Wilcoxon Signed Ranks Test (paired) Ranks | ----- | -------------- | ----- | --------- | ------------ | | | | N | Mean Rank | Sum of Ranks | | ----- | -------------- | ----- | --------- | ------------ | | b2 - | Negative Ranks | 4(a) | 3.50 | 14.00 | | a2 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 3(b) | 4.67 | 14.00 | | | -------------- | ----- | --------- | ------------ | | | Ties | 4(c) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | b3 - | Negative Ranks | 6(d) | 4.50 | 27.00 | | a3 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 3(e) | 6.00 | 18.00 | | | -------------- | ----- | --------- | ------------ | | | Ties | 2(f) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | b4 - | Negative Ranks | 6(g) | 4.08 | 24.50 | | a4 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 3(h) | 6.83 | 20.50 | | | -------------- | ----- | --------- | ------------ | | | Ties | 2(i) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | c1 - | Negative Ranks | 9(j) | 5.56 | 50.00 | | a1 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 1(k) | 5.00 | 5.00 | | | -------------- | ----- | --------- | ------------ | | | Ties | 1(l) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | c2 - | Negative Ranks | 9(m) | 5.72 | 51.50 | | a2 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 1(n) | 3.50 | 3.50 | | | -------------- | ----- | --------- | ------------ | | | Ties | 1(o) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | c3 - | Negative Ranks | 10(p) | 6.40 | 64.00 | | a3 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 1(q) | 2.00 | 2.00 | | | -------------- | ----- | --------- | ------------ | | | Ties | 0(r) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | d0 - | Negative Ranks | 0(s) | .00 | .00 | | a0 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 9(t) | 5.00 | 45.00 | | | -------------- | ----- | --------- | ------------ | | | Ties | 2(u) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | d1 - | Negative Ranks | 1(v) | 6.00 | 6.00 | | a1 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 8(w) | 4.88 | 39.00 | | | -------------- | ----- | --------- | ------------ | | | Ties | 2(x) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | d2 - | Negative Ranks | 2(y) | 4.25 | 8.50 | | a2 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 7(z) | 5.21 | 36.50 | | | -------------- | ----- | --------- | ------------ | | | Ties | 2(aa) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | d3 - | Negative Ranks | 2(bb) | 5.50 | 11.00 | | a3 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 6(cc) | 4.17 | 25.00 | | | -------------- | ----- | --------- | ------------ | | | Ties | 3(dd) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | eupe1 | Negative Ranks | 8(ee) | 5.75 | 46.00 | | - pe1 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 2(ff) | 4.50 | 9.00 | | | -------------- | ----- | --------- | ------------ | | | Ties | 1(gg) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | eupe2 | Negative Ranks | 7(hh) | 5.50 | 38.50 | | - pe2 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 2(ii) | 3.25 | 6.50 | | | -------------- | ----- | --------- | ------------ | | | Ties | 2(jj) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | | eupe3 | Negative Ranks | 6(kk) | 5.42 | 32.50 | | - pe3 | -------------- | ----- | --------- | ------------ | | | Positive Ranks | 3(ll) | 4.17 | 12.50 | | | -------------- | ----- | --------- | ------------ | | | Ties | 2(mm) | | | | | -------------- | ----- | --------- | ------------ | | | Total | 11 | | | | ----- | -------------- | ----- | --------- | ------------ | a b2 < a2 b b2 > a2 c b2 = a2 d b3 < a3 e b3 > a3 f b3 = a3 g b4 < a4 h b4 > a4 i b4 = a4 j c1 < a1 k c1 > a1 l c1 = a1 m c2 < a2 n c2 > a2 o c2 = a2 p c3 < a3 q c3 > a3 r c3 = a3 s d0 < a0 t d0 > a0 u d0 = a0 v d1 < a1 w d1 > a1 x d1 = a1 y d2 < a2 z d2 > a2 aa d2 = a2 bb d3 < a3 cc d3 > a3 dd d3 = a3 ee eupe1 < pe1 ff eupe1 > pe1 gg eupe1 = pe1 hh eupe2 < pe2 ii eupe2 > pe2 jj eupe2 = pe2 kk eupe3 < pe3 ll eupe3 > pe3 mm eupe3 = pe3 Test Statistics(d) | ---------------------- | ------- | -------- | -------- | --------- | --------- | --------- | --------- | --------- | --------- | -------- | ----------- | ----------- | ----------- | | | b2 - a2 | b3 - a3 | b4 - a4 | c1 - a1 | c2 - a2 | c3 - a3 | d0 - a0 | d1 - a1 | d2 - a2 | d3 - a3 | eupe1 - pe1 | eupe2 - pe2 | eupe3 - pe3 | | ---------------------- | ------- | -------- | -------- | --------- | --------- | --------- | --------- | --------- | --------- | -------- | ----------- | ----------- | ----------- | | Z | .000(a) | -.533(b) | -.237(b) | -2.310(b) | -2.456(b) | -2.763(b) | -2.666(c) | -1.955(c) | -1.667(c) | -.983(c) | -1.916(b) | -1.914(b) | -1.196(b) | | ---------------------- | ------- | -------- | -------- | --------- | --------- | --------- | --------- | --------- | --------- | -------- | ----------- | ----------- | ----------- | | Asymp. Sig. (2-tailed) | 1.000 !!| .594 !! | .813 !! | .021 | .014 | .006 | .008 | .051 | .095 | .326 | .055 | .056 | .232 | | ---------------------- | ------- | -------- | -------- | --------- | --------- | --------- | --------- | --------- | --------- | -------- | ----------- | ----------- | ----------- | | Exact Sig. (2-tailed) | 1.000 !!| .652 !! | .844 !! | .023 | .012 | .003 | .004 | .055 | .117 | .375 | .068 | .063 | .250 | | ---------------------- | ------- | -------- | -------- | --------- | --------- | --------- | --------- | --------- | --------- | -------- | ----------- | ----------- | ----------- | | Exact Sig. (1-tailed) | .531 | .326 | .422 | .012 !! | .006 !! | .001 !! | .002 !! | .027 !! | .059 !! | .188 !! | .034 !! | .031 !! | .125 !! | | ---------------------- | ------- | -------- | -------- | --------- | --------- | --------- | --------- | --------- | --------- | -------- | ----------- | ----------- | ----------- | | Point Probability | .063 | .041 | .023 | .007 !! | .002 !! | .000 !! | .002 !! | .008 !! | .020 !! | .031 !! | .015 !! | .008 !! | .004 !! | | ---------------------- | ------- | -------- | -------- | --------- | --------- | --------- | --------- | --------- | --------- | -------- | ----------- | ----------- | ----------- | a The sum of negative ranks equals the sum of positive ranks. b Based on positive ranks. c Based on negative ranks. d Wilcoxon Signed Ranks Test !! The relevant tailed test