The Random Effects P^sub Rep^ Continues to Mispredict the Probability of Replication

By Iverson, Geoffrey J.; Lee, Michael D. et al. | Psychonomic Bulletin & Review, April 2010 | Go to article overview

The Random Effects P^sub Rep^ Continues to Mispredict the Probability of Replication


Iverson, Geoffrey J., Lee, Michael D., Wagenmakers, Eric-Jan, Psychonomic Bulletin & Review


In their reply, Lecoutre and Killeen (2010) argue for a random effects version of p^sub rep^, in which the observed effect from one experiment is used to predict the probability that an effect from a different but related experiment will have the same sign. They present a figure giving the impression that this version of p^sub rep^ accurately predicts the probability of replication. We show that their results are incorrect and conceptually limited, even when corrected. We then present a meaningful evaluation of the random effects p^sub rep^ as a predictor and find that, as with the fixed effects p^sub rep^, it performs very poorly.

This reply addresses the two issues raised by Lecoutre and Killeen (2010; hereafter, LK). The first is their claim that we conflated two probabilities. The second is their claim that p^sub rep^ is an accurate predictor.

The first issue is easy to address. LK (2010) assert that Iverson, Lee, and Wagenmakers (2009) conflated two probabilities: the probability of coincidence and Killeen's (2005) probability of replication. On the basis of this supposed conflation, LK argue that "ILW's conclusions are irrelevant for Killeen's (2005) statistic" (p. 269). The fact of the matter is otherwise. We did not confuse these two probabilities. In Iverson, Lee, and Wagenmakers-and all of our earlier commentaries (Iverson, Lee, Zhang, & Wagenmakers, 2009; Iverson, Wagenmakers, & Lee, in press)-we used exactly the fixed effects p^sub rep^ definition that appears in the third column of Table 1 in LK. We most certainly did not confuse the statistic p^sub rep^ with the parameter p^sub coinc^ (for probability of coincidence), and we invite readers to verify this for themselves.

The second claim regarding the accuracy of p^sub rep^ is a more important source of disagreement. In their reply, LK (2010) stress a p^sub rep^ that is conceptually different from the fixed effects version, which they claim returns accurate predictions for both simulated and real-world data (LK, 2010, p. 266). Both versions of p^sub rep^ use a known effect size from an experiment. In the fixed effects formulation, p^sup F^ ^sub rep^, the goal is to predict the probability that a replication of the same experiment would yield an effect size of the same sign as the original. In the random effects version, p^sup R^ ^sub rep^, the goal is to use an effect size from one experiment to predict the probability of getting an effect of the same sign from a different experiment, albeit one coming from the same literature. This new formulation seems to us a strange goal for empirical science. Does it make sense to think that, having observed people preferring oval to square faces, we want to predict whether they will prefer natural to morphed faces?

But whatever the conceptual challenges, it is possible to continue analyzing p^sup R^ ^sub rep^ as a statistic. In more or less technical terms, our previous commentaries showed that p^sup F^ ^sub rep^ made poor predictions about the true replication probability. This reply extends those analyses to evaluate p^sup R^^sub rep^.

The Meaning of LK's (2010) Figure 5

The flowchart simulation presented by LK (2010), culminating in their Figure 5, gives the illusion of successful prediction under uncertainty. The abscissa is p^sup R^^sub rep^. The ordinate is a different random effects formulation of p^sub rep^, for which we derive an analytic expression,1 and which we denote p^sup O^^sub rep^. LK use numerical simulation to evaluate this ordinate.

The relationship between the functions p^sup R^^sub rep^ and p^sup O^^sub rep^, for the same set of total sample sizes N as that considered by LK (2010), is shown in our Figure 1A. Each line corresponds to a different sample size, and, by choosing different effect sizes, the whole curve relating the two prep versions can be traced out. We were surprised that these patterns did not seem to agree with Figure 5 in LK, and so we used their flowchart to calculate the results numerically. …

The rest of this article is only available to active members of Questia

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

The Random Effects P^sub Rep^ Continues to Mispredict the Probability of Replication
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Author Advanced search

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.