STAT:5201 Applied Statistic II

Transcription

1 STAT:5201 Applied Statistic II Two-Factor Experiment (one fixed blocking factor, one fixed factor of interest) Randomized complete block design (RCBD) Primary Factor: Day length (short or long) Blocking Factor: litter (1 to 6) **Considered a fixed effect for now Response: NI enzyme level Six litters of hamsters with 2 hamsters from each litter is available for the experiment. The treatments of short and long are randomly assigned within litter. (We will consider Litter a fixed effect for now). SAS Program Part 1: Input Data and Model Fitting /* This is how SAS recognizes a comment.*/ /* Create the data set using the CARDS statement: */ data hamster; input litter daylength $ enzyme; /* the $ makes daylength a character variable.*/ cards; 1 short short short short short short long long long long long long 2.3 ; /* It s always a good idea to print the data to the Output screen */ /* to make sure SAS is reading it appropriately. */ proc print data=hamster; The SAS System Obs litter daylength enzyme 1 1 short short short short short short long long long long long long 2.3 1

2 /* PROC CONTENTS gives you information on the variables */ proc contents data=hamster; The CONTENTS Procedure Data Set Name WORK.HAMSTER Observations 12 Member Type DATA Variables 3 Engine V9 Indexes 0 Created Tuesday, February 11, Observation Length :43:17 PM Last Modified Tuesday, February 11, Deleted Observations :43:17 PM Protection Compressed NO Data Set Type Sorted NO Label Data Representation WINDOWS_32 Encoding wlatin1 Western (Windows) Alphabetic List of Variables and Attributes # Variable Type Len 2 daylength Char 8 3 enzyme Num 8 1 litter Num 8 /* Assign symbols for treatment groups and plot data. */ SYMBOL1 value=plus c=black; SYMBOL2 value=circle c=blue; proc gplot data=hamster; plot enzyme*litter=daylength; 2

3 /* For now, we will consider litter a fixed block effect.*/ /* Fit the additive model (main effects model only, no interaction). */ proc glm data=hamster; class litter daylength; model enzyme=daylength litter/solution; output out=diagnostics p=predicted r=residual; The SAS System The GLM Procedure Class Level Information Class Levels Values litter daylength 2 long short Number of Observations Read 12 Number of Observations Used 12 The SAS System The GLM Procedure Dependent Variable: enzyme Sum of Source DF Squares Mean Square F Value Pr > F Model Error Corrected Total R-Square Coeff Var Root MSE enzyme Mean Source DF Type I SS Mean Square F Value Pr > F daylength litter Source DF Type III SS Mean Square F Value Pr > F daylength litter

4 Standard Parameter Estimate Error t Value Pr > t Intercept B daylength long B daylength short B... litter B litter B litter B litter B litter B litter B... NOTE: The X X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter B are not uniquely estimable. /* View the residuals and predicted values on the Output screen. */ proc print data=diagnostics; The SAS System Obs litter daylength enzyme predicted residual 1 1 short short short short short short long long long long long long

5 SAS Program Part 2: Fitted Model Visualization, Diagnostics /* Plot the fitted additive model using proc gplot. */ SYMBOL1 value=diamond height=3 interpol=join line=1 c=blue; SYMBOL2 value=circle height=2 interpol=join line=2 c=blue; proc gplot data=diagnostics; plot predicted*litter=daylength/vref=2.075; But PROC GLM will automatically give you this plot when you fit the model (without even asking) as long as your HTML output is turned-on. 5

6 If you switch your listing of class variables, you can get this interaction plot instead... proc glm data=hamster; class daylength litter; model enzyme=daylength litter/solution; output out=diagnostics p=predicted r=residual; /* Check constant variance assumption with primitive resids vs preds plot: */ proc plot data=diagnostics; plot residual*predicted/vref=0; Plot of residual*predicted. Legend: A = 1 obs, B = 2 obs, etc. residual A A A A A A A A A A A A predicted 6

7 If you turn-on the HTML output option (which might actually be the default now), you can get nicer plots using the PLOT=DIAGNOSTICS option within PROC GLM. /* Turn-on HTML output prior to fitting the model.*/ proc glm data=hamster plot=diagnostics; class litter daylength; model enzyme=daylength litter/solutions; output out=diagnostics p=predicted r=residual; 7

8 Another way to get a QQ-plot using PROC CAPABILITY and tests of normality: proc capability data=diagnostics normaltest graphics; var residual; qqplot; The CAPABILITY Procedure Variable: residual Moments N 12 Sum Weights 12 Mean 0 Sum Observations 0 Std Deviation Variance Skewness 0 Kurtosis Uncorrected SS Corrected SS Coeff Variation. Std Error Mean Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode Range Interquartile Range Tests for Normality Test --Statistic p Value Shapiro-Wilk W Pr < W Kolmogorov-Smirnov D Pr > D > Cramer-von Mises W-Sq Pr > W-Sq > Anderson-Darling A-Sq Pr > A-Sq >