Laboratory Topics 1 & 2

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1 PLS205 Lab 1 January 12, 2012 Laboratory Topics 1 & 2 Welcome, introduction, logistics, and organizational matters Introduction to SAS Writing and running programs; saving results; checking for errors Different ways to input/import data Proc Means, Proc Univariate (testing for normality) Introduction to SAS Enterprise Guide Inputting/importing data Saving output Modifying data Hypothesis testing using Enterprise Guide t-test Power Calculations using Proc Power Hypothesis testing using SAS editor t-test Proc Print, Proc Sort Nifty SAS Program: Critical values generator Niftier webpage APPENDIX: Data input examples Logistics and Organizational Matters 1. Homework is due at the beginning of lab, with 10 points off for every day it's late. If you don't submit it by the time the homework key is posted (usually 24 hours later), you will receive a zero. 2. Print the lab handouts before coming to lab; they will be posted on the class website each week by Wednesday night at the latest. 3. To log on to the lab computers, you need a UCD user ID and password. 4. Bring a diskette/flashdrive to lab to copy examples from the class directory (G:\PLS205\*.*). 5. This is a demanding class, so make use of all your resources office hours, lab handouts, homework keys, each other (the 205 Buddy System). Introduction to SAS (your new best friend?) To open SAS Version 9.3: START All Programs Class Software SAS SAS 9.3 (English) The SAS Display Manager There are three basic Windows, listed in the order you should view them: 1) The Program Editor window: Where you tell SAS what to do. 2) The Log window: Where SAS tells you what it did and (usually) what you did wrong. 3) The Output window: Where you find the results of your analysis (i.e. the good stuff). Lab 1.1

2 Example 1 From ST&D p. 29 [Lab1ex1.sas] Data BirdCount; * Creates a new data set called "BirdCount"; Input Field Birds; * Tells SAS the names of variables; * A throwback to the old days; ; * SEMICOLON! SEMICOLON! SEMICOLON!; Proc Means mean var std stderr cv Data = BirdCount; Var Birds; * Generate these requested statistics for the variable "Birds" in the dataset "BirdCount"; Run; Quit; Output Analysis Variable : Birds Coeff of Mean Variance Std Dev Std Error Variation Things to Learn 1. Run (submit) a SAS program with a simple click on the running man icon. 2. Move between windows to scan for red-type errors (Log) and then view results (Output). 3. Clear Log and Output windows with a simple click on the blank page icon. 4. Save program to disk. From Program Editor window: File Save as. 5. Save output to disk. From Output window: File Save as. 6. Set the line size for output to 76 characters (the perfect fit for 10 point Courier font on a page with 1" margins): Tools Options System Log and procedure output control SAS log and procedure output Double click linesize Example 2 From ST&D pg. 30 [Lab1ex2.sas] Data Barley; Input tells SAS to please read to the end of the line; ; Proc Univariate normal plot Data = Barley; var Extract; * Test for normality and generate plots for the variable Extract in the dataset Barley ; Run; Quit; Lab 1.2

3 Comments on the code 1. Use in the input statement when you have more Cards on a row than input variables. 2. The word "plot" in Proc Univariate is an example of an option. Its function is to generate several graphical displays of the data, including a stem-and-leaf display, a boxplot, and a normal probability plot (a.k.a. quantile-quantile or Q-Q plot) [see ST&D for interpretation of these displays: pages 30-32, ]. 3. The word "normal" in Proc Univariate is another option. Its function is to carry out tests for normality. In this class, we will be using the Shapiro-Wilk test for normality. Output Variable: Extract Moments N 14 Sum Weights 14 Mean Sum Observations Std Deviation Variance Skewness 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 Location: Mu0=0 Test -Statistic p Value Student's t t Pr > t <.0001 Sign M 7 Pr >= M Signed Rank S 52.5 Pr >= S 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 > Lab 1.3

4 Quantiles (Definition 5) Quantile Estimate 100% Max % % % % Q % Median % Q % % % % Min 73.9 Extreme Observations ----Lowest Highest--- Value Obs Value Obs Stem Leaf # Boxplot *-----* Normal Probability Plot * *++* * *+*+ * * * *+ ++*+* +++* * NOTE: The Shapiro-Wilk W statistic measures the linear correlation between the data and their normal scores. The closer W is to 1, the better correlated the distribution is to a normal distribution. Normality is rejected when W is sufficiently smaller than one, that is, when the value Pr < W is less than In this example, p = > 0.05, so we conclude the data exhibit a normal distribution. Lab 1.4

5 Introduction to SAS Enterprise Guide 1. To open Enterprise Guide: Start Menu SAS Enterprise Guide There are several ways to input data into Enterprise Guide: a. Import data that was run before in the SAS session: File Open Program Lab 1ex3 b. Type it directly into the Enterprise Guide spreadsheet. c. Import an Excel file: File Import Data (select Microsoft Excel Spreadsheet in the Files of Type menu) Select the file you want to open. d. Import a delimited text file: Same as above but select Delimited File in the Files of Type menu. 3. To analyze the data and check for normality: a. Push the Run button b. Click on the Output Data tab c. Analyze Capability Q-Q Plot d. Choose "Extract" for analysis e. Distribution Normal 4. To save or export the output: a. The easiest way is simply to copy the output or graph and paste it into your Word file: Edit Copy Graph (or Copy to Program Editor if it s text; once in the program editor, highlight what you wish to export and copy and paste as normal). 5. To modify and add data: a. Edit Mode (if Mode is not active, be sure all your Log and Output windows in SAS are clean and the data sheet is saved) Edit b. Add one extreme value (Edit Add rows) and observe the effects on the normality test. You can also add a row by placing the mouse at beginning of a row right click Add rows c. To insert a computed column, click the Calculator icon. d. To add, delete, or duplicate columns, right-click the top of the column. Lab 1.5

6 Hypothesis Testing Using Enterprise Guide In Enterprise Guide, with Barley data loaded: Analyze ANOVA t-tests One Sample t-test for a Mean choose Extract as the variable H0: 78 Confidence Level select 95% Output N Mean Std Dev Std Err MinimumMaximum Mean 95% CL Mean Std Dev 95% CL Std Dev DF t Value Pr > t <.0001 Confidence Interval In Enterprise Guide, with Barley data loaded: Describe Summary Statistics under Data choose Extract as the variable Under Statistics--Additional, select Confidence limits of the mean Analysis Variable : Extract Mean Std Dev Minimum Maximum N Lower 95% CL for Mean Upper 95% CL for Mean Things to Notice 1. The t-test is highly significant (p < 0.001); so we reject H The 95% confidence interval of the mean is [ ]. See that the value 78 is far above the upper limit of this confidence interval. That is why the test is highly significant. In your ample spare time, try repeating the exercise using (the lower extreme of the confidence interval) as the Null Mean. What is the expected probability of the t-test? Power calculation using SAS PROC POWER One Sample power test. What is the power of a test to detect a difference between the observed mean of and alternative means of and (the same value)? proc power; onesamplemeans mean = ntotal = 14 stddev = 1.23 nullmean= alpha= 0.05 power =.; run; The POWER Procedure Lab 1.6

7 One-sample t Test for Mean Fixed Scenario Elements Distribution Normal Method Exact Alpha 0.05 Mean Standard Deviation 1.23 Total Sample Size 14 Number of Sides 2 Computed Power Null Index Mean Power One curve is on top of the other! >.999 Things to Notice 1. The. after power indicates that you are requesting the power 2. The onesamplemeans is one line of code up to the to the ;. It is split in multiple lines to make it easier to read 3. The power to detect a difference from a null mean of 77 is 0.846, and the power increases to almost 1 when the alternative mean is 78. The minimum value of the power is =alpha when the alternative mean is the same as the observed mean. You generally want a power of at least 0.80 (80%). Notice that a 95% confidence interval of the mean is [ ] excludes both 77 and 78. See that the value 78 is far above the upper limit of this confidence interval. That is why the test is highly significant. Proc Power can be also used to estimate the number of samples required to obtain a certain power proc power; onesamplemeans mean = ntotal =. stddev = 1.23 nullmean= 77 alpha= 0.05 power = ; run; Lab 1.7

8 The POWER Procedure One-sample t Test for Mean Fixed Scenario Elements Distribution Normal Method Exact Null Mean 77 Alpha 0.05 Mean Standard Deviation 1.23 Number of Sides 2 Computed N Total Nominal Actual N Index Power Power Total SAS rounds the number estimation conservatively to the upper number if there are decimals, to guarantee at least the requested power. Two sample power test. What is the power of a test to detect a difference between two samples owith the following mean and variances: Mean Variance N Sample Sample Mean difference= 5 Pooled s= SQRT( (15+17)/2)= 4 (not the same as the average of the standard deviations) proc power; twosamplemeans test=diff meandiff = 5 stddev = 4 npergroup = power =.; run; The POWER Procedure Two-sample t Test for Mean Difference Fixed Scenario Elements Distribution Normal Method Exact Mean Difference 5 Standard Deviation 4 Number of Sides 2 Null Difference 0 Alpha 0.05 Lab 1.8

9 Computed Power N Per Index Group Power Hypothesis Testing Using SAS To use Proc Univariate to do a t-test (e.g. testing if = xx), we must create: new variable = old variable expected In the following example, we will test the hypothesis that = 78 by creating a new variable TEST78 = Extract We will then perform a t-test for the new variable against the hypothesis = 0 (see similar example ST&D pg ). Example 3 [Lab1ex3.sas] Data Barley; Input Test78 = Extract ; * Here's that new variable; ; Proc Print; * Proc Print displays the inputted data, a nice check; Title 'Hypothesis mean = 78.0'; Proc Univariate; Var Test78; * Indicates we want to use the new variable Test78; Proc GChart; * Proc GChart creates fancy charts in new windows; Run; Quit; Hbar Test78; * Hbar = horizontal bar. Could be vbar, pie, etc; Output [Note: In your work, you would accompany this output with a line of interpretation.] Variable: Test78 Tests for Location: Mu0=0 Test -Statistic p Value Student's t t Pr > t <.0001 Lab 1.9

10 Example 4 [Lab1ex4.sas] This next example illustrates the use of Proc Sort, Proc Print, and Proc Means: Data Grades; Input StudentNo GradUG $ HWGrade Midterm Final; * $ indicates a non-numeric class variable; FinalGrade = 0.25*HWgrade *Midterm *Final; 13 G G G UG G UG ; Proc Sort; * Orders the data by the variable named below; By StudentNo; Proc Print; * Displays the inputted data in whatever order you wish; Title 'Roster in order of Student Number'; ID StudentNo; Var HWGrade Midterm Final FinalGrade; Proc Means n mean std var stderr maxdec=1;* MaxDec limits all numbers to 1 decimal place; Title 'Descriptive statistics'; Var HWGrade Midterm Final FinalGrade; Proc Sort; By GradUG; * Sorting is needed because of the Proc Means below; Proc Means n mean std var stderr maxdec=1; Title 'Descriptive statistics by student level'; Var HWGrade Midterm Final FinalGrade; By GradUG; * Without Proc Sort above, this would confuse SAS; Proc Plot; Plot Final*FinalGrade; * Generates plot of Final (y) vs. FinalGrade(x); Run; Quit; Note: If you add a title to one Proc statement but not to the others, all the Proc outputs will have the same label. In fact, they will carry over to future programs! To avoid confusion, you should label everything, especially as your programs become more complicated and the output more profuse. Lab 1.10

11 Nifty SAS Program [SASCritValues.sas] Tables of critical values rarely contain the exact values you are looking for. Here's a way to use SAS to find critical values and p-values with precision: Data ValueFinder; TITLE 'CRITICAL VALUES'; * The functions below find the critical value for a specified probability 'p'; * where 'p' is the proportion of the area to the **LEFT** of the critical value; * [e.g will be the 'p' for a 5% two-tailed test]; Nvalue = PROBIT (0.975); * This is Z; Tvalue = TINV (0.975, 20); * This is t (p, df); Chivalue = CINV (0.975, 20); * This is chi-square (p, df); Fvalue = FINV (0.975, 20, 4); * This is F (p, NUM df, DEN df); TITLE 'PROBABILITY'; * These functions return the probability that an observation is < x; Nprob = PROBNORM (1.96); * Z; Tprob = PROBT (2.086, 20); * t; Chiprob = PROBCHI (34.2, 20); * chi-square; Fprob = PROBF (8.56, 20, 4); * F; Proc Print; Run; Quit; Very very handy; but if you use this, please be aware of what SAS is telling you, namely that it is the areas to the LEFT of the critical values that are being considered. Double-check your results with a table until you get the hang of it. Niftier Website There are a lot of free critical values calculators available on-line as well. Feel free to use them, but be sure you understand how they work. The best way to do this is by checking some test values against the tables in the book (or on the class webpage). A good site: Caution: Be aware of what these calculators are telling you, namely that it is the areas to the LEFT or RIGHT of the critical values that are being considered. Double-check your results with a table until you get the hang of it. APPENDIX: Data Input Examples Students lose a shocking number of points on homeworks and exams due to incorrect data input (i.e. careless typographical errors). Very rarely should you ever have to input data number-by-number because almost all the datasets will be provided to you already typed into Word documents. The challenge you have is to structure your data input routine in SAS such that it will read correctly whatever you cut-and-paste into your code. The "Do-End-loops" illustrated below may look complicated, but it is worth your time to understand how they work, especially as our data sets become bigger and bigger. Example dataset 1 5 treatments with 5 replications each Lab 1.11

12 Possible SAS data entry code: Data Example1; Input Treatment Do Replication = 1 to 5; Input Output; A B C D E ; A B C D E If this is scary, you can also paste the above table into Excel and manipulate it (again, by cutting and pasting and transposing, not by retyping numbers) to give you something like this: A 3.08 A 5.51 A 5.07 A 4.41 A 3.85 B 3.3 B 3.19 B 4.29 B 1.87 B 1.32 C 5.73 C 5.18 C 5.06 C 3.96 C 3.74 D 1.87 D 3.3 D 2.64 D 3.08 D 3.85 E 2.25 E 4.78 E 3.13 E 2.91 E 2.58 Lab 1.12

13 Once you are here, the SAS code is straightforward: Data Example1; Input Treatment Response; A 3.08 A E 2.91 E 2.58 ; The two approaches are equivalent, but as the data sets become bigger, the Excel manipulations needed for the second approach will become more and more cumbersome. Example data set 2 Combinations of treatments with 10 replications each Trt1A Trt1B Trt2A Trt2B Trt2C Trt2A Trt2B Trt2C Possible SAS data entry code: Data Example2; Do Trt1 = 1 to 2; Do Trt2 = 1 to 3; Do Rep = 1 to 10; Input Output; ; Here we ve set up the input routine in such a way that we could just cut-and-paste the data table into SAS. No chance for typographical errors. Lab 1.13

14 Example data set 3 Each data point identified by four classification variables A1 A2 C1 C2 C3 C4 D1 D2 D3 D1 D2 D3 D1 D2 D3 D1 D2 D3 B B B B B B B B Possible SAS data entry code: Data Example3; Do ClassA = 1 to 2; Do ClassB = 1 to 4; Do ClassC = 1 to 4; Do ClassD = 1 to 3; Input Output; ; Voila! Without the Do-End loops, the same dataset would be five times as large because you would have to input the individual classification address for each and every data point (e.g. A2, B3, C2, D1). Again, this may seem unnecessary to you now; but please take the time to learn it. And if you have any questions, just ask. Lab 1.14