ࡱ> zwxy P\p Sean Wallis Ba= de =)11%58X@"1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Symbol1Arial1Symbol1Arial1Arial1Arial1Arial1Arial1=Arial1 Arial1Arial1Arial1Arial1Arial1Arial1.Times New Roman1.Times New Roman1.Times New Roman1Arial1Arial1Arial1Symbol1Arial1Arial1<Arial1<Arial1<Arial1<Arial1<Arial1<Symbol1<Arial1Arial1Arial1Arial1.Times New Roman1.Times New Roman1Arial1.Times New Roman1.Times New Roman1<Symbol1.Times New Roman1.Times New Roman1.Times New Roman1.Times New Roman1 Arial1Symbol1.Times New Roman1.Times New Roman1Arial1Symbol1.Times New Roman1.Times New Roman1.Times New Roman1.Times New Roman""#,##0;\-""#,##0""#,##0;[Red]\-""#,##0""#,##0.00;\-""#,##0.00#""#,##0.00;[Red]\-""#,##0.005*0_-""* #,##0_-;\-""* #,##0_-;_-""* "-"_-;_-@_-,)'_-* #,##0_-;\-* #,##0_-;_-* "-"_-;_-@_-=,8_-""* #,##0.00_-;\-""* #,##0.00_-;_-""* "-"??_-;_-@_-4+/_-* #,##0.00_-;\-* #,##0.00_-;_-* "-"??_-;_-@_-"Yes";"Yes";"No""True";"True";"False""On";"On";"Off"],[$ -2]\ #,##0.00_);[Red]\([$ -2]\ #,##0.00\) 0.00000.0 #,##0.0000 0.0000000.000000000000000000                + ) , *               l@@   (@@  (@       @  D  D  @+   H+  D+  L+  l@+  l +   L+  H+  h@+  h +  H  L+  (   h   "    "8 " #X  $ @  $ #  $@  $  $ #  $  @)  h) "x)  $  h)  d@ )  H)  !  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L & L  h  L  L  L  L+  `  (  h  `@@+  d @+  d@ +  d +  ` +   l@+  l +  l +  H+  L+  D+ , H+ , H 8 H  , @  ,  d  ,@  ,  ,    h , h   h 9 H " h  L  H+  L+  h+  D+ , L+  H  L  l @+  l +  @+  @   h  l@  l@ " (   8dq:F3ffff̙̙3f3fff3f3f33333f33333\`Q2x2 homogeneity3x2 homogeneityqX3x3 homogeneity2x1 goodness of fit(3x1 goodness of fit$subset homogeneity~V subset gofqpBishop et al (1)Bishop et al (2),82x2x2-subset-sep-test.xls2 x 2 homogeneity testYZ \-ue?c(]`?Z  ĵ? 27!!     3 A@@  `_It employs chi-square summation over d = p1 - p2 to test the separability of these two results.% &) +. /*We also include Zar's test for comparison.uThs summation takes a difference from table 1 and a difference from table 2 and divides it by the sum of the squares,same populationindependent populationWilson3Gaussian and Wilson versions of the test are given.ZGaussian and Wilson intervals are computed for data obtained from independent populations.TThe preferred test here is the Wilson test, which is more precise than the Gaussian.The Gaussian test compares "within subject" subtests, whereas the Newcombe-Wilson version is optimum for "between subject" subtests."Difference in initial observations(Newcombe-Wilson) p1(1) - p1(2) p^(1) - p^(2) $Difference in sample mean (pooled p) c partialsGaussian, using chi-squareJThis spreadsheet contains two 3x1 gof chi-square tests, TEST 1 and TEST 2.cGaussian and Newcombe-Wilson intervals are computed for data obtained from independent populations.EThe method assumes that both tests come from independent populations.chi-square for homogeneityRThis spreadsheet contains two 3x2 homogeneity chi-square tests, TEST 1 and TEST 2.variance differences The method sums squared differences of differences, (d1 - d2), over the independent variance, s1 + s2, obtaining a c score.5 6: ;_ `e fv wRThis spreadsheet contains two 3x3 homogeneity chi-square tests, TEST 1 and TEST 2.^It employs chi-square summation over d = p - p^ to test the separability of these two results.% &) *- .d = p-p^[This chi-square must be tested against the critical value of c for two degrees of freedom.= >Gaussian and Newcombe-Wilson versions of the test are given as is the phi test employing Liebetrau's interval (Bishop et al 1975).chi-square for heterogeneity POOLED TESTNotesWe also include Zar's heterogeneity test, which subtracts the c test of pooled cells from the sum of the c tests.> ?j kSThis chi-square is tested against the critical value of c for 1 degree of freedom.8 9cc(pool)c(sum)c(het)d=p1-p2p3d3Heterogeneity (Zar 1999) !c"c partials (heterogeneity)"c(pool)"c(sum)"c(het)"Heterogeneity (Zar 1999) <This table also includes Zar's test for comparison purposes.rZar's heterogeneity test is not recommended. This gives unreliable results if the prior distribution is different.+}We also translate the Gaussian into a c score for comparison: this shows why Zar's test is not recommended for our purposes.& '\kpEp^p1p2c.i.TEST 1TEST 2aabbfcComments ReferencesGaussian! Enter data in highlighted cells Newcombe-Wilsonz/np'z.s'w+w- significant?z(crit)" Level the test is carried out at VMoreover if the two swings are separable, so are the two tests, the two f values, etc.H IoThere is only one degree of freedom in each test, hence it is appropriate to plot a single confidence interval.oNote that two swings can be separable even if neither test is significant, if they move in opposite directions!K cWilson intervals2 x 2 chi-squaredfdatadependent variableccritobservedtotalNindependent variable chi-squaresall chi-squareexpected sig level Cramer's f p/prod.sumsq p^2/prod.sumtrianglecddiagonalc2c2/Nsstd errPhiep1-p2diff 2diff 1 indep popTESTS: For plottingOThis spreadsheet contains two standard 2x2 chi-square tests, TEST 1 and TEST 2.It then tests the difference of the differences (diff 1, diff 2) to evaluate whether the two tests are statistically separable.Ag diff Dc.i. DAJThis spreadsheet contains two 2x1 gof chi-square tests, TEST 1 and TEST 2.d1d2g.o.f. chi-squaree'Gaussian serial point test$Wilson score intervals, for plottingobs 2obs 3NW serial point testinner interval p1(2) - p1(1) p^(2) - p^(1) Point test using chi-squarerow1row2row3 c partials,col1col2col3Summed over DVSummed over IV]Note this test is not associative, i.e. it obtains a different result if you sum over the DV.p2-p1Newcombe-Wilson point testswd-wd+2(n+z) z-1/n+4npq2-4pwcc+wcc-continuity-correctedu+u- section 3.3 section 3.2 section 3.4Yatesc=1/2n section 4.1! Enter data in highlighted cellslowerupper Gaussian (f) 5 ,NW (f)5,continuity-correctionKIntervals computed using Wallis's algebraic derivation for signed 2 x 2 phi/Capable of accepting continuity correction, etcd-d+diff(f) 122 - 1 section 4.2Bhttps://corplingstats.wordpress.com/2012/03/31/comparing-c2-tests/8Wallis, S.A. (2012), Comparing c tests for separability  5Chapter 15 in Wallis (2020), sections labelled in red Wallis, S.A. 2019. Comparing 2 Tables for Separability of Distribution and Effect: Meta-Tests for Comparing Homogeneity and Goodness of Fit Contingency Test Outcomes. Journal of Quantitative Linguistics. 26:4, 330-355. Gaussian ('Wald')wd+(f)5wd-(f)5 section 4.3c.c.u+(f)5u-(f)5 ed-(f1,f2)5 ed+(f1,f2)5 -(u-)cd section 5.1NWNWcc section 5.2 section 4.4serial point testwd-ccwd+cccSUPERSETSUBSETSThis spreadsheet contains two standard 2x2 chi-square tests, SUPERTEST and SUBTEST.fVisually, if the superset (blue line) is within the interval the point is not significantly different.>The two tables are assumed to have a superset-subset relation.>The point test is a goodness of fit test against the superset.cThe gradient test compares the difference in (gradients) assuming the uncertainty is in the subset.`Variation (uncertainty) is assumed to be in the subset. The superset is given / known / certain.fThe multi-point test is summed over variable A as to whether each point is a good fit to the superset.0Confidence intervals are plotted for the subset.I/weotherwhowhom" Level the test is carried out at!2 x 2 homogeneity and point tests3 x 2 homogeneity3 x 3 (r x c) homogeneity2 x 1 goodness of fit3 x 1 goodness of fitMulti-point testSerial point tests(Wilson score test method)Superset (no interval)Gradient subset test section 6.1 section 6.3 section 6.2P1P2d - D$Subset 'homogeneity' and point testsSubset goodness of fitAJPAJPPdDP^continuity correctedWilson score interval method section 6.4This test compares a goodness of fit test within the subset (fitting p2 against p1) and asks whether this result is consistent with the same comparison in its superset.Used in Wallis (2019), Investigating the additive probability of repeated language production decisions. 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