Sampling¶

Sampling activities (the “bowl” of balls, tactile samples) are how ModernDive builds intuition for sampling variation. rep_slice_sample takes repeated samples and stacks them with a replicate column — the analog of R moderndive::rep_slice_sample() / infer::rep_sample_n().

The bowl¶

import moderndive as md
import polars as pl

bowl = md.load_bowl()      # 2400 red/white balls
bowl.head()

shape: (5, 2)

ball_ID	color
i64	str
1	"white"
2	"white"
3	"white"
4	"red"
5	"white"

One virtual sample¶

from moderndive import rep_slice_sample

sample = rep_slice_sample(bowl, n=50, seed=1)
# proportion red in this sample
sample.select((pl.col("color") == "red").mean().alias("prop_red"))

shape: (1, 1)

prop_red
f64
0.38

Many samples → a sampling distribution¶

Take 1000 samples of size 50 and compute the proportion red in each:

samples = rep_slice_sample(bowl, n=50, reps=1000, seed=1)

prop_red = (
    samples
    .group_by("replicate")
    .agg((pl.col("color") == "red").mean().alias("prop_red"))
)
prop_red.head()

shape: (5, 2)

replicate	prop_red
i64	f64
1	0.38
2	0.42
3	0.42
4	0.42
5	0.46

That prop_red column is a sampling distribution. Visualize its spread the same way you would any distribution (see Bootstrapping & confidence intervals for building one with the inference pipeline instead).

With vs. without replacement¶

rep_slice_sample samples without replacement by default (like dealing from a deck). Pass replace=True for bootstrap-style resampling:

rep_slice_sample(bowl, n=50, reps=1000, replace=True, seed=1)

shape: (50_000, 3)

replicate	ball_ID	color
i64	i64	str
1	1136	"white"
1	1229	"red"
1	1813	"white"
1	2282	"red"
1	84	"white"
…	…	…
1000	439	"white"
1000	1203	"red"
1000	252	"white"
1000	1113	"white"
1000	1277	"red"

Tactile samples¶

The hand-collected counterparts are bundled too:

md.load_tactile_prop_red()   # 33 groups' samples of 50 balls

shape: (33, 4)

group	replicate	red_balls	prop_red
str	i64	i64	f64
"Ilyas, Yohan"	1	21	0.42
"Morgan, Terrance"	2	17	0.34
"Martin, Thomas"	3	21	0.42
"Clark, Frank"	4	21	0.42
"Riddhi, Karina"	5	18	0.36
…	…	…	…
"Julie, Hailin"	29	15	0.3
"Katie, Caroline"	30	21	0.42
"Mallory, Damani, Melissa"	31	21	0.42
"Katie"	32	16	0.32
"Francis, Vignesh"	33	19	0.38