PLS205 Lab 1 January 9, Laboratory Topics 1 & 2

Transcription

1 PLS205 Lab 1 January 9, 2014 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) Hypothesis testing t-tests: One sample Two sample (Independent) Two sample (Paired) Power Calculations using Proc Power Proc Sort, Proc Print, Proc Means 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 Cards * 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 PROC UNIVARIATE test of Normality From ST&D pg. 30 [Lab1ex2.sas] Data Barley Input tells SAS to please read to the end of the line Cards 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 > Stem Leaf # Boxplot *-----* Lab 1.3

4 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. Example 3 PROC TTEST One sample [Lab1ex3.sas] One sample TTEST To use Proc TTEST to do a t-test (e.g. testing if µ = xx), we must create: new variable = old variable expected µ In the following example, we will test the hypothesis that µ = 78 by creating a new variable TEST78 = Extract We will then perform a t-test for the new variable against the hypothesis µ= 0 (see similar example ST&D pg ). Data Barley Input Extract78 = Extract * Here's that new variable Cards Proc Print * Proc Print displays the inputted data, a nice check Proc TTEST Var Extract * T TEST original variety Var Extract78 * T TEST new variable Extract78 Run Quit Output [Note: In your work, you would accompany this output with a line of interpretation.] The one sample PROC TTEST produces a nice Q-Q graph and tests the probability that the mean is 0 (In this case P<0.0001, since 0 is not included in the confidence vale). For the original Extract variable: Lab 1.4

5 Variable: Extract N Mean Std Dev Std Err Mean 95% CL Mean Std Dev DF t Value Pr > t <.0001 To test if the mean is equal to a certain value, We generate a new variable Extract78 =Extract 78 (the mean we want to test). TTEST of this new variable produces the same nice graphs as before (not shown). Variable: Extract78 N Mean Std Dev Std Err Minimum Maximum Mean 95% CL Mean Std Dev DF t Value Pr > t <.0001 Things to Notice 1. The t-test is highly significant (p < 0.001) so we reject H The 95% confidence interval of the mean for Extract is [ ]. See that the value 78 is far above the upper limit of this confidence interval. That is why the test is highly significant. 3. The 95% confidence interval of the mean for Extract78 is [-2.77 to -1.35] which does not include the 0, so the mean of this sample is significantly different from 78 (P<0.0001). 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? Lab 1.5

6 Example 4 PROC TTEST 2 independent samples [Lab1ex4.sas] A classification variable (named in this case Trt) is required to tell SAS which values belong to each group. Alphanumeric variables are indicated by $ after the name. Data Barley Input Trt $ Cards Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Var Proc TTEST class trt * assumes independent samples var extract Proc sort by Trt Proc Univariate normal plot Data = Barley var Extract by Trt Run Quit Confidence Interval TTEST Trt N Mean Std Dev Std Err Var Var Trt Mean 95% CL Mean Var Var Method Variances DF t Value Pr > t Pooled Equal Satterthwaite Unequal Equality of Variances Method Num DF Den DF F Value Pr > F Folded F In this case there are no significant differences in malt extract between the two varieties (P=0.16). The test for the equality of variances is NS so we use the P value for the Equal variances. If the test for the equality of variances is significant use the P value for the Unequal variances Lab 1.6

7 Tests for Normality using the by statement Test Statistic p Value Var1 Shapiro-Wilk W Pr < W NS (then we do not reject Normality) Var2 Shapiro-Wilk W Pr < W NS Example 5 PROC TTEST paired samples [Lab1ex5.sas] The two values are taken from the same experimental unit (NOT INDEPENDENT). For example, assume that Var2 is the same sample extracted at a different temperature. The code for paired TTEST is different. Data Barley Input Var1 *paired samples Cards Proc TTEST paired var1*var2 * assumes paired samples Run Quit The Paired TTEST Procedure generates a new variable equal to the difference: Var1 - Var2 and then performs a one sample TTEST to see if that difference is 0. Note that the 95% confidence interval [ ] does not include the 0. This agrees with the highly significance of this test P< N Mean Std Dev Std Err Minimum Maximum Mean 95% CL Mean Std Dev 95% CL Std Dev DF t Value Pr > t Lab 1.7

8 Example 6 Power calculation with PROC POWER [Lab1ex6.sas] 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 quit The POWER Procedure One-sample t Test for Mean Fixed Scenario Elements Distribution Method Normal Exact Alpha 0.05 Mean Standard Deviation 1.23 Total Sample Size 14 Number of Sides 2 Computed Power Index Null Mean Power >.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. 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. Lab 1.8

9 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 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 with 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 quit Lab 1.9

10 The POWER Procedure Two-sample t Test for Mean Difference Distribution Normal Method Exact Mean Difference 5 Standard Deviation 4 Number of Sides 2 Null Difference 0 Alpha 0.05 Computed Power N Per Index Group Power Example 7 [Lab1ex7.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 Cards 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 Lab 1.10

11 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. 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. Lab 1.11

12 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 Possible SAS data entry code: Data Example1 Input Treatment Do Replication = 1 to 5 Input Output End Cards 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 Lab 1.12

13 Once you are here, the SAS code is straightforward: Data Example1 Input Treatment Response Cards A 3.08 A E 2.91 E 2.58 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 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 End End End Lab 1.13

14 Cards 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. 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 End End End End Cards Lab 1.14

15 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. Example data set 3 Each data point identified by four classification variables data read input score datalines The following statements invoke the TTEST procedure to test if the mean test score is equal to 30. proc ttest data=read h0=30 var score freq count run Lab 1.15