One Sample Tests of Proportion - R

Binomial Test

• Samples: 1

• Response Categories: 2

• Exact?: Yes, use with N≤200

• Reporting: “Out of 60 outcomes, 19 were ‘x’ and 41 were ‘y’. A two-sided exact binomial test indicated that these proportions were statistically significantly different from chance (p < .05)”

# Example data
# df is a long-format data table w/columns for subject (S) and 2-category outcome (Y)
df <- read.csv("data/0F0LBs_binomial.csv")
head(df, 20)

A data.frame: 20 × 2

	S	Y
	<int>	<chr>
1	1	y
2	2	y
3	3	x
4	4	y
5	5	y
6	6	x
7	7	y
8	8	x
9	9	y
10	10	y
11	11	x
12	12	y
13	13	y
14	14	y
15	15	y
16	16	x
17	17	x
18	18	y
19	19	y
20	20	x

df$S = factor(df$S) # Subject id is nominal (unused)
df$Y = factor(df$Y) # Y is an outcome of 2 categories
xt = xtabs( ~ Y, data=df) # make counts
binom.test(xt, p=0.5, alternative="two.sided")

	Exact binomial test

data:  xt
number of successes = 19, number of trials = 60, p-value = 0.006218
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
 0.2025755 0.4495597
sample estimates:
probability of success 
             0.3166667 

Multinomial Test

• Samples: 1

• Response Categories: ≥2

• Exact?: Yes, use with N≤200

• Reporting: “Out of 60 outcomes, 17 were ‘x’ and 8 were ‘y’, and 35 were ‘z’. An exact multinomial test indicated that these proportions were statistically significantly different from chance (p < .0001)”

# Example data
# df is a long-format data table w/columns for subject (S) and N-category outcome (Y)
df <- read.csv("data/0F0LBs_multinomial.csv")
head(df, 20)

A data.frame: 20 × 2

	S	Y
	<int>	<chr>
1	1	z
2	2	z
3	3	z
4	4	x
5	5	z
6	6	z
7	7	z
8	8	z
9	9	z
10	10	z
11	11	z
12	12	x
13	13	z
14	14	y
15	15	z
16	16	y
17	17	x
18	18	z
19	19	z
20	20	z

# install.packages("XNomial")
library(XNomial) # import for xmulti

df$S = factor(df$S) # Subject id is nominal (unused)
df$Y = factor(df$Y) # Y is an outcome of ≥2 categories
xt = xtabs( ~ Y, data=df) # make counts
xmulti(xt, rep(1/length(xt), length(xt)), statName="Prob")

P value (Prob) = 8.756e-05

# This can also be shortened using the RVAideMemoire library
# install.packages("RVAideMemoire")
# on Ubuntu you may have trouble installing, see: TODO
library(RVAideMemoire)

multinomial.test(df$Y)

*** Package RVAideMemoire v 0.9-81-2 ***

	Exact multinomial test

data:  $(df,Y)
p-value = 8.756e-05

One-Sample Pearson Chi-Squared Test

• Samples: 1

• Response Categories: ≥2

• Exact?: No, use with N>200

• Reporting: “Out of 60 outcomes, 17 were ‘x’, 8 were ‘y’, and 35 were ‘z’. A one-sample Pearson Chi-Squared test indicated that these proportions were statistically significantly different from chance (χ2 (2, N=60) = 18.90, p < .0001).”

# Example data
# df is a long-format data table w/columns for subject (S) and N-category outcome (Y)
df <- read.csv("data/0F0LBs_multinomial.csv")
head(df, 20)

A data.frame: 20 × 2

	S	Y
	<int>	<chr>
1	1	z
2	2	z
3	3	z
4	4	x
5	5	z
6	6	z
7	7	z
8	8	z
9	9	z
10	10	z
11	11	z
12	12	x
13	13	z
14	14	y
15	15	z
16	16	y
17	17	x
18	18	z
19	19	z
20	20	z

df$S = factor(df$S) # Subject id is nominal (unused)
df$Y = factor(df$Y) # Y is an outcome of ≥2 categories
xt = xtabs( ~ Y, data=df) # make counts
chisq.test(xt)

	Chi-squared test for given probabilities

data:  xt
X-squared = 18.9, df = 2, p-value = 7.869e-05