# PHP syntax for calculating WWC standardized group difference (Hedges' g and Cox Index)

<?php
function compute()
{
\$Tmean = \$_POST['Tmean'];
\$Cmean = \$_POST['Cmean'];
\$TSD = \$_POST['TSD'];
\$CSD = \$_POST['CSD'];
\$TN = \$_POST['TN'];
\$CN = \$_POST['CN'];
\$mean_dif=\$Tmean-\$Cmean;
\$SE=sqrt(
((\$TSD*\$TSD) / \$TN)+((\$CSD*\$CSD) / \$CN)
);
\$T=\$mean_dif/\$SE;
\$DF=\$TN+\$CN-2;
\$P="Under Development (Still working on this)";
/*\$P=stats_dens_normal(\$T, 0,1);*/
/*\$P=stats_dens_gamma(float \$X, float \$shape, float \$scale);*/
/*\$P= \$T / 100 ;*/
/*Hedges g*/
/*g numerator*/
\$g_numerator=(\$Tmean-\$Cmean)*(1-3/((4*(\$TN+\$CN))-9));
/*g demnominator*/
\$g_denominator=SQRT((((\$TN-1)* (\$TSD**2) )+((\$CN-1)* (\$CSD**2) ))/(\$TN+\$CN-2));
\$hedges_d=\$g_numerator/\$g_denominator;
\$hedges_d_abs=abs(\$hedges_d);
/*if binary variabels*/
\$T_Odds=\$Tmean/(1-\$Tmean);
\$C_Odds=\$Cmean/(1-\$Cmean);
\$Odds_ratio=\$T_Odds/\$C_Odds;
\$Tstep1=log(\$T_Odds);
\$Cstep1=log(\$C_Odds);
\$step2=\$Tstep1-\$Cstep1;
\$WWC_binary_effect=\$step2/1.65;
/*Use omega factor to adjust for data size*/
\$total_num=\$TN + \$CN;
\$omega=(1-3/( 4*\$total_num -9));
\$WWC_binary_effect_omega=(\$omega*\$step2)/1.65;
/*
if (\$hedges_d >= 0.2) echo "Small Effect (Cohen)";
if (\$hedges_d >= 0.5) echo "Medium Effect (Cohen)";
if (\$hedges_d >= 0.8) echo "Large Effect (Cohen)";
*/
echo "<br>";
echo "WWC group comparison of continuous variables";
echo "<br>";
echo "<br>";
echo "Values you entered:";
echo "<br>";
echo "<br>";
echo "Treatment N:" .\$TN;
echo "<br>";
echo "Treatment mean:" .\$Tmean;
echo "<br>";
echo "Treatment SD:" .\$TSD;
echo "<br>";
echo "Comparison N:" .\$CN;
echo "<br>";
echo "Comparison mean:" .\$Cmean;
echo "<br>";
echo "Comparison SD:" .\$CSD;
echo "<br>";
echo "The group mean difference:".round(\$mean_dif,2);
echo "<br>";
echo "without rounding:".round(\$mean_dif,5);
echo "<br><br>";
/*echo "Probability " .round(\$P,2);*/
echo "Probability: " .\$P;
echo "<br>";
\$abs_T=abs(\$T);
echo "T-score is: " .round(\$T,2);
echo "<br>";
echo "without rounding: " .round(\$T,5);
echo "<br>";
if(\$abs_T < 1.96 ) {
echo "Not significant at alpha 0.05 (two tail test;I used a z-test and ignored degree of freedom; threshold 1.96)";
}elseif(\$abs_T >=1.96){
echo "Significant at alpha 0.05 (two tail test;I used a z-test and ignored degree freedom; threshold 1.96)";
}
echo "<br>";
echo "<br>";
echo "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";echo "<br>";
echo "If a variable is an interval scale:";
echo "<br>";
echo "Hedges g " .round(\$hedges_d,2);
echo "<br>";
echo "without rounding: " .round(\$hedges_d,5);
echo "<br>";
echo "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";echo "<br>";
echo "<br>";
echo "<br>";
echo "Hedges g description";
echo "<br>";
echo "Page 16 of https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC_Procedures_Handbook_V4_1_Draft.pdf";
echo "<br>";
echo "<br>";
echo "For continuous outcomes, the WWC has adopted the most commonly used effect size";
echo "<br>";
echo "index, the standardized mean difference known as Hedges’ g, with an adjustment for small";
echo "<br>";
echo "sample bias. For group design studies, this effect size is defined as the difference between the";
echo "<br>";
echo "mean outcome for the intervention group and the mean outcome for the comparison group, ";
echo "<br>";
echo "divided by the pooled within-group standard deviation of the outcome measure. Defining yi and ";
echo "<br>";
echo "yc as the means of the outcome for students in the intervention and comparison groups, ni and nc";
echo "<br>";
echo "as the student sample sizes, si and sc as the student-level standard deviations, given by ....";
echo "<br>";
echo "In addition, we define as the small sample size correction the effect size (Hedges 1981), which is given by ";
echo "<br>";
echo "<br>";
echo "<br>";
/*cohen's rule of thumb*/
echo "Cohen's rule of thumb";echo "<br>";
echo "if d >= 0.2 small effect -- if d >= 0.5 medium effect if --- d >= 0.8 large effect";echo "<br>";
if(\$hedges_d_abs < 0.2) {
echo "Close to zero and Not even small Effect (Cohen)";
}elseif(\$hedges_d_abs>=0.2 and \$hedges_d_abs < 0.5){
echo "Small effect (Cohen)";
}elseif(\$hedges_d_abs>=0.5 and \$hedges_d_abs < 0.8){
echo "Medium effect (Cohen)";
}elseif(\$hedges_d_abs>=0.8){
echo "Large effect (Cohen)";
}else {
echo "others";
}
echo "<br>";
echo "<br>";
echo "If a variable is obviously a continuous variable (e.g., MAX is greater than 1), ignore the result below (It says NAN)";
echo "<br>";
echo "<br>";
echo "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";echo "<br>";
echo "If the variable is a binary variable (0 or 1), the Cox index value is " .round(\$WWC_binary_effect,2);
echo "<br>";
echo "with a lot of digits without rounding " .round(\$WWC_binary_effect,5);echo "<br>";
echo "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";echo "<br>";
echo "<br>";
echo "<br>";
echo "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";echo "<br>";
echo "Omega adjusted (data size taken into consideration) " .round(\$WWC_binary_effect_omega,2);
echo "<br>";
echo "with a lot of digits without rounding " .round(\$WWC_binary_effect_omega,5);
echo "<br>";
echo "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";echo "<br>";
echo "<br>";
echo "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";echo "<br>";
echo "Odds ratio:" .round(\$Odds_ratio,2);
echo "<br>";
echo "without rounding " .round(\$Odds_ratio,5);
echo "<br>";
echo "XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";echo "<br>";
echo "<br>";
echo "Cox Index description";
echo "<br>";
echo "Page 16 of https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC_Procedures_Handbook_V4_1_Draft.pdf";
echo "<br>";
echo "<br>";
echo "For dichotomous outcomes, the difference in group means is calculated as the difference in";
echo "<br>";
echo "the probability of the occurrence of an event. The effect size measure of choice for dichotomous ";
echo "<br>";
echo "outcomes is the Cox index, which yields effect size values similar to the values of Hedges’ g that";
echo "<br>";
echo "one would obtain if group means, standard deviations, and sample sizes were available, assuming";
echo "<br>";
echo "the dichotomous outcome measure is based on an underlying logistic similar to a normal";
echo "<br>";
echo "distribution. Defining pi and pc as the probability of an outcome for students in the intervention";
echo "<br>";
echo "and comparison groups, the effect size is given by";
echo "<br>";
echo "";
echo "<br>";
}
/*echo "The result is: " . compute();*/
compute();
?>
<br>
REFERENCE
<br>
Cohen's rule of thumb about effect sizes:
<br>
<li>If greater than 02, Small Effect
<br>
<li>If greater than 0.5, Medium Effect
<br>
<li>If greater 0.8 then Large Effect
<br>
Cohen, J. Statistical power for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum (1988).
<br>
<ahref="https://wmich.edu/sites/default/files/attachments/u58/2015/Effect_Size_Substantive_Interpretation_Guidelines.pdf">
Effect Size Substantive Interpretation Guidelines: Issues in the Interpretation of Effect Sizes Jeff Valentine and Harris Cooper, Duke University(see page. 5)</a>
<br>
<br>
WWC related info:
<br>
<a href="https://ies.ed.gov/ncee/wwc/Docs/ReferenceResources/wwc_procedures_handbook_v4_draft.pdf">WWC procedures handbook (see page. 14)</a>
<br>
<a href="https://ies.ed.gov/ncee/wwc/Docs/OnlineTraining/wwc_training_m3.pdf">WWC standards slides (Definition of small sample size correction, slide 14)</a>
<br>
WWC considers the effect size greater than .25 substnatively important.
<a href="https://ies.ed.gov/ncee/wwc/Docs/referenceresources/wwc_procedures_handbook_v4.pdf">P.22 of WWC standards</a>
<br>
<br>
<a href="calc_t_test1.php">Back to the calculcator </a>
<br>
<a href="https://www.estat.us">My website</a>
<br>
Look at calc process t..1
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