baseCode.math.metaanalysis
Class MetaAnalysis

java.lang.Object
  baseCode.math.metaanalysis.MetaAnalysis

Direct Known Subclasses:

CorrelationEffectMetaAnalysis, MeanDifferenceMetaAnalysis

public abstract class MetaAnalysis

extends java.lang.Object

Statistics for meta-analysis. Methods from Cooper and Hedges (CH); Hunter and Schmidt (HS).

In this class "conditional variance" means the variance for one data set. Unconditional means "between data set", or across data set.

Copyright (c) 2004

Institution: Columbia University

Version:

$Id: MetaAnalysis.java,v 1.5 2005/03/21 18:01:03 pavlidis Exp $

Author:

Paul Pavlidis

Constructor Summary

MetaAnalysis()

Method Summary

protected double	fisherCombineLogPvalues(cern.colt.list.DoubleArrayList pvals) Fisher's method for combining p values (Cooper and Hedges 15-8)
protected double	fisherCombinePvalues(cern.colt.list.DoubleArrayList pvals) Fisher's method for combining p values.
protected cern.colt.list.DoubleArrayList	metaFEWeights(cern.colt.list.DoubleArrayList variances) Weights under a fixed effects model.
protected double	metaRESampleVariance(cern.colt.list.DoubleArrayList effectSizes) CH sample variance under random effects model, equation 18-20
protected double	metaREVariance(cern.colt.list.DoubleArrayList effectSizes, cern.colt.list.DoubleArrayList variances, cern.colt.list.DoubleArrayList weights) CH equation 18-23.
protected cern.colt.list.DoubleArrayList	metaREWeights(cern.colt.list.DoubleArrayList variances, double sampleVariance) Under a random effects model, CH eqn.
protected double	metaVariance(cern.colt.list.DoubleArrayList variances) CH 18-3.
protected double	metaVariance(cern.colt.list.DoubleArrayList weights, cern.colt.list.DoubleArrayList qualityIndices) CH 18-3 version 2 for quality weighted.
protected double	metaZscore(double metaEffectSize, double metaVariance) Test statistic for H0: effectSize == 0.
protected double	qStatistic(cern.colt.list.DoubleArrayList effectSizes, cern.colt.list.DoubleArrayList variances, double globalMean) The "Q" statistic used to test homogeneity of effect sizes.
double	qTest(double Q, double N) Test for statistical significance of Q.
protected double	weightedMean(cern.colt.list.DoubleArrayList effectSizes, cern.colt.list.DoubleArrayList weights) General formula for weighted mean of effect sizes.
protected double	weightedMean(cern.colt.list.DoubleArrayList effectSizes, cern.colt.list.DoubleArrayList weights, cern.colt.list.DoubleArrayList qualityIndices) General formula for weighted mean of effect sizes including quality index scores for each value.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

MetaAnalysis

public MetaAnalysis()

Method Detail

fisherCombinePvalues

protected double fisherCombinePvalues(cern.colt.list.DoubleArrayList pvals)

Fisher's method for combining p values. (Cooper and Hedges 15-8)

Parameters:

pvals - DoubleArrayList

Returns:

double

fisherCombineLogPvalues

protected double fisherCombineLogPvalues(cern.colt.list.DoubleArrayList pvals)

Fisher's method for combining p values (Cooper and Hedges 15-8)

Use for p values that have already been log transformed.

Parameters:

pvals - DoubleArrayList

Returns:

double

qStatistic

protected double qStatistic(cern.colt.list.DoubleArrayList effectSizes,
                            cern.colt.list.DoubleArrayList variances,
                            double globalMean)

The "Q" statistic used to test homogeneity of effect sizes. (Cooper and Hedges 18-6)

Parameters:

effectSizes - DoubleArrayList

variances - DoubleArrayList

globalMean - double

Returns:

double

qTest

public double qTest(double Q,
                    double N)

Test for statistical significance of Q.

Parameters:

Q - - computed using qStatistic

N - - number of studies.

Returns:

The upper tail chi-square probability for Q with N - degrees of freedom.

See Also:

qStatistic

weightedMean

protected double weightedMean(cern.colt.list.DoubleArrayList effectSizes,
                              cern.colt.list.DoubleArrayList weights)

General formula for weighted mean of effect sizes. Cooper and Hedges 18-1, or HS pg. 100.

In HS, the weights are simply the sample sizes. For CH, the weights are 1/v for a fixed effect model. Under a random effects model, we would use 1/(v + v_bs) where v_bs is the between-studies variance.

Parameters:

effectSizes -

Returns:

weightedMean

protected double weightedMean(cern.colt.list.DoubleArrayList effectSizes,
                              cern.colt.list.DoubleArrayList weights,
                              cern.colt.list.DoubleArrayList qualityIndices)

General formula for weighted mean of effect sizes including quality index scores for each value. Cooper and Hedges 18-1, or HS pg. 100.

Parameters:

effectSizes -

qualityIndices -

Returns:

metaVariance

protected double metaVariance(cern.colt.list.DoubleArrayList variances)

CH 18-3. Can be used for fixed or random effects model, the variances just have to computed differently.

      
          v_dot = 1/sum_i=1ˆk ( 1/v_i) 
 

Parameters:

variances -

Returns:

metaVariance

protected double metaVariance(cern.colt.list.DoubleArrayList weights,
                              cern.colt.list.DoubleArrayList qualityIndices)

CH 18-3 version 2 for quality weighted. ( page 266 ) in Fixed effects model.

 
  
   
    
     
      
       
          v_dot = [ sum_i=1ˆk ( q_i ˆ 2 * w_i) ]/[ sum_i=1ˆk  q_i * w_i ]ˆ2
        
       
      
     
    
   
  
 

Returns:

metaZscore

protected double metaZscore(double metaEffectSize,
                            double metaVariance)

Test statistic for H0: effectSize == 0. CH 18-5. For fixed effects model.

Parameters:

metaEffectSize -

metaVariance -

Returns:

metaRESampleVariance

protected double metaRESampleVariance(cern.colt.list.DoubleArrayList effectSizes)

CH sample variance under random effects model, equation 18-20

Returns:

metaREVariance

protected double metaREVariance(cern.colt.list.DoubleArrayList effectSizes,
                                cern.colt.list.DoubleArrayList variances,
                                cern.colt.list.DoubleArrayList weights)

CH equation 18-23. Another estimator of the between-studies variance s² for random effects model. This is non-zero only if Q is larger than expected under the null hypothesis that the variance is zero.

 
  
   
    sˆ2 = [Q - ( k - 1 ) ] / c
    
   
  
 

where

 
  
   
    c = Max(sum_i=1ˆk w_i - [ sum_iˆk w_iˆ2 / sum_iˆk w_i ], 0)
    
   
  
 

Parameters:

effectSizes -

variances -

weights -

Returns:

metaREWeights

protected cern.colt.list.DoubleArrayList metaREWeights(cern.colt.list.DoubleArrayList variances,
                                                       double sampleVariance)

Under a random effects model, CH eqn. 18-24, we replace the conditional variance with the sum of the between-sample variance and the conditional variance.

 
  
     
    v_iˆ* = sigma-hat_thetaˆ2 + v_i.
    
   
  
 

Parameters:

variances - Conditional variances

sampleVariance - estimated...somehow.

Returns:

metaFEWeights

protected cern.colt.list.DoubleArrayList metaFEWeights(cern.colt.list.DoubleArrayList variances)

Weights under a fixed effects model. Simply w_i = 1/v_i. CH eqn 18-2.

Parameters:

variances -

Returns: