5  Descriptive Statistics

library(tidyverse)
library(scales)
library(janitor)
library(survey)
library(srvyr)
library(gtsummary)

Point estimates such as totals, means, variances, etc. may be the primary objective of the survey, or just an exploratory step prior to a multivariate analysis. Heeringa (2017) explains the math behind sample statistics. Zimmer (2024) explains how to calculate them using the srvyr package.

5.1 Survey Summary

apisrs_des |>
  tbl_svysummary(
    by  = sch.wide, 
    include = c(api00, target, growth, awards, comp.imp)
  ) |>
  modify_spanning_header(all_stat_cols() ~ "Met Growth Target") |>
  as_gt() |>
  gt::tab_header(
    title = "Simple Random Sample Survey Summary"
  ) |>
  gt::tab_options(heading.align = "left")

Simple Random Sample Survey Summary
Characteristic	Met Growth Target
	No N = 1,146 1	Yes N = 5,048 1
api00	541 (482, 708)	675 (577, 772)
target	13 (4, 16)	9 (5, 14)
Unknown	0	588
growth	-1 (-12, 6)	33 (20, 51)
awards	0 (0%)	3,840 (76%)
comp.imp	62 (5.4%)	4,057 (80%)
1 Median (Q1, Q3); n (%)

5.2 Point Estimates

How many schools met the growth target? survey_count() returns a scaled row count. If you are collecting other statistics, use survey_total(1) to sum the rows. Use the vartype parameter to add cols for interval-related data around the estimate.

SRS

apisrs_pe <-
  apisrs_des |>
  group_by(sch.wide) |>
  cascade(
    Schools = survey_total(1, vartype = NULL),
    Proportion = survey_mean(proportion = TRUE, vartype = NULL),
    EnrollSum = survey_total(enroll, vartype = NULL),
    EnrollMean = survey_mean(enroll, vartype = c("se", "ci")),
    EnrollIQR = survey_quantile(enroll, quantiles = c(.25, .75), vartype = NULL)
  )

apisrs_pe |>
  gt::gt() |>
  gt::fmt_number(columns = c(2, 4:10), decimals = 0) |>
  gt::fmt_percent(columns = 3, decimals = 0) |>
  gt::tab_spanner("Mean Enrollment", starts_with("EnrollMean")) |>
  gt::tab_spanner("IQR", starts_with("EnrollIQR")) |>
  gt::cols_label(
    sch.wide = "Met Target",
      EnrollMean = "Mean",
      EnrollMean_se = "SE",
      EnrollMean_low = "Low",
      EnrollMean_upp = "Upp",
      EnrollIQR_q25 = "Q25",
      EnrollIQR_q75 = "Q75"
  )

Met Target	Schools	Proportion	EnrollSum	Mean Enrollment				IQR
				Mean	SE	Low	Upp	Q25	Q75
No	1,146	19%	948,766	828	91	648	1,008	412	1,252
Yes	5,048	81%	2,672,308	529	24	481	578	339	639
NA	6,194	100%	3,621,074	585	27	531	639	339	664

Stratified

apistrat_pe <-
  apistrat_des |>
  group_by(sch.wide) |>
  cascade(
    Schools = survey_total(1, vartype = NULL),
    Proportion = survey_mean(proportion = TRUE, vartype = NULL),
    EnrollSum = survey_total(enroll, vartype = NULL),
    EnrollMean = survey_mean(enroll, vartype = c("se", "ci")),
    EnrollIQR = survey_quantile(enroll, quantiles = c(.25, .75), vartype = NULL)
  )

apistrat_pe |>
  gt::gt() |>
  gt::fmt_number(columns = c(2, 4:10), decimals = 0) |>
  gt::fmt_percent(columns = 3, decimals = 0) |>
  gt::tab_spanner("Mean Enrollment", starts_with("EnrollMean")) |>
  gt::tab_spanner("IQR", starts_with("EnrollIQR")) |>
  gt::cols_label(
    sch.wide = "Met Target",
      EnrollMean = "Mean",
      EnrollMean_se = "SE",
      EnrollMean_low = "Low",
      EnrollMean_upp = "Upp",
      EnrollIQR_q25 = "Q25",
      EnrollIQR_q75 = "Q75"
  )

Met Target	Schools	Proportion	EnrollSum	Mean Enrollment				IQR
				Mean	SE	Low	Upp	Q25	Q75
No	1,066	17%	1,013,067	951	95	764	1,137	441	1,515
Yes	5,128	83%	2,674,110	521	19	484	558	325	613
NA	6,194	100%	3,687,178	595	19	559	632	334	660

Cluster

apiclus2_pe <-
  apiclus2_des |>
  group_by(sch.wide) |>
  cascade(
    Schools = survey_total(1, vartype = NULL),
    Proportion = survey_mean(proportion = TRUE, vartype = NULL),
    EnrollSum = survey_total(enroll, vartype = NULL),
    EnrollMean = survey_mean(enroll, vartype = c("se", "ci")),
    # EnrollIQR = survey_quantile(enroll, quantiles = c(.25, .75), vartype = NULL)
  )

apiclus2_pe |>
  gt::gt() |>
  gt::fmt_number(columns = c(2, 4:8), decimals = 0) |>
  gt::fmt_percent(columns = 3, decimals = 0) |>
  gt::tab_spanner("Mean Enrollment", starts_with("EnrollMean")) |>
  gt::tab_spanner("IQR", starts_with("EnrollIQR")) |>
  gt::cols_label(
    sch.wide = "Met Target",
    EnrollMean = "Mean",
    EnrollMean_se = "SE",
    EnrollMean_low = "Low",
    EnrollMean_upp = "Upp"
    # EnrollIQR_q25 = "Q25",
    # EnrollIQR_q75 = "Q75"
  )

Met Target	Schools	Proportion	EnrollSum	Mean Enrollment
				Mean	SE	Low	Upp
No	1,276	25%	1,104,845	866	106	653	1,080
Yes	3,853	75%	NA	NA	NA	NA	NA
NA	5,129	100%	NA	NA	NA	NA	NA

5.3 Bivariate Relationships

Bivariate statistics include ratios and correlations.

SRS

apisrs_bv <-
  apisrs_des |>
  group_by(sch.wide) |>
  cascade(
    Meals = survey_total(meals, vartype = NULL),
    Enrollment = survey_total(enroll, vartype = NULL),
    RatioEst = survey_ratio(meals, enroll),
    CorrEst = survey_corr(meals, enroll)
  )

apisrs_bv |>
  gt::gt() |>
  gt::fmt_number(columns = c(2:3), decimals = 0) |>
  gt::fmt_number(columns = c(4:7), decimals = 4) |>
  gt::fmt_percent(columns = 3, decimals = 0) |>
  gt::tab_spanner("Ratio", starts_with("Ratio")) |>
  gt::tab_spanner("Correlation", starts_with("Corr")) |>
  gt::cols_label(
    sch.wide = "Met Target",
    RatioEst = "Est",
    RatioEst_se = "SE",
    CorrEst = "Est",
    CorrEst_se = "SE"
  )

Met Target	Meals	Enrollment	Ratio		Correlation
			Est	SE	Est	SE
No	58,038	94,876,595%	0.0612	0.0096	−0.1103	0.1523
Yes	251,724	267,230,839%	0.0942	0.0062	−0.0360	0.0560
NA	309,762	362,107,434%	0.0855	0.0055	−0.0511	0.0590

Stratified

apistrat_bv <-
  apisrs_des |>
  group_by(sch.wide) |>
  cascade(
    Meals = survey_total(meals, vartype = NULL),
    Enrollment = survey_total(enroll, vartype = NULL),
    RatioEst = survey_ratio(meals, enroll),
    CorrEst = survey_corr(meals, enroll)
  )

apistrat_bv |>
  gt::gt() |>
  gt::fmt_number(columns = c(2:3), decimals = 0) |>
  gt::fmt_number(columns = c(4:7), decimals = 4) |>
  gt::fmt_percent(columns = 3, decimals = 0) |>
  gt::tab_spanner("Ratio", starts_with("Ratio")) |>
  gt::tab_spanner("Correlation", starts_with("Corr")) |>
  gt::cols_label(
    sch.wide = "Met Target",
    RatioEst = "Est",
    RatioEst_se = "SE",
    CorrEst = "Est",
    CorrEst_se = "SE"
  )

Met Target	Meals	Enrollment	Ratio		Correlation
			Est	SE	Est	SE
No	58,038	94,876,595%	0.0612	0.0096	−0.1103	0.1523
Yes	251,724	267,230,839%	0.0942	0.0062	−0.0360	0.0560
NA	309,762	362,107,434%	0.0855	0.0055	−0.0511	0.0590

Cluster

apiclus2_bv <-
  apisrs_des |>
  group_by(sch.wide) |>
  cascade(
    Meals = survey_total(meals, vartype = NULL),
    Enrollment = survey_total(enroll, vartype = NULL),
    RatioEst = survey_ratio(meals, enroll),
    CorrEst = survey_corr(meals, enroll)
  )

apiclus2_bv |>
  gt::gt() |>
  gt::fmt_number(columns = c(2:3), decimals = 0) |>
  gt::fmt_number(columns = c(4:7), decimals = 4) |>
  gt::fmt_percent(columns = 3, decimals = 0) |>
  gt::tab_spanner("Ratio", starts_with("Ratio")) |>
  gt::tab_spanner("Correlation", starts_with("Corr")) |>
  gt::cols_label(
    sch.wide = "Met Target",
    RatioEst = "Est",
    RatioEst_se = "SE",
    CorrEst = "Est",
    CorrEst_se = "SE"
  )

Met Target	Meals	Enrollment	Ratio		Correlation
			Est	SE	Est	SE
No	58,038	94,876,595%	0.0612	0.0096	−0.1103	0.1523
Yes	251,724	267,230,839%	0.0942	0.0062	−0.0360	0.0560
NA	309,762	362,107,434%	0.0855	0.0055	−0.0511	0.0590

Heeringa, West, S. G. 2017. Applied Survey Data Analysis (2nd Ed.). Chapman; Hall/CRC. https://doi.org/10.1201/9781315153278.

Zimmer, Powell, S. A. 2024. Exploring Complex Survey Data Analysis Using r: A Tidy Introduction with Srvyr and Survey. Chapman & Hall: CRC Press. https://tidy-survey-r.github.io/tidy-survey-book/.