Sas project: Equivalency test of word lists in noisy background

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project for Stats class using RCBD

project for Stats class using RCBD

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  • 1. STAT 7010 Auburn UniversityFeb 21, 2011 Equivalency Test of Word Lists in Noisy Background Abstract Randomized Complete Block Design was used to test the equality of four standardaudiology word lists in the presence of background noise. Twenty-four participants conductedthe hearing tests, in which four word list tapes were played to each participant in a random order.Considering that the differences in personal traits may interfere with environmental factors, eachparticipant was treated as a block in this study. ANOVA, multiply comparisons, and diagnostictests were conducted. The results indicated a significant difference among the four word lists.Specifically, words in list 1 were much easier to be recognized in the presence of backgroundnoise than their counterparts in list 3 and 4. Model diagnostic tests gave an overall reliable resultthat the normal and addictive requirements were satisfied, except for a distractive yet smallconcern on equal variance. In conclusion, the four standard word lists were not as suitable to usein noisy background as in quiet environment. Introduction Hearing aids assist people’s hearing by amplifying the voice volume (DASL, 1996).However, the background noise can be amplified as well. This project focused on whetherdifferent word lists, which are the standard audiology tools for assessing hearing in quietconditions, are equal in the level of difficulty in the presence of background noise. Fifty Englishwords, calibrated to be equally difficult to perceive under no noise condition, were used in thisstudy. Randomized Complete Block Design (RCBD) was used by considering individualdifferences as the block variable. Twenty-four participants with normal hearing was invited tothe experiment. Background noise was present during the experiment. They were guided to listen 1
  • 2. STAT 7010 Auburn UniversityFeb 21, 2011to four lists of standard audiology tapes at low volume. The order of tapes was randomized. Eachword was repeated by the participants in order to check whether they had correctly recognizedthe word. The number of correct words was recorded as the dependent variable. The order of listwas randomized. Data The data set was obtained from online resources (DASL, 1996). It contains threevariables with 96 observations. Twenty-four subjects were recorded as the block variable. Fourword lists were considered as the independent variable while the hearing score corresponding toeach participant was the dependent variable. Whether the four lists were detected to havedifferent level of hearing scores was of our interest. Methods ANOVA test was conducted to explore the potential differences among four word lists innoise background. If significant differences were shown as predicted, pairwise comparison wasfurther applied to analyze the inequality of means between pairs of lists. Additionally, thenormality, constant variance, and additivity assumption were tested to ensure the validity of thedesign. The statistical model for RCBD was: yij = μ + τi + βj + εij, i=1, 2, 3, 4, j=1,…,24where μ is the overall mean of hearing scores, τ is the effect due to treatment, β is the effect dueto block, ε is the effect due to random error, i (i=1, 2, 3, 4) represents four treatment levels, j(j=1,…,24) is the block or the assigned identification number of each participant. The nullhypothesis of ANOVA analysis was: H0: μ1 =μ2=μ3 =μ4, and thus the alternative hypothesis was:HA μi ≠ μj for at least one pair i ≠ j. Pairwise comparisons of means (Turkey, Bonferroni, & 2
  • 3. STAT 7010 Auburn UniversityFeb 21, 2011Scheffe procedure) were conducted to identify all possible differences between hearing scores oftwo word lists. Additionally, we assumed that error term ε follows normal distribution N (0, σ2) and σ2should be equal cross all treatments (i.e., four lists). Thus, the constant variance assumptionwould be: H0: and HA: . Shapiro-Wilk, Kolmogorov-Smirnov test, Cramer-vonMises, and Anderson-Darling tests were conducted to test the normality assumption whileLevene’s test was used to check the constant variance assumption. Since RCBD assumed that the effects due to blocks and treatments are additive, Tukey’s1 df test was also included in our diagnostic tests. The interactive model in contrast to our initialmodel was: yij = μ + τi + βj + γ τi βj + εij, i=1, 2, 3, 4, j=1,…,24where γ represents the interaction coefficients. Thus H0: γ = 0 and HA: γ ≠ 0 was the null andalternative hypotheses, respectively. ResultsPrinciple Analysis There were significant differences among the four word lists (F(3, 69) = 8.45, p < .0001,for more information, please refer to Appendix - 1). Thus, multiple comparisons were employedto check the potential differences among pairs of lists. All three pairwise comparison tests(Turkey, Bonferroni, & Scheffe) indicated a same pattern that List 2, 3, and 4 were notsignificantly different from each other while List 1 was not significantly different from List 2 butdistinguishable from the other two lists (Table 1). The easiest word lists was List 1 (Mean =32.750) compared with other three lists. 3
  • 4. STAT 7010 Auburn UniversityFeb 21, 2011 Table 1 Comparison of Means List N Mean 1 24 32.750a 2 24 29.667ab 4 24 25.583b 3 24 25.250b *Means with the same letter are not significantly different from each otherDiagnostic Analysis Tukeys test of additivity (1 df Nonadditivity Test, Table 2) verified the assumption thatthe RCBD model was additive and thus ruled out the possibility of interaction effect betweenlists and participants (F0(1, 68) = 0.11, p = .7561, no evidence to declare nonadditivity). Table 2 Turkeys 1 df Nonadditivity Test Source df SS MS F-statistic P-value Lists 3 920.4583 306.8194 8.34 <.0001 Subjects 23 3231.6250 140.5054 3.82 <.0001 Psquare 1 3.8888 3.8888 0.11 0.7461 Error 68 2502.6529 36.8037 Total 96 6658.6250 <.0001 Brown and Forsythe’s test for homogeneity showed no evident to indicate varianceheterogeneity among hearing scores of four word lists (F = 0.57, p = 0.63). Plots of residualsfurther verified the homogeneity of variance assumption. However, the spread of residuals seemsto differ from subject to subject (F = 1.88, p = 0.228). Several outliers in Figure 1 (L) and (R)suggested their peculiarity among other data points. Thus, there might be some concerns onequal variance. In addition, the normality assumption was also verified since all four normalitytests gave a consensus result (Shapiro-Wilk test, p = .7811; Kolmogorov-Smirnov test, p >.1500;Cramer-von Mises test, p > .2500; Anderson-Darling test, p > .2500, for residual plot, pleaserefer to Appendix - 2). 4
  • 5. STAT 7010 Auburn UniversityFeb 21, 2011 Figure 1 Residual Plot: (L) Residual vs. Predict; (R) Residual vs. Block, (B) Residual vs. Treatment Discussion and Summary The RCBD was successful in this study considering a noticeable MS of block variable(MSblock =140.5054, MSerror =36.3266, MSlist =306.8194). Since List 1 was the problematic onethat exhibited significant differences in comparison with other lists, the standard tools forevaluation hearing in quiet environment may not be suitable to extend to conditions when thebackground noise is present. To assess the hearing competency in a noisy environment, it mightbe more suitable to pick List 2, 3, and 4 since they were less vulnerability to be unequal.Furthermore, since the homogeneity assumption was not well supported in our analysis, it wouldbe necessary to transfer the data and return the principle analysis. Further studies may considermore specific factors as block variables, such as age, gender, and habit of using headsets. 5
  • 6. STAT 7010 Auburn UniversityFeb 21, 2011 References DASL. (1996). The Data and Story Library: Hearing. Retrieved fromhttp://lib.stat.cmu.edu/DASL/Datafiles/Hearing.html Loven, Faith. (1981). A Study of the Interlist Equivalency of the CID W-22 Word ListPresented in Quiet and in Noise. Unpublished MS Thesis, University of Iowa. Appendices 1 - ANOVA table of principle test Source df SS MS F-statistic P-value List 3 920.458333 306.8194 8.45 <.0001 Subject 23 3231.625000 140.5054 3.87 <.0001 Error 69 2506.541667 36.3266 Corrected Total 95 6658.625000 <.0001 2 – Plot of normality test 3 – SAS codedata hearing; 10 1 32input subject list score; 11 1 32cards; 12 1 381 1 28 13 1 322 1 24 14 1 403 1 32 15 1 284 1 30 16 1 485 1 34 17 1 346 1 30 18 1 287 1 36 19 1 408 1 32 20 1 189 1 48 21 1 20 6
  • 7. STAT 7010 Auburn UniversityFeb 21, 201122 1 26 6 4 3023 1 36 7 4 2224 1 40 8 4 281 2 20 9 4 302 2 16 10 4 163 2 38 11 4 184 2 20 12 4 345 2 34 13 4 326 2 30 14 4 347 2 30 15 4 328 2 28 16 4 189 2 42 17 4 2010 2 36 18 4 2011 2 32 19 4 4012 2 36 20 4 2613 2 28 21 4 1414 2 38 22 4 1415 2 36 23 4 3016 2 28 24 4 4217 2 34 ;18 2 1619 2 3420 2 22 *f-test;21 2 20 proc glm;22 2 30 class subject list;23 2 20 model score = subject list;24 2 44 means list / lines bon scheffe tukey;1 3 24 output out=diag r = residual p = predict;2 3 32 run;3 3 20 quit;4 3 145 3 326 3 22 *normality;7 3 20 proc univariate data = diag;8 3 26 var residual;9 3 26 qqplot residual / normal (l=1 mu=010 3 38 sigma=est);11 3 30 hist residual / normal (l=1 mu=0 sigma=est);12 3 16 run;13 3 3614 3 32 *constant variance;15 3 3816 3 14 proc glm;17 3 26 class list;18 3 14 model score = list;19 3 38 means list / hovtest=bf hovtest=levene;20 3 20 run;21 3 14 quit;22 3 1823 3 22 proc glm;24 3 34 class subject;1 4 26 model score = subject;2 4 24 means subject / hovtest=bf hovtest=levene;3 4 22 run;4 4 18 quit;5 4 24 7
  • 8. STAT 7010 Auburn UniversityFeb 21, 2011symbol1 v=symbol v=circle i=r c=green; plot residual * predict;quit; run; quit;proc gplot;title1 Residual vs Block; plot residual * subject; *additivity;run; Data tukey;quit; set diag; psquare = predict*predict;proc gplot; run;title2 Residual vs Treatment; quit; plot residual * list;run; proc glm;quit; class subject list; model score = subject list psquare;proc gplot; run;title3 Residual vs Predict; quit; 8