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The Effects of Sanction Intensity on Criminal Conduct - JDAI Helpdesk

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Appendix C: Meta-Analytic Procedures<br />

Odds ratio effect size<br />

<str<strong>on</strong>g>The</str<strong>on</strong>g> odds ratio (OR) is given by the following formula, based <strong>on</strong> a 2x2 table:<br />

Events<br />

N<strong>on</strong>-Events<br />

Treatment Group a b<br />

C<strong>on</strong>trol Group c d<br />

ES OR<br />

= ad<br />

bc<br />

(1)<br />

Analyses are performed <strong>on</strong> the natural log <str<strong>on</strong>g>of</str<strong>on</strong>g> the OR and c<strong>on</strong>verted back for presentati<strong>on</strong>.<br />

Standard error <str<strong>on</strong>g>of</str<strong>on</strong>g> the ! logged OR:<br />

SE LOR<br />

= 1 + 1 + 1 + 1 (2)<br />

a b c d<br />

Inverse variance weight <str<strong>on</strong>g>of</str<strong>on</strong>g> the logged OR (fixed effects):<br />

!<br />

w LOR<br />

=<br />

1<br />

2<br />

(3)<br />

SE LOR<br />

Heterogeneity (Q-statistic)<br />

!<br />

Q is distributed as a chi-square with k – 1 d.f.<br />

Q = "w i ( ES i<br />

# E S ) 2 (4)<br />

ES i = individual effect size for i = 1 to k (the number <str<strong>on</strong>g>of</str<strong>on</strong>g> effect sizes).<br />

E S = weighted mean effect size over the k effect sizes.<br />

!<br />

w i = weight for ES i .<br />

!<br />

Random effects model<br />

A sec<strong>on</strong>d variance comp<strong>on</strong>ent<br />

" #<br />

is computed, reflecting between-study error. We use<br />

the DerSim<strong>on</strong>ian and Laird method <str<strong>on</strong>g>of</str<strong>on</strong>g> moments estimator <str<strong>on</strong>g>of</str<strong>on</strong>g> " #<br />

(5). <str<strong>on</strong>g>The</str<strong>on</strong>g> inverse variance<br />

!<br />

193<br />

!

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