probability: Problems in Elementary Probability Theory

Description Usage Format Source Examples

Description

This data set contains responses to problems in elementary probability theory observed before and after some instructions (the so-called learning object) were given. Data were collected both in the lab and via an online questionnaire. Of the 1127 participants eligible in the online study, 649 were excluded because they did not complete the first set of problems (p101, ..., p112) or they responded too quickly or too slowly. Based on similar criteria, further participants were excluded for the second set of problems, indicated by missing values in the variables b201, ..., b212. Problems were presented in random order.

Participants were randomized to two conditions: an enhanced learning object including instructions with examples and a basic learning object without examples. Instructions were given on four concepts: how to calculate the classic probability of an event (pb), the probability of the complement of an event (cp), of the union of two disjoint events (un), and of two independent events (id).

The questionnaire was organized as follows:

Page 1

Welcome page.

Page 2

Demographic data.

Page 3

First set of problems.

Page 4 to 8

Instructions (learning object).

Page 9

Second set of problems.

Page 10

Feedback about number of correctly solved problems.

Usage

1

Format

A data frame with 504 cases and 68 variables:

The twelve problems of the first part (before the learning object):

The twelve problems of the second part (after the learning object):

Further variables:

Source

Data were collected by Pasquale Anselmi and Florian Wickelmaier at the Department of Psychology, University of Tuebingen, in February and March 2010.

Examples

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data(probability)

## "Completer" sample
pb <- probability[!is.na(probability$b201), ]

## Response frequencies for first and second part
N.R1 <- as.pattern(pb[, sprintf("b1%.2i", 1:12)], freq = TRUE)
N.R2 <- as.pattern(pb[, sprintf("b2%.2i", 1:12)], freq = TRUE)

## Conjunctive skill function, one-to-one problem function
sf1 <- read.table(header = TRUE, text = "
  item cp id pb un
     1  0  0  1  0
     2  1  0  0  0
     3  0  0  0  1
     4  0  1  0  0
     5  1  0  1  0
     6  1  0  1  0
     7  0  0  1  1
     8  0  0  1  1
     9  0  1  1  0
    10  1  1  0  0
    11  1  1  1  0
    12  0  1  1  1
")

## Extended skill function
sf2 <- rbind(sf1, read.table(header = TRUE, text = "
  item cp id pb un
     2  0  0  0  1
     3  1  0  0  0
     6  0  0  1  1
     7  1  0  1  0
    12  1  1  1  0
"))

## Delineated knowledge structures
K1 <- delineate(sf1)$K
K2 <- delineate(sf2)$K

## After instructions, fit of knowledge structures improves
sapply(list(N.R1, N.R2), function(n) blim(K1, n)$discrepancy)
sapply(list(N.R1, N.R2), function(n) blim(K2, n)$discrepancy)

pks documentation built on May 29, 2017, 11:26 p.m.