, pool=False, hoch=False)

All pairwise comparisons among levels of Factor B in a mixed design using trimmed means. The pool option allows you to pool dependent groups across Factor A for each level of Factor B.

Rom's method is used to control for FWE (when alpha is 0.5, .01, or when number of comparisons are > 10). Hochberg's method can also be used. Note that CIs are adjusted based on the corresponding critical p-value after controling for FWE.

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Each column represents a cell in the factorial design. For example, a 2x3 design would correspond to a DataFrame with 6 columns (levels of Factor A x levels of Factor B).

Order your columns according to the following pattern (traversing each row in a matrix):

the first column contains data for level 1 of Factor A and level 1 of Factor B
the second column contains data for level 1 of Factor A and level 2 of Factor B
column K contains the data for level 1 of Factor A and level K of Factor B
column K + 1 contains the data for level 2 of Factor A and level 1 of Factor B
and so on ...

tr: float

Proportion to trim (default is .2)

con: array

con is a K by d (number of contrasts) matrix containing the contrast coefficents of interest. All linear constrasts can be created automatically by using the function con1way (the result of which can be used for con).

alpha: float

Alpha level (default is .05)

dif: bool

When True, use difference scores, otherwise use marginal distributions

pool: bool

If True, pool dependent groups together (default is False). Otherwise generate pairwise contrasts across factor A for each level of factor B.

hoch: bool

When True, Hochberg's sequentially rejective method can be used to control FWE

Return:

Dictionary or List of Dictionaries depending on pool parameter. If pool is set to False, all pairwise comparisons for Factor B are computed and returned as elements in a list corresponding to each level of Factor A.

con: array

Contrast matrix

n: int

Number of observations for Factor B

num_sig: int

Number of statistically significant results

psihat: DataFrame

Difference score between group X and group Y, and CI for each contrast

test: DataFrame

Test statistic, p-value, critical value, and standard error for each contrast

bwmcp¶

hypothesize.compare_groups_with_two_factors.bwmcp(J, K, x, alpha=.05, tr=.2, nboot=599, seed=False)

A bootstrap-t for multiple comparisons among for all main effects and interactions in a between-by-within design. The analysis is done by generating bootstrap samples and using an appropriate linear contrast.

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Each column represents a cell in the factorial design. For example, a 2x3 design would correspond to a DataFrame with 6 columns (levels of Factor A x levels of Factor B).

Order your columns according to the following pattern (traversing each row in a matrix):

the first column contains data for level 1 of Factor A and level 1 of Factor B
the second column contains data for level 1 of Factor A and level 2 of Factor B
column K contains the data for level 1 of Factor A and level K of Factor B
column K + 1 contains the data for level 2 of Factor A and level 1 of Factor B
and so on ...

alpha: float

Alpha level (default is .05)

tr: float

Proportion to trim (default is .2)

nboot: int

Number of bootstrap samples (default is 500)

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

contrast_coef: dict

Dictionary of arrays where each value corresponds to the contrast matrix for factor A, factor B, and the interaction

factor_A: DataFrame

Difference score, standard error, test statistic, critical value, and p-value for each contrast relating to Factor A

factor_B: DataFrame

Difference score, standard error, test statistic, critical value, and p-value for each contrast relating to Factor B

factor_AB: DataFrame

Difference score, standard error, test statistic, critical value, and p-value for each contrast relating to the interaction

bwimcp¶

hypothesize.compare_groups_with_two_factors.bwimcp(J, K, x, tr=.2, alpha=.05)

Multiple comparisons for interactions in a split-plot design. The analysis is done by taking difference scores among all pairs of dependent groups and determining which of these differences differ across levels of Factor A using trimmed means. FWE is controlled via Hochberg's method. For MOM or M-estimators (possibly not implemented yet), use spmcpi which uses a bootstrap method

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Each column represents a cell in the factorial design. For example, a 2x3 design would correspond to a DataFrame with 6 columns (levels of Factor A x levels of Factor B).

Order your columns according to the following pattern (traversing each row in a matrix):

the first column contains data for level 1 of Factor A and level 1 of Factor B
the second column contains data for level 1 of Factor A and level 2 of Factor B
column K contains the data for level 1 of Factor A and level K of Factor B
column K + 1 contains the data for level 2 of Factor A and level 1 of Factor B
and so on ...

tr: float

Proportion to trim (default is .2)

alpha: float

Alpha level (default is .05)

Return:

Dictionary of results

con: array

Contrast matrix

output: DataFrame

Difference score, p-value, and critical value for each contrast relating to the interaction

bwmcppb¶

hypothesize.compare_groups_with_two_factors.bwmcppb(J, K, x, est, *args, alpha=.05,nboot=500, bhop=True, seed=True)

(note: this is for trimmed means only depite the est arg. This will be fixed eventually. Use trim_mean from SciPy)

A percentile bootstrap for multiple comparisons for all main effects and interactions The analysis is done by generating bootstrap samples and using an appropriate linear contrast.

Uses Rom's method to control FWE. Setting the argument bhop to True uses the Benjamini–Hochberg method instead.

Note that arguments up to and including args are positional arguments

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Each column represents a cell in the factorial design. For example, a 2x3 design would correspond to a DataFrame with 6 columns (levels of Factor A x levels of Factor B).

Order your columns according to the following pattern (traversing each row in a matrix):

the first column contains data for level 1 of Factor A and level 1 of Factor B
the second column contains data for level 1 of Factor A and level 2 of Factor B
column K contains the data for level 1 of Factor A and level K of Factor B
column K + 1 contains the data for level 2 of Factor A and level 1 of Factor B
and so on ...

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

alpha: float

Alpha level. Default is .05.

nboot: int

Number of bootstrap samples (default is 500)

bhop: bool

When True, use the Benjamini–Hochberg method to control FWE

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of DataFrames for each Factor and the interaction. See the keys 'factor_A', 'factor_B', and 'factor_AB'

Each DataFrame contains the difference score, p-value, critical value, and CI for each contrast.

spmcpa¶

hypothesize.compare_groups_with_two_factors.spmcpa(J, K, x, est, *args,avg=False, alpha=.05, nboot=None, seed=False)

All pairwise comparisons among levels of Factor A in a mixed design. A sequentially rejective method is used to control FWE. The avg option controls whether or not to average data across levels of Factor B prior to performing the statistical test. If False, contrasts are created to test across Factor A for each level of Factor B.

Note that arguments up to and including args are positional arguments

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Data for group one

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

avg: bool

If False, contrasts are created to test across Factor A for each level of Factor B (default is False)

alpha: float

Alpha level (default is .05)

nboot: int

Number of bootstrap samples (default is None in which case the number is chosen based on the number of contrasts).

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

con: array

Contrast matrix

num_sig: int

Number of statistically significant results

output: DataFrame

Difference score, p-value, critical value, and CI for each contrast

spmcpb¶

hypothesize.compare_groups_with_two_factors.spmcpb(J, K, x, est, *args, dif=True,alpha=.05, nboot=599, seed=False)

All pairwise comparisons among levels of Factor B in a split-plot design. A sequentially rejective method is used to control FWE.

If est is onestep or mom (not be implemeted yet), method SR is used to control the probability of at least one Type I error. Otherwise, Hochberg is used.

Note that arguments up to and including args are positional arguments

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Data for group one

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

dif: bool

When True, use difference scores, otherwise use marginal distributions

alpha: float

Alpha level (default is .05)

nboot: int

Number of bootstrap samples (default is 599)

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

con: array

Contrast matrix

num_sig: int

Number of statistically significant results

output: DataFrame

Difference score, p-value, critical value, and CI for each contrast

spmcpi¶

hypothesize.compare_groups_with_two_factors.spmcpi(J, K, x, est, *args, alpha=.05,nboot=None, SR=False, seed=False)

Multiple comparisons for interactions in a split-plot design. The analysis is done by taking difference scores among all pairs of dependent groups and determining which of these differences differ across levels of Factor A.

The so-called the SR method, which is a slight modification of Hochberg's (1988) "sequentially rejective" method can be applied to control FWE, especially when comparing one-step M-estimators or M-estimators.

Note that arguments up to and including args are positional arguments

Parameters:

J: int

Number of J levels associated with Factor A

K: int

Number of K levels associated with Factor B

x: Pandas DataFrame

Data for group one

est: function

Measure of location (currently only trim_mean is supported)

*args: list/value

Parameter(s) for measure of location (e.g., .2)

alpha: float

Alpha level. Default is .05.

nboot: int

Number of bootstrap samples (default is None in which case the number is chosen based on the number of contrasts)

SR: bool

When True, use the slight modification of Hochberg's (1988) "sequentially rejective" method to control FWE

seed: bool

Random seed for reproducible results (default is False)

Return:

Dictionary of results

con: array

Contrast matrix

num_sig: int

Number of statistically significant results

output: DataFrame

Difference score, p-value, critical value, and CI for each contrast

Measuring associations¶

For statistical tests and measurements that include robust correlations and tests of independence. Note that regression functions will be added here eventually.

corb¶

hypothesize.measuring_associations.corb(corfun, x, y, alpha, nboot, *args, seed=False)

Compute a 1-alpha confidence interval for a correlation using percentile bootstrap method The function corfun is any function that returns a correlation coefficient. The functions pbcor and wincor follow this convention. When using Pearson's correlation, and when n<250, use lsfitci instead (not yet implemented).

Note that arguments up to and including args are positional arguments

Parameters:

corfun: function

corfun is any function that returns a correlation coefficient

x: Pandas Series

Data for group one

y: Pandas Series

Data for group two

alpha: float

Alpha level (default is .05)

nboot: int

Number of bootstrap samples

*args: list/value

List of arguments to corfun (e.g., .2)

seed: bool

Random seed for reproducible results. Default is False.

Return:

Dictionary of results

ci: list

Confidence interval

cor: float

Correlation estimate

p_value: float

p-value

pball¶

hypothesize.measuring_associations.pball(x, beta=.2)

Compute the percentage bend correlation matrix for all pairs of columns in x. This function also returns the two-sided significance level for all pairs of variables, plus a test of zero correlation among all pairs.

Parameters:

x: Pandas DataFrame

Each column represents a variable to use in the correlations

beta: float

0 < beta < .5. Beta is analogous to trimming in other functions and related to the measure of dispersion used in the percentage bend calculation.

Return:

Dictionary of results

H: float

The test statistic $H$ .Reject null if $H > \chi^2_{1−\alpha}$ , the 1−α quantile.

H_p_value: float

p-value corresponding to the test that all correlations are equal to zero

p_value: array

p-value matrix corresponding to each pairwise correlation

pbcorm: array

Correlation matrix

pbcor¶

hypothesize.measuring_associations.pbcor(x, y, beta=.2)

Compute the percentage bend correlation between x and y

Parameters:

x: Pandas Series

Data for group one

y: Pandas Series

Data for group two

beta: float

0 < beta < .5. Beta is analogous to trimming in other functions and related to the measure of dispersion used in the percentage bend calculation.

Return:

Dictionary of results

cor: float

Correlation

nval: int

Number of observations

p_value

p-value

test: float

Test statistic

winall¶

hypothesize.measuring_associations.winall(x, tr=.2)

Compute the Winsorized correlation and covariance matrix for all pairs of columns in x. This function also returns the two-sided significance level for all pairs of variables, plus a test of zero correlation among all pairs.

Parameters:

x: Pandas DataFrame

Each column represents a variable to use in the correlations

tr: float

Proportion to winsorize (default is .2)

Return:

Dictionary of results

center: array

Trimmed mean for each group

p_value: array

p-value array corresponding to the pairwise correlations

wcor: array

Winsorized correlation matrix

wcov: array

Winsorized covariance matrix

wincor¶

hypothesize.measuring_associations.wincor(x, y, tr=.2)

Compute the winsorized correlation between x and y. This function also returns the winsorized covariance.

Parameters:

x: Pandas Series

Data for group one

y: Pandas Series

Data for group two

tr: float

Proportion to winsorize (default is .2)

Return:

Dictionary of results

cor: float

Winsorized correlation

nval: int

Number of observations

sig: float

p-value

wcov: float

Winsorized covariance

Other important functions¶

The following functions are sometimes required by Hypothesize as input arguments. They are also potentially useful on their own.

trim_mean¶

Calculate the sample mean after removing a proportion of values from each tail. This is Scipy's implementation of the trimmed mean.

hypothesize.utilities.trim_mean(x, proportiontocut, axis=0)

Parameters:

x: array or DataFrame

Array or DataFrame of observations

proportiontocut: float

Proportion to trim from both tails of the distribution

axis: int or None

Axis along which the trimmed means are computed. Default is 0. If None, compute over the whole array/DataFrame.

Return:

float or list

The trimmed mean(s)

con1way¶

hypothesize.utilities.con1way(J)

Return all linear contrasts for J groups

Parameters:

J: int

Number of groups

Return:

array

Array of contrasts where the rows correspond to groups and the columns are the contrasts to be used

con2way¶

hypothesize.utilities.con2way(J, K)

Return all linear contrasts for Factor A, Factor B, and the interaction

Parameters:

J: int

Number of levels for Factor A

K: int

Number of levels for Factor B

Return:

list of arrays

Each item in the list contains the contrasts for Factor A, Factor B, and the interaction, in that order. For each array, the rows correspond to groups and the columns are the contrasts to be used

create_example_data¶

hypothesize.utilities.create_example_data(design_values, missing_data_proportion=0, save_array_path=None, seed=False)

Create a Pandas DataFrame of random data with a certain number of columns which correspond to a design of a given shape (e.g., 1-way, two groups, 2-way design). There is also an option to randomly add a proportion of null values. The purpose of this function is to make it easy to demonstrate and test the package.

Parameters:

design_values: int or list

An integer or list indicating the design shape. For example, [2,3] indicates a 2-by-3 design and will produce a six column DataFrame with appropriately named columns.

missing_data_proportion: float

Proportion of randomly missing data

save_array_path: str (default is None)

Save each group as an array for loading into R by specifying a path (e.g. , '/home/allan/'). If left unset (i.e., None), no arrays will be saved.

seed: bool

Set random seed for reproducible results