Fsdb::Filter::dbrvstatdiff(3)

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.)

SEE ALSO
Fsdb. dbcolstats. dbcolcopylast.

CLASS FUNCTIONS

  new
    $filter = new Fsdb::Filter::dbrvstatdiff(@arguments);

Create a new dbrvstatdiff object, taking command-line arguments.

  set_defaults
    $filter->set_defaults();

Internal: set up defaults.

  parse_options
    $filter->parse_options(@ARGV);

Internal: parse command-line arguments.

  setup
    $filter->setup();

Internal: setup, parse headers.

  run
    $filter->run();

Internal: run over each rows.

AUTHOR and COPYRIGHT
Copyright (C) 1991-2018 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.