fsml_tst – FSML

Module for common statistical tests.

Uses

- fsml_utl
- fsml_ini
- fsml_sts
- fsml_err
- fsml_con
- fsml_dst
Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Used by

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Subroutines

public impure subroutine s_tst_anova_1w(x, f, df_b, df_w, p)

Impure wrapper procedure for s_tst_anova_1w_core.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x(:,:)	2D array, each column is a group
real(kind=wp),	intent(out)	::	f	F-statistic
real(kind=wp),	intent(out)	::	df_b	degrees of freedom between groups
real(kind=wp),	intent(out)	::	df_w	degrees of freedom within groups
real(kind=wp),	intent(out)	::	p	p-value from F distribution

public impure subroutine s_tst_kruskalwallis(x, h, df, p)

Impure wrapper procedure for s_tst_kruskalwallis_core.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x(:,:)	2D array, each column is a group
real(kind=wp),	intent(out)	::	h	Kruskal-Wallis H-statistic
real(kind=wp),	intent(out)	::	df	degrees of freedom (k - 1)
real(kind=wp),	intent(out)	::	p	p-value from chi-squared distribution

public impure subroutine s_tst_ranksum(x1, x2, u, p, h1)

Impure wrapper procedure for s_tst_ranksum_core.

Arguments

Type	Intent	Optional		Name
real(kind=wp),	intent(in)		::	x1(:)	x1 vector (samples)
real(kind=wp),	intent(in)		::	x2(:)	x2 vector (samples)
real(kind=wp),	intent(out)		::	u	U statistic
real(kind=wp),	intent(out)		::	p	p-value
character(len=*),	intent(in),	optional	::	h1	$H_{1}$ option: "two" (default), "lt", or "gt"

public impure subroutine s_tst_signedrank_1s(x, mu0, w, p, h1)

Impure wrapper procedure for s_tst_signedrank_1s_core.

Arguments

Type	Intent	Optional		Name
real(kind=wp),	intent(in)		::	x(:)	x vector (samples)
real(kind=wp),	intent(in)		::	mu0	population mean (null hypothesis expected value)
real(kind=wp),	intent(out)		::	w	W statistic (sum of signed ranks)
real(kind=wp),	intent(out)		::	p	p-value
character(len=*),	intent(in),	optional	::	h1	$H_{1}$ : "two" (default), "lt", "gt"

public impure subroutine s_tst_signedrank_2s(x1, x2, w, p, h1)

Impure wrapper procedure for s_tst_signedrank_2s_core.

Arguments

Type	Intent	Optional		Name
real(kind=wp),	intent(in)		::	x1(:)	sample 1 (paired data)
real(kind=wp),	intent(in)		::	x2(:)	sample 2 (paired data)
real(kind=wp),	intent(out)		::	w	W statistic (sum of signed ranks)
real(kind=wp),	intent(out)		::	p	p-value
character(len=*),	intent(in),	optional	::	h1	$H_{1}$ : "two" (default), "lt", "gt"

public impure subroutine s_tst_ttest_1s(x, mu0, t, df, p, h1)

Impure wrapper procedure for s_tst_ttest_1s_core.

Arguments

Type	Intent	Optional		Name
real(kind=wp),	intent(in)		::	x(:)	x vector (samples)
real(kind=wp),	intent(in)		::	mu0	population mean (null hypothesis expected value)
real(kind=wp),	intent(out)		::	t	test statistic
real(kind=wp),	intent(out)		::	df	degrees of freedom
real(kind=wp),	intent(out)		::	p	p-value
character(len=*),	intent(in),	optional	::	h1	$H_{1}$ option: two (default), le, ge

public impure subroutine s_tst_ttest_2s(x1, x2, t, df, p, eq_var, h1)

Impure wrapper procedure for s_tst_ttest_2s_core.

Arguments

Type	Intent	Optional		Name
real(kind=wp),	intent(in)		::	x1(:)	x1 vector (samples)
real(kind=wp),	intent(in)		::	x2(:)	x2 vector (samples)
real(kind=wp),	intent(out)		::	t	test statistic
real(kind=wp),	intent(out)		::	df	degrees of freedom
real(kind=wp),	intent(out)		::	p	p-value
logical,	intent(in),	optional	::	eq_var	true if equal variances assumed
character(len=*),	intent(in),	optional	::	h1	$H_{1}$ option: two (default), le, ge

public impure subroutine s_tst_ttest_paired(x1, x2, t, df, p, h1)

Impure wrapper procedure for s_tst_ttest_paired_core.

Arguments

Type	Intent	Optional		Name
real(kind=wp),	intent(in)		::	x1(:)	x1 vector (samples)
real(kind=wp),	intent(in)		::	x2(:)	x2 vector (samples); must be same length as x1
real(kind=wp),	intent(out)		::	t	test statistic
real(kind=wp),	intent(out)		::	df	degrees of freedom
real(kind=wp),	intent(out)		::	p	p-value
character(len=*),	intent(in),	optional	::	h1	$H_{1}$ option: two (default), le, ge

private pure subroutine s_tst_anova_1w_core(x, f, df_b, df_w, p)

One-way ANOVA.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x(:,:)	2D array, each column is a group
real(kind=wp),	intent(out)	::	f	F-statistic
real(kind=wp),	intent(out)	::	df_b	degrees of freedom between groups
real(kind=wp),	intent(out)	::	df_w	degrees of freedom within groups
real(kind=wp),	intent(out)	::	p	p-value from F distribution

private pure subroutine s_tst_kruskalwallis_core(x, h, df, p)

Kruskal-Wallis H-test for independent samples. No tie correction.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x(:,:)	2D array, each column is a group
real(kind=wp),	intent(out)	::	h	Kruskal-Wallis H-statistic
real(kind=wp),	intent(out)	::	df	degrees of freedom (k - 1)
real(kind=wp),	intent(out)	::	p	p-value from chi-squared distribution

private pure subroutine s_tst_ranksum_core(x1, x2, u, p, h1)

The ranks sum test (Wilcoxon rank-sum test or Mann–Whitney U test).

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x1(:)	x1 vector (samples)
real(kind=wp),	intent(in)	::	x2(:)	x2 vector (samples)
real(kind=wp),	intent(out)	::	u	U statistic
real(kind=wp),	intent(out)	::	p	p-value
character(len=*),	intent(in)	::	h1	$H_{1}$ option: "two" (default), "lt", or "gt"

private pure subroutine s_tst_signedrank_1s_core(x, mu0, w, p, h1)

The 1-sample Wilcoxon signed rank test.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x(:)	x vector (samples)
real(kind=wp),	intent(in)	::	mu0	population mean (null hypothesis expected value)
real(kind=wp),	intent(out)	::	w	W statistic (sum of signed ranks)
real(kind=wp),	intent(out)	::	p	p-value
character(len=*),	intent(in)	::	h1	$H_{1}$ : "two" (default), "lt", "gt"

private pure subroutine s_tst_signedrank_2s_core(x1, x2, w, p, h1)

The Wilcoxon signed rank test.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x1(:)	sample 1 (paired data)
real(kind=wp),	intent(in)	::	x2(:)	sample 2 (paired data)
real(kind=wp),	intent(out)	::	w	W statistic (sum of signed ranks)
real(kind=wp),	intent(out)	::	p	p-value
character(len=*),	intent(in)	::	h1	$H_{1}$ : "two" (default), "lt", "gt"

private pure subroutine s_tst_ttest_1s_core(x, mu0, t, df, p, h1)

The 1-sample t-test.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x(:)	x vector (samples)
real(kind=wp),	intent(in)	::	mu0	population mean (null hypothesis expected value)
real(kind=wp),	intent(out)	::	t	test statistic
real(kind=wp),	intent(out)	::	df	degrees of freedom
real(kind=wp),	intent(out)	::	p	p-value
character(len=*),	intent(in)	::	h1	$H_{1}$ option: two (default), le, ge

private pure subroutine s_tst_ttest_2s_core(x1, x2, t, df, p, eq_var, h1)

The 2-sample t-test.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x1(:)	x1 vector (samples)
real(kind=wp),	intent(in)	::	x2(:)	x2 vector (samples)
real(kind=wp),	intent(out)	::	t	test statistic
real(kind=wp),	intent(out)	::	df	degrees of freedom
real(kind=wp),	intent(out)	::	p	p-value
logical,	intent(in)	::	eq_var	true if equal variances assumed
character(len=*),	intent(in)	::	h1	$H_{1}$ option: two (default), le, ge

private pure subroutine s_tst_ttest_paired_core(x1, x2, t, df, p, h1)

The paired sample t-test (or dependent sample t-test). It is a special case of s_tst_ttest_1s offered and uses the same pure procedure (s_tst_ttest_1s_core).

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	x1(:)	x1 vector (samples)
real(kind=wp),	intent(in)	::	x2(:)	x2 vector (samples); must be same length as x1
real(kind=wp),	intent(out)	::	t	test statistic
real(kind=wp),	intent(out)	::	df	degrees of freedom
real(kind=wp),	intent(out)	::	p	p-value
character(len=*),	intent(in)	::	h1	$H_{1}$ option: two (default), le, ge

fsml_tst Module

Contents

Subroutines

Uses

Used by

Subroutines

public impure subroutine s_tst_anova_1w(x, f, df_b, df_w, p)

Arguments

public impure subroutine s_tst_kruskalwallis(x, h, df, p)

Arguments

public impure subroutine s_tst_ranksum(x1, x2, u, p, h1)

Arguments

public impure subroutine s_tst_signedrank_1s(x, mu0, w, p, h1)

Arguments

public impure subroutine s_tst_signedrank_2s(x1, x2, w, p, h1)

Arguments

public impure subroutine s_tst_ttest_1s(x, mu0, t, df, p, h1)

Arguments

public impure subroutine s_tst_ttest_2s(x1, x2, t, df, p, eq_var, h1)

Arguments

public impure subroutine s_tst_ttest_paired(x1, x2, t, df, p, h1)

Arguments

private pure subroutine s_tst_anova_1w_core(x, f, df_b, df_w, p)

Arguments

private pure subroutine s_tst_kruskalwallis_core(x, h, df, p)

Arguments

private pure subroutine s_tst_ranksum_core(x1, x2, u, p, h1)

Arguments

private pure subroutine s_tst_signedrank_1s_core(x, mu0, w, p, h1)

Arguments

private pure subroutine s_tst_signedrank_2s_core(x1, x2, w, p, h1)

Arguments

private pure subroutine s_tst_ttest_1s_core(x, mu0, t, df, p, h1)

Arguments

private pure subroutine s_tst_ttest_2s_core(x1, x2, t, df, p, eq_var, h1)

Arguments

private pure subroutine s_tst_ttest_paired_core(x1, x2, t, df, p, h1)

Arguments