# dbrvstatdiff (1) - Linux Man Pages

## dbrvstatdiff: evaluate statistical differences between two random variables

## NAME

dbrvstatdiff - 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 diff_pct diff_conf_half diff_conf_low diff_conf_high diff_conf_pct_half diff_conf_pct_low diff_conf_pct_high 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.)

## AUTHOR and COPYRIGHT

Copyright (C) 1991-2015 by John Heidemann <johnh [at] 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.