# difference_in_means

##### Design-based difference-in-means estimator

Difference-in-means estimators that selects the appropriate point estimate, standard errors, and degrees of freedom for a variety of designs: unit randomized, cluster randomized, block randomized, block-cluster randomized, matched-pairs, and matched-pair cluster randomized designs

##### Usage

```
difference_in_means(formula, data, blocks, clusters, weights, subset,
se_type = c("default", "none"), condition1 = NULL, condition2 = NULL,
ci = TRUE, alpha = 0.05)
```

##### Arguments

- formula
an object of class formula, as in

`lm`

, such as`Y ~ Z`

with only one variable on the right-hand side, the treatment.- data
A

`data.frame`

.- blocks
An optional bare (unquoted) name of the block variable. Use for blocked designs only.

- clusters
An optional bare (unquoted) name of the variable that corresponds to the clusters in the data; used for cluster randomized designs. For blocked designs, clusters must nest within blocks.

- weights
the bare (unquoted) names of the weights variable in the supplied data.

- subset
An optional bare (unquoted) expression specifying a subset of observations to be used.

- se_type
An optional string that can be one of

`c("default", "none")`

. If "default" (the default), it will use the default standard error estimator for the design, and if "none" then standard errors will not be computed which may speed up run time if only the point estimate is required.- condition1
value in the treatment vector of the condition to be the control. Effects are estimated with

`condition1`

as the control and`condition2`

as the treatment. If unspecified,`condition1`

is the "first" condition and`condition2`

is the "second" according to levels if the treatment is a factor or according to a sortif it is a numeric or character variable (i.e if unspecified and the treatment is 0s and 1s,`condition1`

will by default be 0 and`condition2`

will be 1). See the examples for more.- condition2
value in the treatment vector of the condition to be the treatment. See

`condition1`

.- ci
logical. Whether to compute and return p-values and confidence intervals, TRUE by default.

- alpha
The significance level, 0.05 by default.

##### Details

This function implements a difference-in-means estimator, with support for blocked, clustered, matched-pairs, block-clustered, and matched-pair clustered designs. One specifies their design by passing the blocks and clusters in their data and this function chooses which estimator is most appropriate.

If you pass only `blocks`

, if all blocks are of size two, we will
infer that the design is a matched-pairs design. If they are all size four
or larger, we will infer that it is a regular blocked design. If you pass
both `blocks`

and `clusters`

, we will similarly
infer whether it is a matched-pairs clustered design or a block-clustered
design the number of clusters per block. If the user passes only
`clusters`

, we will infer that the design was cluster-randomized. If
the user specifies neither the `blocks`

nor the `clusters`

,
a regular Welch's t-test will be performed.

Importantly, if the user specifies weights, the estimation is handed off
to `lm_robust`

with the appropriate robust standard errors
as weighted difference-in-means estimators are not implemented here.
More details of the about each of the estimators can be found in the
mathematical notes.

##### Value

Returns an object of class `"difference_in_means"`

.

The post-estimation commands functions `summary`

and `tidy`

return results in a `data.frame`

. To get useful data out of the return,
you can use these data frames, you can use the resulting list directly, or
you can use the generic accessor functions `coef`

and
`confint`

.

An object of class `"difference_in_means"`

is a list containing at
least the following components:

the estimated difference in means

the estimated standard error

the t-statistic

the estimated degrees of freedom

the p-value from a two-sided t-test using `coefficients`

, `std.error`

, and `df`

the lower bound of the `1 - alpha`

percent confidence interval

the upper bound of the `1 - alpha`

percent confidence interval

a character vector of coefficient names

the significance level specified by the user

the number of observations used

the name of the outcome variable

the name of the design learned from the arguments passed

##### References

Gerber, Alan S, and Donald P Green. 2012. Field Experiments: Design, Analysis, and Interpretation. New York: W.W. Norton.

Imai, Kosuke, Gary King, Clayton Nall. 2009. "The Essential Role of Pair Matching in Cluster-Randomized Experiments, with Application to the Mexican Universal Health Insurance Evaluation." Statistical Science 24 (1). Institute of Mathematical Statistics: 29-53. https://doi.org/10.1214/08-STS274.

##### See Also

##### Examples

```
# NOT RUN {
library(fabricatr)
library(randomizr)
# Get appropriate standard errors for unit-randomized designs
# ----------
# 1. Unit randomized
# ----------
dat <- fabricate(
N = 100,
Y = rnorm(100),
Z_comp = complete_ra(N, prob = 0.4),
)
table(dat$Z_comp)
difference_in_means(Y ~ Z_comp, data = dat)
# ----------
# 2. Cluster randomized
# ----------
# Accurates estimates and standard errors for clustered designs
dat$clust <- sample(20, size = nrow(dat), replace = TRUE)
dat$Z_clust <- cluster_ra(dat$clust, prob = 0.6)
table(dat$Z_clust, dat$clust)
summary(difference_in_means(Y ~ Z_clust, clusters = clust, data = dat))
# ----------
# 3. Block randomized
# ----------
dat$block <- rep(1:10, each = 10)
dat$Z_block <- block_ra(dat$block, prob = 0.5)
table(dat$Z_block, dat$block)
difference_in_means(Y ~ Z_block, blocks = block, data = dat)
# ----------
# 4. Block cluster randomized
# ----------
# Learns this design if there are two clusters per block
dat$small_clust <- rep(1:50, each = 2)
dat$big_blocks <- rep(1:5, each = 10)
dat$Z_blcl <- block_and_cluster_ra(
blocks = dat$big_blocks,
clusters = dat$small_clust
)
difference_in_means(
Y ~ Z_blcl,
blocks = big_blocks,
clusters = small_clust,
data = dat
)
# ----------
# 5. Matched-pairs
# ----------
# Matched-pair estimates and standard errors are also accurate
# Specified same as blocked design, function learns that
# it is matched pair from size of blocks!
dat$pairs <- rep(1:50, each = 2)
dat$Z_pairs <- block_ra(dat$pairs, prob = 0.5)
table(dat$pairs, dat$Z_pairs)
difference_in_means(Y ~ Z_pairs, blocks = pairs, data = dat)
# ----------
# 6. Matched-pair cluster randomized
# ----------
# Learns this design if there are two clusters per block
dat$small_clust <- rep(1:50, each = 2)
dat$cluster_pairs <- rep(1:25, each = 4)
table(dat$cluster_pairs, dat$small_clust)
dat$Z_mpcl <- block_and_cluster_ra(
blocks = dat$cluster_pairs,
clusters = dat$small_clust
)
difference_in_means(
Y ~ Z_mpcl,
blocks = cluster_pairs,
clusters = small_clust,
data = dat
)
# ----------
# Other examples
# ----------
# Also works with multi-valued treatments if users specify
# comparison of interest
dat$Z_multi <- simple_ra(
nrow(dat),
conditions = c("Treatment 2", "Treatment 1", "Control"),
prob_each = c(0.4, 0.4, 0.2)
)
# Only need to specify which condition is treated `condition2` and
# which is control `condition1`
difference_in_means(
Y ~ Z_multi,
condition1 = "Treatment 2",
condition2 = "Control",
data = dat
)
difference_in_means(
Y ~ Z_multi,
condition1 = "Treatment 1",
condition2 = "Control",
data = dat
)
# Specifying weights will result in estimation via lm_robust()
dat$w <- runif(nrow(dat))
difference_in_means(Y ~ Z_comp, weights = w, data = dat)
lm_robust(Y ~ Z_comp, weights = w, data = dat)
# }
```

*Documentation reproduced from package estimatr, version 0.10.0, License: MIT + file LICENSE*