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STAT 7010                                                                         Auburn University
Feb 21, 2011


               Equivalency Test of Word Lists in Noisy Background

                                              Abstract

         Randomized Complete Block Design was used to test the equality of four standard

audiology word lists in the presence of background noise. Twenty-four participants conducted

the 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, each

participant was treated as a block in this study. ANOVA, multiply comparisons, and diagnostic

tests 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 background

noise than their counterparts in list 3 and 4. Model diagnostic tests gave an overall reliable result

that the normal and addictive requirements were satisfied, except for a distractive yet small

concern on equal variance. In conclusion, the four standard word lists were not as suitable to use

in 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 whether

different word lists, which are the standard audiology tools for assessing hearing in quiet

conditions, are equal in the level of difficulty in the presence of background noise. Fifty English

words, calibrated to be equally difficult to perceive under no noise condition, were used in this

study.

         Randomized Complete Block Design (RCBD) was used by considering individual

differences as the block variable. Twenty-four participants with normal hearing was invited to

the experiment. Background noise was present during the experiment. They were guided to listen



                                                      1
STAT 7010                                                                           Auburn University
Feb 21, 2011


to four lists of standard audiology tapes at low volume. The order of tapes was randomized. Each

word was repeated by the participants in order to check whether they had correctly recognized

the word. The number of correct words was recorded as the dependent variable. The order of list

was randomized.

                                                     Data

          The data set was obtained from online resources (DASL, 1996). It contains three

variables with 96 observations. Twenty-four subjects were recorded as the block variable. Four

word lists were considered as the independent variable while the hearing score corresponding to

each participant was the dependent variable. Whether the four lists were detected to have

different level of hearing scores was of our interest.

                                                   Methods

          ANOVA test was conducted to explore the potential differences among four word lists in

noise background. If significant differences were shown as predicted, pairwise comparison was

further applied to analyze the inequality of means between pairs of lists. Additionally, the

normality, constant variance, and additivity assumption were tested to ensure the validity of the

design.

          The statistical model for RCBD was:

          yij = μ + τi + βj + εij, i=1, 2, 3, 4, j=1,…,24

where μ is the overall mean of hearing scores, τ is the effect due to treatment, β is the effect due

to 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 null

hypothesis 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
STAT 7010                                                                         Auburn University
Feb 21, 2011


Scheffe procedure) were conducted to identify all possible differences between hearing scores of

two word lists.

       Additionally, we assumed that error term ε follows normal distribution N (0, σ2) and σ2

should be equal cross all treatments (i.e., four lists). Thus, the constant variance assumption

would be: H0:           and HA:          . Shapiro-Wilk, Kolmogorov-Smirnov test, Cramer-von

Mises, and Anderson-Darling tests were conducted to test the normality assumption while

Levene’s test was used to check the constant variance assumption.

       Since RCBD assumed that the effects due to blocks and treatments are additive, Tukey’s

1 df test was also included in our diagnostic tests. The interactive model in contrast to our initial

model was:

       yij = μ + τi + βj + γ τi βj + εij, i=1, 2, 3, 4, j=1,…,24

where γ represents the interaction coefficients. Thus H0: γ = 0 and HA: γ ≠ 0 was the null and

alternative hypotheses, respectively.

                                                 Results

Principle 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 employed

to 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 not

significantly different from each other while List 1 was not significantly different from List 2 but

distinguishable from the other two lists (Table 1). The easiest word lists was List 1 (Mean =

32.750) compared with other three lists.




                                                         3
STAT 7010                                                                                  Auburn University
Feb 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 other

Diagnostic Analysis

       Tukey's test of additivity (1 df Nonadditivity Test, Table 2) verified the assumption that

the RCBD model was additive and thus ruled out the possibility of interaction effect between

lists and participants (F0(1, 68) = 0.11, p = .7561, no evidence to declare nonadditivity).

                                     Table 2 Turkey's 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 variance

heterogeneity among hearing scores of four word lists (F = 0.57, p = 0.63). Plots of residuals

further verified the homogeneity of variance assumption. However, the spread of residuals seems

to 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 on

equal variance. In addition, the normality assumption was also verified since all four normality

tests 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, please

refer to Appendix - 2).




                                                            4
STAT 7010                                                                                   Auburn University
Feb 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 one

that exhibited significant differences in comparison with other lists, the standard tools for

evaluation hearing in quiet environment may not be suitable to extend to conditions when the

background noise is present. To assess the hearing competency in a noisy environment, it might

be 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 would

be necessary to transfer the data and return the principle analysis. Further studies may consider

more specific factors as block variables, such as age, gender, and habit of using headsets.




                                                            5
STAT 7010                                                                                             Auburn University
Feb 21, 2011




                                                    References

         DASL. (1996). The Data and Story Library: Hearing. Retrieved from

http://lib.stat.cmu.edu/DASL/Datafiles/Hearing.html

         Loven, Faith. (1981). A Study of the Interlist Equivalency of the CID W-22 Word List

Presented 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 code

data hearing;                                                   10        1          32
input subject list score;                                       11        1          32
cards;                                                          12        1          38
1        1          28                                          13        1          32
2        1          24                                          14        1          40
3        1          32                                          15        1          28
4        1          30                                          16        1          48
5        1          34                                          17        1          34
6        1          30                                          18        1          28
7        1          36                                          19        1          40
8        1          32                                          20        1          18
9        1          48                                          21        1          20



                                                               6
STAT 7010                                          Auburn University
Feb 21, 2011
22    1        26   6        4        30
23    1        36   7        4        22
24    1        40   8        4        28
1     2        20   9        4        30
2     2        16   10       4        16
3     2        38   11       4        18
4     2        20   12       4        34
5     2        34   13       4        32
6     2        30   14       4        34
7     2        30   15       4        32
8     2        28   16       4        18
9     2        42   17       4        20
10    2        36   18       4        20
11    2        32   19       4        40
12    2        36   20       4        26
13    2        28   21       4        14
14    2        38   22       4        14
15    2        36   23       4        30
16    2        28   24       4        42
17    2        34   ;
18    2        16
19    2        34
20    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        14
5     3        32
6     3        22   *normality;
7     3        20   proc univariate data = diag;
8     3        26           var residual;
9     3        26           qqplot residual / normal (l=1 mu=0
10    3        38   sigma=est);
11    3        30           hist residual / normal (l=1 mu=0 sigma=est);
12    3        16   run;
13    3        36
14    3        32   *constant variance;
15    3        38
16    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        18
23    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
STAT 7010                                                               Auburn University
Feb 21, 2011
symbol1 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

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Sas project: Equivalency test of word lists in noisy background

  • 1. STAT 7010 Auburn University Feb 21, 2011 Equivalency Test of Word Lists in Noisy Background Abstract Randomized Complete Block Design was used to test the equality of four standard audiology word lists in the presence of background noise. Twenty-four participants conducted the 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, each participant was treated as a block in this study. ANOVA, multiply comparisons, and diagnostic tests 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 background noise than their counterparts in list 3 and 4. Model diagnostic tests gave an overall reliable result that the normal and addictive requirements were satisfied, except for a distractive yet small concern on equal variance. In conclusion, the four standard word lists were not as suitable to use in 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 whether different word lists, which are the standard audiology tools for assessing hearing in quiet conditions, are equal in the level of difficulty in the presence of background noise. Fifty English words, calibrated to be equally difficult to perceive under no noise condition, were used in this study. Randomized Complete Block Design (RCBD) was used by considering individual differences as the block variable. Twenty-four participants with normal hearing was invited to the experiment. Background noise was present during the experiment. They were guided to listen 1
  • 2. STAT 7010 Auburn University Feb 21, 2011 to four lists of standard audiology tapes at low volume. The order of tapes was randomized. Each word was repeated by the participants in order to check whether they had correctly recognized the word. The number of correct words was recorded as the dependent variable. The order of list was randomized. Data The data set was obtained from online resources (DASL, 1996). It contains three variables with 96 observations. Twenty-four subjects were recorded as the block variable. Four word lists were considered as the independent variable while the hearing score corresponding to each participant was the dependent variable. Whether the four lists were detected to have different level of hearing scores was of our interest. Methods ANOVA test was conducted to explore the potential differences among four word lists in noise background. If significant differences were shown as predicted, pairwise comparison was further applied to analyze the inequality of means between pairs of lists. Additionally, the normality, constant variance, and additivity assumption were tested to ensure the validity of the design. The statistical model for RCBD was: yij = μ + τi + βj + εij, i=1, 2, 3, 4, j=1,…,24 where μ is the overall mean of hearing scores, τ is the effect due to treatment, β is the effect due to 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 null hypothesis 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 University Feb 21, 2011 Scheffe procedure) were conducted to identify all possible differences between hearing scores of two word lists. Additionally, we assumed that error term ε follows normal distribution N (0, σ2) and σ2 should be equal cross all treatments (i.e., four lists). Thus, the constant variance assumption would be: H0: and HA: . Shapiro-Wilk, Kolmogorov-Smirnov test, Cramer-von Mises, and Anderson-Darling tests were conducted to test the normality assumption while Levene’s test was used to check the constant variance assumption. Since RCBD assumed that the effects due to blocks and treatments are additive, Tukey’s 1 df test was also included in our diagnostic tests. The interactive model in contrast to our initial model was: yij = μ + τi + βj + γ τi βj + εij, i=1, 2, 3, 4, j=1,…,24 where γ represents the interaction coefficients. Thus H0: γ = 0 and HA: γ ≠ 0 was the null and alternative hypotheses, respectively. Results Principle 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 employed to 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 not significantly different from each other while List 1 was not significantly different from List 2 but distinguishable 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 University Feb 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 other Diagnostic Analysis Tukey's test of additivity (1 df Nonadditivity Test, Table 2) verified the assumption that the RCBD model was additive and thus ruled out the possibility of interaction effect between lists and participants (F0(1, 68) = 0.11, p = .7561, no evidence to declare nonadditivity). Table 2 Turkey's 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 variance heterogeneity among hearing scores of four word lists (F = 0.57, p = 0.63). Plots of residuals further verified the homogeneity of variance assumption. However, the spread of residuals seems to 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 on equal variance. In addition, the normality assumption was also verified since all four normality tests 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, please refer to Appendix - 2). 4
  • 5. STAT 7010 Auburn University Feb 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 one that exhibited significant differences in comparison with other lists, the standard tools for evaluation hearing in quiet environment may not be suitable to extend to conditions when the background noise is present. To assess the hearing competency in a noisy environment, it might be 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 would be necessary to transfer the data and return the principle analysis. Further studies may consider more specific factors as block variables, such as age, gender, and habit of using headsets. 5
  • 6. STAT 7010 Auburn University Feb 21, 2011 References DASL. (1996). The Data and Story Library: Hearing. Retrieved from http://lib.stat.cmu.edu/DASL/Datafiles/Hearing.html Loven, Faith. (1981). A Study of the Interlist Equivalency of the CID W-22 Word List Presented 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 code data hearing; 10 1 32 input subject list score; 11 1 32 cards; 12 1 38 1 1 28 13 1 32 2 1 24 14 1 40 3 1 32 15 1 28 4 1 30 16 1 48 5 1 34 17 1 34 6 1 30 18 1 28 7 1 36 19 1 40 8 1 32 20 1 18 9 1 48 21 1 20 6
  • 7. STAT 7010 Auburn University Feb 21, 2011 22 1 26 6 4 30 23 1 36 7 4 22 24 1 40 8 4 28 1 2 20 9 4 30 2 2 16 10 4 16 3 2 38 11 4 18 4 2 20 12 4 34 5 2 34 13 4 32 6 2 30 14 4 34 7 2 30 15 4 32 8 2 28 16 4 18 9 2 42 17 4 20 10 2 36 18 4 20 11 2 32 19 4 40 12 2 36 20 4 26 13 2 28 21 4 14 14 2 38 22 4 14 15 2 36 23 4 30 16 2 28 24 4 42 17 2 34 ; 18 2 16 19 2 34 20 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 14 5 3 32 6 3 22 *normality; 7 3 20 proc univariate data = diag; 8 3 26 var residual; 9 3 26 qqplot residual / normal (l=1 mu=0 10 3 38 sigma=est); 11 3 30 hist residual / normal (l=1 mu=0 sigma=est); 12 3 16 run; 13 3 36 14 3 32 *constant variance; 15 3 38 16 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 18 23 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 University Feb 21, 2011 symbol1 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