# dbrvstatdiff - Man Page

evaluate statistical differences between two random variables

## Synopsis

dbrvstatdiff [-f format] [-c ConfRating] [-h HypothesizedDifference] m1c sd1c n1c m2c sd2c n2c

`OR`

dbrvstatdiff [-f format] [-c ConfRating] m1c n1c m2c n2c

## Description

Produce statistics on the difference of sets of random variables. If a hypothesized difference is given (with `-h`

), to does a Student's t-test.

Random variables are specified by:

- m1c, m2c
The column names of means of random variables.

- sd1c, sd2c
The column names of standard deviations of random variables.

- n1c, n2c
Counts of number of samples for each random variable

These values can be computed with dbcolstats.

Creates up to ten new columns:

- diff
The difference of RV 2 - RV 1.

- diff_pct
The percentage difference (RV2-RV1)/1

- diff_conf_{half,low,high} and diff_conf_pct_{half,low,high}
The half half confidence intervals and low and high values for absolute and relative confidence.

- t_test
The T-test value for the given hypothesized difference.

- t_test_result
Given the confidence rating, does the test pass? Will be either "rejected" or "not-rejected".

- t_test_break
The hypothesized value that is break-even point for the T-test.

- t_test_break_pct
Break-even point as a percent of m1c.

Confidence intervals are not printed if standard deviations are not provided. Confidence intervals assume normal distributions with common variances.

T-tests are only computed if a hypothesized difference is provided. Hypothesized differences should be proceeded by <=, >=, =. T-tests assume normal distributions with common variances.

## Options

**-c FRACTION**or**--confidence FRACTION**Specify FRACTION for the confidence interval. Defaults to 0.95 for a 95% confidence factor (alpha = 0.05).

**-f FORMAT**or**--format FORMAT**Specify a printf(3)-style format for output statistics. Defaults to

`%.5g`

.**-h DIFF**or**--hypothesis DIFF**Specify the hypothesized difference as

`DIFF`

, where`DIFF`

is something like`<=0`

or`>=0`

, etc.

This module also supports the standard fsdb options:

- -d
Enable debugging output.

- -i or --input InputSource
Read from InputSource, typically a file name, or

`-`

for standard input, or (if in Perl) a IO::Handle, Fsdb::IO or Fsdb::BoundedQueue objects.- -o or --output OutputDestination
Write to OutputDestination, typically a file name, or

`-`

for standard output, or (if in Perl) a IO::Handle, Fsdb::IO or Fsdb::BoundedQueue objects.- --autorun or --noautorun
By default, programs process automatically, but Fsdb::Filter objects in Perl do not run until you invoke the

**run()**method. The`--(no)autorun`

option controls that behavior within Perl.- --help
Show help.

- --man
Show full manual.

## Sample Usage

### Input

#fsdb title mean2 stddev2 n2 mean1 stddev1 n1 example6.12 0.17 0.0020 5 0.22 0.0010 4

### Command

cat data.fsdb | dbrvstatdiff mean2 stddev2 n2 mean1 stddev1 n1

### Output

#fsdb title mean2 stddev2 n2 mean1 stddev1 n1 diff:d diff_pct:d diff_conf_half:d diff_conf_low:d diff_conf_high:d diff_conf_pct_half:d diff_conf_pct_low:d diff_conf_pct_high:d example6.12 0.17 0.0020 5 0.22 0.0010 4 0.05 29.412 0.0026138 0.047386 0.052614 1.5375 27.874 30.949 # | dbrvstatdiff mean2 stddev2 n2 mean1 stddev1 n1

### Input 2

(example 7.10 from Scheaffer and McClave):

#fsdb title x2 sd2 n2 x1 sd1 n1 example7.10 9 35.22 24.44 9 31.56 20.03

### Command 2

dbrvstatdiff -h '<=0' x2 sd2 n2 x1 sd1 n1

### Output 2

#fsdb title n1 x1 sd1 n2 x2 sd2 diff diff_pct diff_conf_half diff_conf_low diff_conf_high diff_conf_pct_half diff_conf_pct_low diff_conf_pct_high t_test t_test_result example7.10 9 35.22 24.44 9 31.56 20.03 3.66 0.11597 4.7125 -1.0525 8.3725 0.14932 -0.033348 0.26529 1.6465 not-rejected # | /global/us/edu/ucla/cs/ficus/users/johnh/BIN/DB/dbrvstatdiff -h <=0 x2 sd2 n2 x1 sd1 n1

### Case 3

A common use case is to have one file with a set of trials from two experiments, and to use dbrvstatdiff to see if they are different.

*Input 3:*

#fsdb case trial value a 1 1 a 2 1.1 a 3 0.9 a 4 1 a 5 1.1 b 1 2 b 2 2.1 b 3 1.9 b 4 2 b 5 1.9

### Command 3

cat two_trial.fsdb | dbmultistats -k case value | dbcolcopylast mean stddev n | dbrow '_case eq "b"' | dbrvstatdiff -h '=0' mean stddev n copylast_mean copylast_stddev copylast_n | dblistize

*Output 3:*

#fsdb -R C case mean stddev pct_rsd conf_range conf_low conf_high conf_pct sum sum_squared min max n copylast_mean copylast_stddev copylast_n diff diff_pct diff_conf_half diff_conf_low diff_conf_high diff_conf_pct_half diff_conf_pct_low diff_conf_pct_high t_test t_test_result t_test_break t_test_break_pct case: b mean: 1.98 stddev: 0.083666 pct_rsd: 4.2256 conf_range: 0.10387 conf_low: 1.8761 conf_high: 2.0839 conf_pct: 0.95 sum: 9.9 sum_squared: 19.63 min: 1.9 max: 2.1 n: 5 copylast_mean: 1.02 copylast_stddev: 0.083666 copylast_n: 5 diff: -0.96 diff_pct: -48.485 diff_conf_half: 0.12202 diff_conf_low: -1.082 diff_conf_high: -0.83798 diff_conf_pct_half: 6.1627 diff_conf_pct_low: -54.648 diff_conf_pct_high: -42.322 t_test: -18.142 t_test_result: rejected t_test_break: -1.082 t_test_break_pct: -54.648 # | dbmultistats -k case value # | dbcolcopylast mean stddev n # | dbrow _case eq "b" # | dbrvstatdiff -h =0 mean stddev n copylast_mean copylast_stddev copylast_n # | dbfilealter -R C

(So one cannot say that they are statistically equal.)

## See Also

Fsdb, dbcolstats, dbcolcopylast, dbcolscorrelate.

## AUTHOR and COPYRIGHT

Copyright (C) 1991-2021 by John Heidemann <johnh@isi.edu>

This program is distributed under terms of the GNU general public license, version 2. See the file COPYING with the distribution for details.