Merge pull request #21 from msrosenberg/dev-branch

I2 confidence interval bug fix

resources/metawin_help.html

@@ -951,7 +951,7 @@ <h3>Output</h3>
 <pre><code>
 Source     I<sup>2</sup>            95% CI
 -------------------------------------
-Total    48.4444   34.9546 to 59.1366
+Total    48.4444   17.9350 to 67.6113
 </code></pre>
 <p>
 → Citations: Higgins and Thompson (2002), Huedo-Medina <em>et al.</em> (2006)
@@ -1008,7 +1008,7 @@ <h3>Output</h3>
 <p>Dixon, P.M. (1993) The bootstrap and the jackknife: Describing the precision of ecological indices. Pp. 290—318 in <em>Design and Analysis of Ecological Experiments</em>, S.M. Scheiner and J. Gurevitch, eds. Chapman and Hall, New York.</p>
 <p>Hedges, L.V. and I. Olkin (1985) <em>Statistical Methods for Meta-analysis</em>. Academic Press, Orlando, FL.</p>
 <p>Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. <em>Statistics in Medicine</em> 21:1539–1558.</p>
-<p>Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? <em>Psychological Methods</em> 11:193–206.</p>
+<p>Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? <em>Psychological Methods</em> 11:193–206.</p>
 <p>Orwin, R.G. (1983) A fail-safe N for effect size in meta-analysis. <em>Journal of Educational Statistics</em> 8(2):157–159.</p>
 <p>Rosenberg, M.S. (2005) The file-drawer problem revisited: A general weighted method for calculating fail-safe numbers in meta-analysis. <em>Evolution</em> 59(2):464–468.</p>
 <p>Rosenthal, R. (1979) The “file drawer problem” and tolerance for null results. <em>Psychological Bulletin</em> 86(3):638–641.</p>
@@ -1331,7 +1331,7 @@ <h3>Output</h3>
 <pre><code>
 Source     I2            95% CI
 -------------------------------------
-Total    48.4444   34.9546 to 59.1366
+Total    48.4444   17.9350 to 67.6113
 </code></pre>
 <p>
 → Citations: Higgins and Thompson (2002), Huedo-Medina <em>et al.</em> (2006)
@@ -1360,7 +1360,7 @@ <h3>Output</h3>
 <p>Hedges, L.V. and I. Olkin (1985) <em>Statistical Methods for Meta-analysis</em>. Academic Press, Orlando, FL.</p>
 <p>Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. <em>Statistics in
     Medicine</em> 21:1539–1558.</p>
-<p>Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
+<p>Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
     meta-analysis: Q statistic or I2 index? <em>Psychological Methods</em> 11:193–206.</p>
 </blockquote>
 
@@ -1652,8 +1652,8 @@ <h3>Output</h3>
 <pre><code>
        Source            I2            95% CI
 ---------------------------------------------------
-Heterocera (within)    57.8379   45.2319 to 67.5424
-Rhopalocera (within)    3.0254    0.0000 to 16.5089
+Heterocera (within)    57.8379   28.8567 to 75.0132
+Rhopalocera (within)    3.0254    0.0000 to 28.1177
 </code></pre>
 <p>
 → Citations: Higgins and Thompson (2002), Huedo-Medina <em>et al.</em> (2006)
@@ -1693,7 +1693,7 @@ <h3>Output</h3>
 <pre><code>
 Source     I2            95% CI
 -------------------------------------
-Total    48.4444   34.9546 to 59.1366
+Total    48.4444   17.9350 to 67.6113
 </code></pre>
 <p>
 → Citations: Higgins and Thompson (2002), Huedo-Medina <em>et al.</em> (2006)
@@ -1722,7 +1722,7 @@ <h3>Output</h3>
 <p>Hedges, L.V. and I. Olkin (1985) <em>Statistical Methods for Meta-analysis</em>. Academic Press, Orlando, FL.</p>
 <p>Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. <em>Statistics in
     Medicine</em> 21:1539–1558.</p>
-<p>Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
+<p>Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
     meta-analysis: Q statistic or I2 index? <em>Psychological Methods</em> 11:193–206.</p>
 </blockquote>
 
@@ -1888,7 +1888,7 @@ <h3>Output</h3>
 <pre><code>
 Source     I2            95% CI
 -------------------------------------
-Total    53.3385   40.5512 to 63.3753
+Total    53.3385   24.2595 to 71.2532
 </code></pre>
 <p>
 → Citations: Higgins and Thompson (2002), Huedo-Medina <em>et al.</em> (2006)
@@ -1917,7 +1917,7 @@ <h3>Output</h3>
 <p>Hedges, L.V. and I. Olkin (1985) <em>Statistical Methods for Meta-analysis</em>. Academic Press, Orlando, FL.</p>
 <p>Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis.
     <em>Statistics in Medicine</em> 21:1539–1558.</p>
-<p>Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
+<p>Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
     meta-analysis: Q statistic or I2 index? <em>Psychological Methods</em> 11:193–206.</p>
 <p>Rosenberg, M.S. (2013) Moment and least-squares based approaches to meta-analytic inference. Pp. 108–124 in
     <em>Handbook of Meta-analysis in Ecology and Evolution</em>, J. Koricheva, J. Gurevitch and K.L. Mengersen, eds.
@@ -2091,7 +2091,7 @@ <h3>Output</h3>
 <pre><code>
 Source     I2            95% CI
 -------------------------------------
-Total    54.3676   41.9334 to 64.1391
+Total    54.3676   26.1112 to 71.8182
 </code></pre>
 <p>
 → Citations: Higgins and Thompson (2002), Huedo-Medina <em>et al.</em> (2006)
@@ -2121,7 +2121,7 @@ <h3>Output</h3>
 <p>Hedges, L.V. and I. Olkin (1985) <em>Statistical Methods for Meta-analysis</em>. Academic Press, Orlando, FL.</p>
 <p>Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis.
     <em>Statistics in Medicine</em> 21:1539–1558.</p>
-<p>Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
+<p>Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
     meta-analysis: Q statistic or I2 index? <em>Psychological Methods</em> 11:193–206.</p>
 </blockquote>
 
@@ -2322,7 +2322,7 @@ <h3>Output</h3>
 <pre><code>
 Source     I2            95% CI
 -------------------------------------
-Total    54.3676   41.9334 to 64.1391
+Total    54.3676   26.1112 to 71.8182
 </code></pre>
 <p>
 → Citations: Higgins and Thompson (2002), Huedo-Medina <em>et al.</em> (2006)
@@ -2351,7 +2351,7 @@ <h3>Output</h3>
 <p>Hedges, L.V. and I. Olkin (1985) <em>Statistical Methods for Meta-analysis</em>. Academic Press, Orlando, FL.</p>
 <p>Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. <em>Statistics in
     Medicine</em> 21:1539–1558.</p>
-<p>Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
+<p>Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in
     meta-analysis: Q statistic or I2 index? <em>Psychological Methods</em> 11:193–206.</p>
 <p>Rosenberg, M.S., D.C. Adams, and J. Gurevitch (2000) <em>MetaWin: Statistical Software for Meta-analysis</em>.
     Sinauer Associates, Sunderland, MA.</p>

src/MetaWinAnalysisFunctions.py

@@ -368,16 +368,16 @@ def bootstrap_means(bootstrap_n, boot_data, obs_mean, pooled_var, random_effects
 def calc_i2(qt, n, alpha: float = 0.05):
     try:
         i2 = max(0, 100 * (qt - (n - 1))/qt)
-        ln_h2 = math.log(qt/(n - 1))
+        ln_h = math.log(math.sqrt(qt/(n - 1)))
         if qt > n - 1:
-            se = (math.log(qt) - math.log(n-1))/(2*(math.sqrt(2*qt)-math.sqrt(2*n - 3)))
+            se_ln_h = (math.log(qt) - math.log(n-1))/(2*(math.sqrt(2*qt)-math.sqrt(2*n - 3)))
         else:
-            se = math.sqrt((1/(2*(n - 2))) * (1 - (1/(3*(n - 2)**2))))
+            se_ln_h = math.sqrt((1/(2*(n - 2))) * (1 - (1/(3*(n - 2)**2))))
         z = -scipy.stats.norm.ppf(alpha / 2)
-        lower_h2 = math.exp(ln_h2 - z*se)
-        upper_h2 = math.exp(ln_h2 + z*se)
-        lower_i2 = max(0, 100*(lower_h2 - 1)/lower_h2)
-        upper_i2 = max(0, 100*(upper_h2 - 1)/upper_h2)
+        lower_h = math.exp(ln_h - z*se_ln_h)
+        upper_h = math.exp(ln_h + z*se_ln_h)
+        lower_i2 = max(0, 100*(lower_h**2 - 1)/lower_h**2)
+        upper_i2 = max(0, 100*(upper_h**2 - 1)/upper_h**2)
     except ZeroDivisionError:
         i2, lower_i2, upper_i2 = 0, 0, 0
     return i2, lower_i2, upper_i2

src/MetaWinConstants.py

@@ -190,7 +190,7 @@ def resource_path(relative_path: str, inc_file: bool = False) -> str:
     "Higgins_Thompson_2002": ["Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. "
                               "<em>Statistics in Medicine</em> 21:1539&ndash;1558.", "Higgins and Thompson (2002)"],
 
-    "Huedo-Medina_et_2006": ["Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) "
+    "Huedo-Medina_et_2006": ["Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) "
                              "Assessing heterogeneity in meta-analysis: Q statistic or I2 index? "
                              "<em>Psychological Methods</em> 11:193&ndash;206.", "Huedo-Medina <em>et al.</em> (2006)"],
 

tests/borenstein_chap18.txt

@@ -0,0 +1,7 @@
+yi	vi
+0.09452	0.03295
+0.27736	0.03070
+0.36654	0.04988
+0.66438	0.01051
+0.46181	0.04266
+0.18516	0.02342

tests/test_metawin.py

@@ -348,6 +348,19 @@ def test_simple_meta_analysis_lep():
     assert round(analysis_values.i2, 2) == i2_answer
 
 
+def test_i2_confidence_interval():
+    # not a formal test, just crosschecking values
+    data, _ = import_test_data("borenstein_chap18.txt")
+    options = MetaWinAnalysis.MetaAnalysisOptions()
+    options.structure = MetaWinAnalysis.SIMPLE_MA
+    options.effect_data = data.cols[0]
+    options.effect_vars = data.cols[1]
+    options.create_graph = False
+
+    output, figure, chart_data, analysis_values = MetaWinAnalysis.do_meta_analysis(data, options, 4)
+    print_test_output(output)
+
+
 def test_simple_meta_analysis_lep_randeff():
     # answers from Chapter 9, Handbook of Meta-Analysis in Ecology and Evolution
     qt_answer = 23.01