Source I2 95% CI
-------------------------------------
-Total 48.4444 34.9546 to 59.1366
+Total 48.4444 17.9350 to 67.6113
→ Citations: Higgins and Thompson (2002), Huedo-Medina et al. (2006) @@ -1008,7 +1008,7 @@
Dixon, P.M. (1993) The bootstrap and the jackknife: Describing the precision of ecological indices. Pp. 290—318 in Design and Analysis of Ecological Experiments, S.M. Scheiner and J. Gurevitch, eds. Chapman and Hall, New York.
Hedges, L.V. and I. Olkin (1985) Statistical Methods for Meta-analysis. Academic Press, Orlando, FL.
Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 21:1539–1558.
-Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychological Methods 11:193–206.
+Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychological Methods 11:193–206.
Orwin, R.G. (1983) A fail-safe N for effect size in meta-analysis. Journal of Educational Statistics 8(2):157–159.
Rosenberg, M.S. (2005) The file-drawer problem revisited: A general weighted method for calculating fail-safe numbers in meta-analysis. Evolution 59(2):464–468.
Rosenthal, R. (1979) The “file drawer problem” and tolerance for null results. Psychological Bulletin 86(3):638–641.
@@ -1331,7 +1331,7 @@
Source I2 95% CI
-------------------------------------
-Total 48.4444 34.9546 to 59.1366
+Total 48.4444 17.9350 to 67.6113
→ Citations: Higgins and Thompson (2002), Huedo-Medina et al. (2006) @@ -1360,7 +1360,7 @@
Hedges, L.V. and I. Olkin (1985) Statistical Methods for Meta-analysis. Academic Press, Orlando, FL.
Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 21:1539–1558.
-Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in +
Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychological Methods 11:193–206.
@@ -1652,8 +1652,8 @@
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
→ Citations: Higgins and Thompson (2002), Huedo-Medina et al. (2006) @@ -1693,7 +1693,7 @@
Source I2 95% CI
-------------------------------------
-Total 48.4444 34.9546 to 59.1366
+Total 48.4444 17.9350 to 67.6113
→ Citations: Higgins and Thompson (2002), Huedo-Medina et al. (2006) @@ -1722,7 +1722,7 @@
Hedges, L.V. and I. Olkin (1985) Statistical Methods for Meta-analysis. Academic Press, Orlando, FL.
Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 21:1539–1558.
-Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in +
Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychological Methods 11:193–206.
@@ -1888,7 +1888,7 @@
Source I2 95% CI
-------------------------------------
-Total 53.3385 40.5512 to 63.3753
+Total 53.3385 24.2595 to 71.2532
→ Citations: Higgins and Thompson (2002), Huedo-Medina et al. (2006) @@ -1917,7 +1917,7 @@
Hedges, L.V. and I. Olkin (1985) Statistical Methods for Meta-analysis. Academic Press, Orlando, FL.
Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 21:1539–1558.
-Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in +
Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychological Methods 11:193–206.
Rosenberg, M.S. (2013) Moment and least-squares based approaches to meta-analytic inference. Pp. 108–124 in Handbook of Meta-analysis in Ecology and Evolution, J. Koricheva, J. Gurevitch and K.L. Mengersen, eds. @@ -2091,7 +2091,7 @@
Source I2 95% CI
-------------------------------------
-Total 54.3676 41.9334 to 64.1391
+Total 54.3676 26.1112 to 71.8182
→ Citations: Higgins and Thompson (2002), Huedo-Medina et al. (2006) @@ -2121,7 +2121,7 @@
Hedges, L.V. and I. Olkin (1985) Statistical Methods for Meta-analysis. Academic Press, Orlando, FL.
Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 21:1539–1558.
-Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in +
Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychological Methods 11:193–206.
@@ -2322,7 +2322,7 @@
Source I2 95% CI
-------------------------------------
-Total 54.3676 41.9334 to 64.1391
+Total 54.3676 26.1112 to 71.8182
→ Citations: Higgins and Thompson (2002), Huedo-Medina et al. (2006) @@ -2351,7 +2351,7 @@
Hedges, L.V. and I. Olkin (1985) Statistical Methods for Meta-analysis. Academic Press, Orlando, FL.
Higgins, J.P.T. and S.G. Thompson (2002) Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 21:1539–1558.
-Huedo-Medina, T.B., F. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in +
Huedo-Medina, T.B., J. Sánchez-Meca, F. Marín-Martínez, and J. Botella (2006) Assessing heterogeneity in meta-analysis: Q statistic or I2 index? Psychological Methods 11:193–206.
Rosenberg, M.S., D.C. Adams, and J. Gurevitch (2000) MetaWin: Statistical Software for Meta-analysis. Sinauer Associates, Sunderland, MA.
diff --git a/src/MetaWinAnalysisFunctions.py b/src/MetaWinAnalysisFunctions.py index ab2eb4d..f1b7872 100644 --- a/src/MetaWinAnalysisFunctions.py +++ b/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 diff --git a/src/MetaWinConstants.py b/src/MetaWinConstants.py index 618fd69..0b083b6 100644 --- a/src/MetaWinConstants.py +++ b/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. " "Statistics in Medicine 21:1539–1558.", "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? " "Psychological Methods 11:193–206.", "Huedo-Medina et al. (2006)"], diff --git a/tests/borenstein_chap18.txt b/tests/borenstein_chap18.txt new file mode 100644 index 0000000..1884ae0 --- /dev/null +++ b/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 diff --git a/tests/test_metawin.py b/tests/test_metawin.py index 404521d..4cb021c 100644 --- a/tests/test_metawin.py +++ b/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