Type: Package
Title: Datasets to Help Teach Statistics
Version: 0.1.1
Description: In the spirit of Anscombe's quartet, this package includes datasets that demonstrate the importance of visualizing your data, the importance of not relying on statistical summary measures alone, and why additional assumptions about the data generating mechanism are needed when estimating causal effects. The package includes "Anscombe's Quartet" (Anscombe 1973) <doi:10.1080/00031305.1973.10478966>, D'Agostino McGowan & Barrett (2023) "Causal Quartet" <doi:10.48550/arXiv.2304.02683>, "Datasaurus Dozen" (Matejka & Fitzmaurice 2017), "Interaction Triptych" (Rohrer & Arslan 2021) <doi:10.1177/25152459211007368>, "Rashomon Quartet" (Biecek et al. 2023) <doi:10.48550/arXiv.2302.13356>, and Gelman "Variation and Heterogeneity Causal Quartets" (Gelman et al. 2023) <doi:10.48550/arXiv.2302.12878>.
License: MIT + file LICENSE
URL: https://github.com/r-causal/quartets, https://r-causal.github.io/quartets/
BugReports: https://github.com/r-causal/quartets/issues
Encoding: UTF-8
LazyData: true
Depends: R (≥ 2.10)
RoxygenNote: 7.2.3
NeedsCompilation: no
Packaged: 2023-04-13 20:31:30 UTC; lucymcgowan
Author: Lucy D'Agostino McGowan ORCID iD [aut, cre]
Maintainer: Lucy D'Agostino McGowan <lucydagostino@gmail.com>
Repository: CRAN
Date/Publication: 2023-04-13 23:40:02 UTC

Anscombe's Quartet High Leverage Data

Description

This dataset contains 11 observations generated by Francis Anscombe to demonstrate that statistical summary measures alone cannot capture the full relationship between two variables (here, x and y). Anscombe emphasized the importance of visualizing data prior to calculating summary statistics.

Usage

anscombe_leverage

Format

A dataframe with 11 rows and 2 variables:

Details

This Dataset has a no relationship between x and y with a single high leverage point

Additionally, the following statistical summaries hold:

References

Anscombe, F. J. (1973). "Graphs in Statistical Analysis". American Statistician. 27 (1): 17–21. doi:10.1080/00031305.1973.10478966. JSTOR 2682899.

Anscombe's Quartet Linear Data

Description

This dataset contains 11 observations generated by Francis Anscombe to demonstrate that statistical summary measures alone cannot capture the full relationship between two variables (here, x and y). Anscombe emphasized the importance of visualizing data prior to calculating summary statistics.

Usage

anscombe_linear

Format

A dataframe with 11 rows and 2 variables:

Details

This Dataset has a linear relationship between x and y

Additionally, the following statistical summaries hold:

References

Anscombe, F. J. (1973). "Graphs in Statistical Analysis". American Statistician. 27 (1): 17–21. doi:10.1080/00031305.1973.10478966. JSTOR 2682899.

Anscombe's Quartet Nonlinear Data

Description

This dataset contains 11 observations generated by Francis Anscombe to demonstrate that statistical summary measures alone cannot capture the full relationship between two variables (here, x and y). Anscombe emphasized the importance of visualizing data prior to calculating summary statistics.

Usage

anscombe_nonlinear

Format

A dataframe with 11 rows and 2 variables:

Details

This Dataset has a nonlinear relationship between x and y

Additionally, the following statistical summaries hold:

References

Anscombe, F. J. (1973). "Graphs in Statistical Analysis". American Statistician. 27 (1): 17–21. doi:10.1080/00031305.1973.10478966. JSTOR 2682899.

Anscombe's Quartet Outlier Data

Description

This dataset contains 11 observations generated by Francis Anscombe to demonstrate that statistical summary measures alone cannot capture the full relationship between two variables (here, x and y). Anscombe emphasized the importance of visualizing data prior to calculating summary statistics.

Usage

anscombe_outlier

Format

A dataframe with 11 rows and 2 variables:

Details

This Dataset has a linear relationship between x and y with a single outlier

Additionally, the following statistical summaries hold:

References

Anscombe, F. J. (1973). "Graphs in Statistical Analysis". American Statistician. 27 (1): 17–21. doi:10.1080/00031305.1973.10478966. JSTOR 2682899.

Anscombe's Quartet Data

Description

This dataset contains 44 observations, 11 observations from 4 datasets generated by Francis Anscombe to demonstrate that statistical summary measures alone cannot capture the full relationship between two variables (here, x and y). Anscombe emphasized the importance of visualizing data prior to calculating summary statistics.

Usage

anscombe_quartet

Format

A dataframe with 44 rows and 3 variables:

Details

In each of the datasets the following statistical summaries hold:

References

Anscombe, F. J. (1973). "Graphs in Statistical Analysis". American Statistician. 27 (1): 17–21. doi:10.1080/00031305.1973.10478966. JSTOR 2682899.

Collider Data

Description

This dataset contains 100 observations, generated under the following mechanism: X ~ N(0, 1) (exposure) Y ~ X + N(0,1) (outcome) Z ~ 0.45X + 0.77Y + N(0, 1) (measured factor: collider)

Usage

causal_collider

Format

A dataframe with 100 rows and 3 variables:

References

D'Agostino McGowan L, Barrett M (2023). Causal inference is not a statistical problem. Preprint arXiv:2304.02683v1.

Time-varying Causal Quartet Data

Description

These datasets contains 100 observations, each generated under a different data generating mechanism:

Usage

causal_collider_time

causal_confounding_time

causal_mediator_time

causal_m_bias_time

causal_quartet_time

Format

causal_collider_time: A dataframe with 100 rows and 7 variables:

causal_confounding_time: A dataframe with 100 rows and 7 variables:

causal_mediator_time: A dataframe with 100 rows and 7 variables:

causal_m_bias_time: A dataframe with 100 rows and 9 variables:

An object of class tbl_df (inherits from tbl, data.frame) with 400 rows and 12 columns.

Details

There are two time points:

These datasets help demonstrate that a model that includes only pre-exposure covariates (that is, only adjusting for covariates measured at baseline), will be less prone to potential biases. Adjusting for only pre-exposure covariates "solves" the bias in datasets 1-3. It does not solve the data generated under the "M-bias" scenario, however this is more of a toy example, it has been shown many times that the assumptions needed for this M-bias to hold are often not ones we practically see in data analysis.

References

D'Agostino McGowan L, Barrett M (2023). Causal inference is not a statistical problem. Preprint arXiv:2304.02683v1.

Examples


## incorrect model because covariate is post-treatment
lm(outcome_followup ~ exposure_baseline + covariate_followup,
   data = causal_collider_time)

## correct model because covariate is pre-treatment
## even though the true mechanism dictates that the covariate is a collider,
## because the pre-exposure variable is used, the collider bias does not
## occur.
lm(outcome_followup ~ exposure_baseline + covariate_baseline,
   data = causal_collider_time)

Confounder Data

Description

This dataset contains 100 observations, generated under the following mechanism: Z ~ N(0, 1) (measured factor: confounder) X ~ Z + N(0,1) (exposure) Y ~ 0.5X + Z + N(0, 1) (outcome)

Usage

causal_confounding

Format

A dataframe with 100 rows and 3:

References

D'Agostino McGowan L, Barrett M (2023). Causal inference is not a statistical problem. Preprint arXiv:2304.02683v1.

M-Bias Data

Description

This dataset contains 100 observations, generated under the following mechanism: U1 ~ N(0, 1) U2 ~ N(0, 1) Z ~ 8 U1 + U2 + N(0, 1) (measured factor) X ~ U1 + N(0, 1) (exposure) Y ~ X + U2 + N(0, 1) (outcome)

Usage

causal_m_bias

Format

A dataframe with 100 rows and 5 variables:

References

D'Agostino McGowan L, Barrett M (2023). Causal inference is not a statistical problem. Preprint arXiv:2304.02683v1.

Mediator Data

Description

This dataset contains 100 observations, generated under the following mechanism: X ~ N(0, 1) (exposure) Z ~ X + N(0,1) (measured factor: mediator) Y ~ Z + N(0, 1) (outcome)

Usage

causal_mediator

Format

A dataframe with 100 rows and 3 variables:

References

D'Agostino McGowan L, Barrett M (2023). Causal inference is not a statistical problem. Preprint arXiv:2304.02683v1.

Causal Quartet Data

Description

This dataset contains 400 observations, each generated under a different data generating mechanism:

Usage

causal_quartet

Format

A dataframe with 400 rows and 6 variables:

References

D'Agostino McGowan L, Barrett M (2023). Causal inference is not a statistical problem. Preprint arXiv:2304.02683v1.

Datasaurus Dozen Data

Description

A dataset containing 12 datasets that are equal in mean, variance, and Pearson's correlation but very different when visualized.

Usage

datasaurus_dozen

Format

A data frame with 1846 rows and 3 variables:

References

Davies R, Locke S, D'Agostino McGowan L (2022). datasauRus: Datasets from the Datasaurus Dozen. R package version 0.1.6, https://CRAN.R-project.org/package=datasauRus.

Matejka, J., & Fitzmaurice, G. (2017). Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing. CHI 2017 Conference proceedings: ACM SIGCHI Conference on Human Factors in Computing Systems. Retrieved from https://www.autodesk.com/research/publications/same-stats-different-graphs

Gelman Heterogeneity Causal Quartet Data

Description

This dataset contains 88 observations, each generated under a different mechanism treatment heterogeneity with respect to some pre-exposure characteristic, z:

Usage

heterogeneous_causal_quartet

Format

A dataframe with 88 rows and 5 variables:

References

Gelman, A., Hullman, J., & Kennedy, L. (2023). Causal quartets: Different ways to attain the same average treatment effect. arXiv preprint arXiv:2302.12878.

Hullman J (2023). causalQuartet: Create Causal Quartets for Interrogating Average Treatment Effects. R package version 0.0.0.9000.

Interaction Triptych Data

Description

This dataset contains 2,700 observations, generated under 3 different conditions

Usage

interaction_triptych

Format

A dataframe with 2700 rows and 5 variables:

Details

In the ideal scenario, only the slopes differ by moderator level. In the "floor effect" scenario, there is an illusion of an interaction, even though only main effects were simulated. In the third scenario, the slopes increase with higher moderator values but the correlation decreases. Running only a linear model would not allow for appropriate differentiation between these effects.

In each case there is a potential moderator with "low" "medium" and "high" values.

References

Rohrer, Julia M., and Ruben C. Arslan. "Precise answers to vague questions: Issues with interactions." Advances in Methods and Practices in Psychological Science 4.2 (2021): 25152459211007368.

Rashomon Quartet Data

Description

This dataset contains 2,000 observations, 1,000 training observations and 1,000 testing observations. These were generated such that 4 modeling techniques (regression tree, linear model, neural network, random forest) will yield the same R^2 and RMSE but will fit the models very differently.

Usage

rashomon_quartet

rashomon_quartet_train

rashomon_quartet_test

Format

rashomon_quartet: A dataframe with 2000 rows and 5 variables:

rashomon_quartet_train: A dataframe with 1000 rows and 4 variables:

rashomon_quartet_test: A dataframe with 1000 rows and 4 variables:

Details

There are three explanatory variables x1, x2, x3 and one outcome y generated as:

y = sin((3x_1 + x_2)/5)+\varepsilon

where \varepsilon\sim N(0,1/3) and [x_1,x_2,x_3]\sim N(0, \Sigma_{3x3}) and \Sigma_{3x3} has 1 on the diagonal and 0.9 elsewhere.

If fit using the following hyperparameters, each model will yield an R^2 of 0.73 and an RMSE of 0.354

rashomon_quartet_train contains just the training data and rashomon_quartet_test contains only the test data.

References

P. Biecek, H. Baniecki, M. Krzyziński, D. Cook. Performance is not enough: the story of Rashomon’s quartet. Preprint arXiv:2302.13356v2, 2023.

Gelman Variation Causal Quartet Data

Description

This dataset contains 88 observations, each generated under a different mechanism of variation of the treatment effect with respect to some pre-exposure characteristic, z:

Usage

variation_causal_quartet

Format

A dataframe with 88 rows and 5 variables:

References

Gelman, A., Hullman, J., & Kennedy, L. (2023). Causal quartets: Different ways to attain the same average treatment effect. arXiv preprint arXiv:2302.12878.

Hullman J (2023). causalQuartet: Create Causal Quartets for Interrogating Average Treatment Effects. R package version 0.0.0.9000.