# dbrvstatdiff (1) - Linux Man Pages

## 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.)