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Stata Data Analysis Examples One-way Manova
جمعه چهاردهم فروردین 1388 21:23 Stata Data Analysis Examples Examples of One-way Multivariate Analysis of Variance Example 1. A researcher randomly assigns 33 subjects to one of three groups. The first group receives technical dietary information interactively from an on-line website. Group 2 receives the same information in from a nurse practitioner, while group 3 receives the information from a video tape made by the same nurse practitioner. The researcher looks at three different ratings of the presentation, difficulty, useful and importance, to determine if there is a difference in the modes of presentation. In particular, the researcher is interested in whether the interactive website is superior because that is the most cost-effective way of delivering the information. Description of the Data Let's pursue Example 1 from above. We have a data file, manova.dta, with 33 observations on three response variables. The response variables are ratings of useful, difficulty and importance. Level 1 of the group variable is the treatment group, level 2 is control group 1 and level 3 is control group 2. Let's look at the data. use http://www.ats.ucla.edu/stat/stata/dae/manova, clear
summarize difficulty useful importance
Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- useful | 33 16.3303 3.292461 11.9 24.3 difficulty | 33 5.715152 2.017598 2.4 10.25 importance | 33 6.475758 3.985131 .2 18.8
tabulate group
group | Freq. Percent Cum. ------------+----------------------------------- treatment | 11 33.33 33.33 control_1 | 11 33.33 66.67 control_2 | 11 33.33 100.00 ------------+----------------------------------- Total | 33 100.00
tabstat difficulty useful importance, by(group)
Summary statistics: mean by categories of: group
group | useful diffic~y import~e ----------+------------------------------ treatment | 18.11818 6.190909 8.681818 control_1 | 15.52727 5.581818 5.109091 control_2 | 15.34545 5.372727 5.636364 ----------+------------------------------ Total | 16.3303 5.715152 6.475758
correlate useful difficulty importance (obs=33)
| useful diffic~y import~e -------------+--------------------------- useful | 1.0000 difficulty | 0.0978 1.0000 importance | -0.3411 0.1978 1.0000 Some Strategies You Might Be Tempted To Try Before we show how you can analyze this with a canonical correlation analysis, let's consider some other methods that you might use.
Stata One-way Manova Although this is a multivariate analysis, we will begin with separate univariate anovas to get a feel for what is happening with the data. foreach vname in difficulty useful importance { anova `vname' group } /* useful */ Number of obs = 33 R-squared = 0.1526 Root MSE = 3.13031 Adj R-squared = 0.0961
Source | Partial SS df MS F Prob > F -----------+---------------------------------------------------- Model | 52.9242378 2 26.4621189 2.70 0.0835 | group | 52.9242378 2 26.4621189 2.70 0.0835 | Residual | 293.965442 30 9.79884808 -----------+---------------------------------------------------- Total | 346.88968 32 10.8403025 /* difficulty */ Number of obs = 33 R-squared = 0.0305 Root MSE = 2.05173 Adj R-squared = -0.0341
Source | Partial SS df MS F Prob > F -----------+---------------------------------------------------- Model | 3.97515121 2 1.9875756 0.47 0.6282 | group | 3.97515121 2 1.9875756 0.47 0.6282 | Residual | 126.287277 30 4.20957589 -----------+---------------------------------------------------- Total | 130.262428 32 4.07070087 /* importance */ Number of obs = 33 R-squared = 0.1610 Root MSE = 3.76993 Adj R-squared = 0.1051
Source | Partial SS df MS F Prob > F -----------+---------------------------------------------------- Model | 81.8296936 2 40.9148468 2.88 0.0718 | group | 81.8296936 2 40.9148468 2.88 0.0718 | Residual | 426.370896 30 14.2123632 -----------+---------------------------------------------------- Total | 508.20059 32 15.8812684 While none of the three anovas were statistically significant at the alpha = .05 level, in particular, the anova for difficulty was less than 1. Next, we will run the manova itself. manova difficulty useful importance = group
Number of obs = 33
W = Wilks' lambda L = Lawley-Hotelling trace P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F -----------+-------------------------------------------------- group | W 0.5258 2 6.0 56.0 3.54 0.0049 e | P 0.4767 6.0 58.0 3.02 0.0122 a | L 0.8972 6.0 54.0 4.04 0.0021 a | R 0.8920 3.0 29.0 8.62 0.0003 u |-------------------------------------------------- Residual | 30 -----------+-------------------------------------------------- Total | 32 -------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F Now that we have have determined that the overall multivariate test is significant, we will follow up with several post-hoc tests. /* multivariate test of group 1 versus the average of group 2 & 3 */ matrix c1=(0,2,-1,-1)
manovatest, test(c1)
Test constraint (1) 2 group[1] - group[2] - group[3] = 0
W = Wilks' lambda L = Lawley-Hotelling trace P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F -----------+-------------------------------------------------- manovatest | W 0.5290 1 3.0 28.0 8.31 0.0004 e | P 0.4710 3.0 28.0 8.31 0.0004 e | L 0.8904 3.0 28.0 8.31 0.0004 e | R 0.8904 3.0 28.0 8.31 0.0004 e |-------------------------------------------------- Residual | 30 -------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F
/* multivariate test of group 2 versus group 3 */ matrix c2=(0,0,1,-1)
manovatest, test(c2)
Test constraint (1) group[2] - group[3] = 0
W = Wilks' lambda L = Lawley-Hotelling trace P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F -----------+-------------------------------------------------- manovatest | W 0.9932 1 3.0 28.0 0.06 0.9785 e | P 0.0068 3.0 28.0 0.06 0.9785 e | L 0.0068 3.0 28.0 0.06 0.9785 e | R 0.0068 3.0 28.0 0.06 0.9785 e |-------------------------------------------------- Residual | 30 -------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F
/* we know from the univariate tests above that difficulty by itself was clearly not significant */ /* this test does the multivariate test using the combination of useful and importance */ matrix y=(0,1,1)
manovatest group , ytransform(y)
Transformation of the dependent variables (1) y1 + y3
W = Wilks' lambda L = Lawley-Hotelling trace P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F -----------+-------------------------------------------------- group | W 0.5360 2 2.0 30.0 12.99 0.0001 e | P 0.4640 2.0 30.0 12.99 0.0001 e | L 0.8657 2.0 30.0 12.99 0.0001 e | R 0.8657 2.0 30.0 12.99 0.0001 e |-------------------------------------------------- Residual | 30 -------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F Sample Write-Up of the Analysis There is a lot of variation in the write-ups of multivariate analysis of variance. The write-up below is fairly minimal, more detail may be required for most instances. The multivariate test of differences between groups using the Wilks Lambda criteria was statistically significant (F(6, 56) = 3.54; p=0.0049). Follow-up multivariate comparisons showed that the treatment group was significantly different from the average of control 1 and control 2 (F(3,28) = 8.31; p=0.0004). Further, it was determined that control 1 and control 2 were not significant different (F(3,28) = 0.06; p=0.9785). Each of the F-ratio transformations of the Wilks criteria were exact. None of the separate univariate anovas were statistically significant. In particular, the univariate test for difficulty has an F less than 1, so the multivariate test was rerun using the combination of useful and importance, which was statistically significant (F(2,30) = 12.99; p<0.0001).
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