# Dataplot Solution to the Data Analysis Problem

Problem Setup An analyst has a data set consisting of a response variable and three independent variables (factors). Determine if the factors affect the response. Determine if there is interaction between the factors. Perform an analysis of variance. Perform a graphical analysis of variance.
Dataplot Program This is demonstrated with the built-in data file BOWEN.DAT (stored in the Dataplot auxiliary directory). The following Dataplot program
SKIP 25
READ BOWEN.DAT Y X1 X2 X3
ANOVA Y X1 X2 X3
.
LET TAG = X2 + 2*(X3-1)
CHARACTERS 1 1 2 2
LINES SOLID DOTTED SOLID DOTTED
XTIC OFFSET 0.2 0.2
TITLE AUTOMATIC
PLOT Y X1 TAG
Dataplot Output generated the following output

```
**********************************
**********************************
**  3-WAY ANALYSIS OF VARIANCE  **
**********************************
**********************************

NUMBER OF OBSERVATIONS           =        8
NUMBER OF FACTORS                =        3
NUMBER OF LEVELS FOR FACTOR 1    =        2
NUMBER OF LEVELS FOR FACTOR 2    =        2
NUMBER OF LEVELS FOR FACTOR 3    =        2
RESIDUAL    STANDARD DEVIATION   =    0.65340454102E+02
RESIDUAL    DEGREES OF FREEDOM   =        4
NO REPLICATION CASE
NUMBER OF DISTINCT CELLS         =        8

****************
*  ESTIMATION  *
****************

GRAND MEAN                       =    0.18487500000E+03
GRAND STANDARD DEVIATION         =    0.99256431580E+02

LEVEL-ID      NI      MEAN      EFFECT     SD(EFFECT)
--------------------------------------------------------------------
FACTOR  1--   -1.00000      4.  167.75000  -17.12500   23.10134
--    1.00000      4.  202.00000   17.12500   23.10134

FACTOR  2--   -1.00000      4.  107.75000  -77.12500   23.10134
--    1.00000      4.  262.00000   77.12500   23.10134

FACTOR  3--   -1.00000      4.  169.25000  -15.62500   23.10134
--    1.00000      4.  200.50000   15.62500   23.10134

MODEL               RESIDUAL STANDARD DEVIATION
-------------------------------------------------------
CONSTANT             ONLY--       99.2564315796
CONSTANT & FACTOR  1 ONLY--      105.3697891235
CONSTANT & FACTOR  2 ONLY--       59.6891250610
CONSTANT & FACTOR  3 ONLY--      105.6801376343
CONSTANT & ALL 3 FACTORS --       65.3404541016

*************
*  TESTING  *
*************

NUM. LEVELS    F STAT.       F CDF
------------------------------------------------
FACTOR  1--       2       0.54952424765  50.033%
FACTOR  2--       2      11.14592266083  97.113%
FACTOR  3--       2       0.45747327805  46.410%

RESIDUAL    STANDARD DEVIATION =       65.34045410156
RESIDUAL    DEGREES OF FREEDOM =             4
```

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Date created: 06/05/2001
Last updated: 09/28/2016