`dat.raudenbush1985.Rd`

Results from 19 studies examining how teachers' expectations about their pupils can influence actual IQ levels.

`dat.raudenbush1985`

The data frame contains the following columns:

study | `numeric` | study number |

author | `character` | study author(s) |

year | `numeric` | publication year |

weeks | `numeric` | weeks of contact prior to expectancy induction |

setting | `character` | whether tests were group or individually administered |

tester | `character` | whether test administrator was aware or blind |

n1i | `numeric` | sample size of experimental group |

n2i | `numeric` | sample size of control group |

yi | `numeric` | standardized mean difference |

vi | `numeric` | corresponding sampling variance |

In the so-called ‘Pygmalion study’ (Rosenthal & Jacobson, 1968), “all of the predominantly poor children in the so-called Oak elementary school were administered a test pretentiously labeled the ‘Harvard Test of Inflected Acquisition.’ After explaining that this newly designed instrument had identified those children most likely to show dramatic intellectual growth during the coming year, the experimenters gave the names of these ‘bloomers’ to the teachers. In truth, the test was a traditional IQ test and the ‘bloomers’ were a randomly selected 20% of the student population. After retesting the children 8 months later, the experimenters reported that those predicted to bloom had in fact gained significantly more in total IQ (nearly 4 points) and reasoning IQ (7 points) than the control group children. Further, at the end of the study, the teachers rated the experimental children as intellectually more curious, happier, better adjusted, and less in need of approval than their control group peers” (Raudenbush, 1984).

In the following years, a series of studies were conducted attempting to replicate this rather controversial finding. However, the great majority of those studies were unable to demonstrate a statistically significant difference between the two experimental groups in terms of IQ scores. Raudenbush (1984) conducted a meta-analysis based on 19 such studies to further examine the evidence for the existence of the ‘Pygmalion effect’. The dataset includes the results from these studies.

The outcome measure used for the meta-analysis was the standardized mean difference (`yi`

), with positive values indicating that the supposed ‘bloomers’ had, on average, higher IQ scores than those in the control group. The `weeks`

variable indicates the number of weeks of prior contact between teachers and students before the expectancy induction. Testing was done either in a group setting or individually, which is indicated by the `setting`

variable. Finally, the `tester`

variable indicates whether the test administrators were either aware or blind to the researcher-provided designations of the children's intellectual potential.

The data in this dataset were obtained from Raudenbush and Bryk (1985) with information on the `setting`

and `tester`

variables extracted from Raudenbush (1984).

Raudenbush, S. W. (1984). Magnitude of teacher expectancy effects on pupil IQ as a function of the credibility of expectancy induction: A synthesis of findings from 18 experiments. *Journal of Educational Psychology*, **76**(1), 85–97. https://doi.org/10.1037/0022-0663.76.1.85

Raudenbush, S. W., & Bryk, A. S. (1985). Empirical Bayes meta-analysis. *Journal of Educational Statistics*, **10**(2), 75–98. https://doi.org/10.3102/10769986010002075

education, standardized mean differences, meta-regression

```
### copy data into 'dat' and examine data
dat <- dat.raudenbush1985
dat
#>
#> study author year weeks setting tester n1i n2i yi vi
#> 1 1 Rosenthal et al. 1974 2 group aware 77 339 0.0300 0.0156
#> 2 2 Conn et al. 1968 21 group aware 60 198 0.1200 0.0216
#> 3 3 Jose & Cody 1971 19 group aware 72 72 -0.1400 0.0279
#> 4 4 Pellegrini & Hicks 1972 0 group aware 11 22 1.1800 0.1391
#> 5 5 Pellegrini & Hicks 1972 0 group blind 11 22 0.2600 0.1362
#> 6 6 Evans & Rosenthal 1969 3 group aware 129 348 -0.0600 0.0106
#> 7 7 Fielder et al. 1971 17 group blind 110 636 -0.0200 0.0106
#> 8 8 Claiborn 1969 24 group aware 26 99 -0.3200 0.0484
#> 9 9 Kester 1969 0 group aware 75 74 0.2700 0.0269
#> 10 10 Maxwell 1970 1 indiv blind 32 32 0.8000 0.0630
#> 11 11 Carter 1970 0 group blind 22 22 0.5400 0.0912
#> 12 12 Flowers 1966 0 group blind 43 38 0.1800 0.0497
#> 13 13 Keshock 1970 1 indiv blind 24 24 -0.0200 0.0835
#> 14 14 Henrikson 1970 2 indiv blind 19 32 0.2300 0.0841
#> 15 15 Fine 1972 17 group aware 80 79 -0.1800 0.0253
#> 16 16 Grieger 1970 5 group blind 72 72 -0.0600 0.0279
#> 17 17 Rosenthal & Jacobson 1968 1 group aware 65 255 0.3000 0.0193
#> 18 18 Fleming & Anttonen 1971 2 group blind 233 224 0.0700 0.0088
#> 19 19 Ginsburg 1970 7 group aware 65 67 -0.0700 0.0303
#>
### load metafor package
library(metafor)
### random-effects model
res <- rma(yi, vi, data = dat)
res
#>
#> Random-Effects Model (k = 19; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of total heterogeneity): 0.0188 (SE = 0.0155)
#> tau (square root of estimated tau^2 value): 0.1372
#> I^2 (total heterogeneity / total variability): 41.86%
#> H^2 (total variability / sampling variability): 1.72
#>
#> Test for Heterogeneity:
#> Q(df = 18) = 35.8295, p-val = 0.0074
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> 0.0837 0.0516 1.6208 0.1051 -0.0175 0.1849
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
### create weeks variable where values larger than 3 are set to 3
dat$weeks.c <- ifelse(dat$weeks > 3, 3, dat$weeks)
### mixed-effects model with weeks.c variable as moderator
res <- rma(yi, vi, mods = ~ weeks.c, data = dat, digits = 3)
res
#>
#> Mixed-Effects Model (k = 19; tau^2 estimator: REML)
#>
#> tau^2 (estimated amount of residual heterogeneity): 0.000 (SE = 0.007)
#> tau (square root of estimated tau^2 value): 0.001
#> I^2 (residual heterogeneity / unaccounted variability): 0.00%
#> H^2 (unaccounted variability / sampling variability): 1.00
#> R^2 (amount of heterogeneity accounted for): 100.00%
#>
#> Test for Residual Heterogeneity:
#> QE(df = 17) = 16.571, p-val = 0.484
#>
#> Test of Moderators (coefficient 2):
#> QM(df = 1) = 19.258, p-val < .001
#>
#> Model Results:
#>
#> estimate se zval pval ci.lb ci.ub
#> intrcpt 0.407 0.087 4.678 <.001 0.237 0.578 ***
#> weeks.c -0.157 0.036 -4.388 <.001 -0.227 -0.087 ***
#>
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
```