The coordinates of a funnel plot, and the funnel itself

A funnel plot is only interpretable against its own null: without the contour that a no-bias world would produce, an eye reading the scatter is reading noise. The contour is the fixed-effect summary plus and minus a critical value times each study's own standard error, which is why the plot is a funnel rather than a band.

Usage

Mafnpr(yi, se_i, level = 0.95)

Arguments

yi: Study effect estimates.
se_i: Their standard errors, strictly positive.
level: Contour level.

Value

List with x_funnel, y_funnel, precision, center, ci_lo, ci_hi, k.

Details

Formula: points (y_i, se_i); contour \(theta_FE +- z_{1-alpha/2} se\) with theta_FE = sum(y_i/v_i)/sum(1/v_i) – Light and Pillemer (1984), Chapter 3.

References

Light, R. J. and Pillemer, D. B. (1984). Summing Up: The Science of Reviewing Research. Harvard University Press, Chapter 3.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Mafnpr(V, V)
#> $x_funnel
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $y_funnel
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $precision
#> [1] 1.0000000 0.5000000 0.3333333 0.2500000 0.2000000 0.1666667 0.1428571
#> [8] 0.1250000
#> 
#> $center
#> [1] 1.779375
#> 
#> $ci_lo
#> [1]  -0.1805886  -2.1405526  -4.1005166  -6.0604806  -8.0204446  -9.9804086
#> [7] -11.9403725 -13.9003365
#> 
#> $ci_hi
#> [1]  3.739339  5.699303  7.659267  9.619231 11.579195 13.539159 15.499123
#> [8] 17.459087
#> 
#> $se_center
#> [1] 0.809134
#> 
#> $z_crit
#> [1] 1.959964
#> 
#> $k
#> [1] 8
#> 
#> $method
#> [1] "Funnel-plot coordinates with pseudo-confidence contours"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"