高校数学の質問スレ（医者・東大卒専用） Part438

高校数学の質問スレ（医者・東大卒専用） Part438 (991ﾚｽ)
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809: １３２人目の素数さん [sage] 2025/04/30(水) 08:07:44.58 ID:wedVH8wl

options(warn = -1)
alpha <- 0.05

sim_fisher <- function(N = 100) {
# Function to simulate data for three groups and perform Fisher's exact test.
# N: Total sample size.

# Determine sample sizes for each of the three groups.
A <- sample(1:(N - 2), 1) # Ensure A leaves enough room for B and C.
remaining <- N - A
if (remaining > 1) {
B <- sample(1:(remaining - 1), 1) # Ensure B is at least 1.
C <- N - A - B
ABC <- c(A, B, C) # Vector of group sizes.

# Randomly generate the number of successes for each group (cannot exceed group size).
abc <- sapply(ABC, function(x) if (x > 0) sample(0:x, 1) else 0)
x <- abc # Vector of number of successes per group.
n <- ABC # Vector of total samples per group.

# Create a data frame for the overall Fisher's exact test.
data_all <- data.frame(
group = factor(rep(c("A", "B", "C"), times = n)),
success = unlist(sapply(1:3, function(i) c(rep(1, x[i]), rep(0, n[i] - x[i]))))
)
table_all <- table(data_all$group, data_all$success)
fisher_pg <- fisher.test(table_all)$p.value # P-value of the overall Fisher's exact test.

# Perform pairwise Fisher's exact tests with Bonferroni correction.
pairwise_p_values <- numeric(3)
pairs <- combn(levels(data_all$group), 2, simplify = FALSE)

for (i in seq_along(pairs)) {
pair <- pairs[[i]]
subset_data <- subset(data_all, group %in% pair)
table_pair <- table(subset_data$group, subset_data$success)
pairwise_p_values[i] <- fisher.test(table_pair)$p.value # P-value of the pairwise Fisher's exact test.
}

min_pairwise_p_bonf <- min(p.adjust(pairwise_p_values, method = "bonferroni"), na.rm = TRUE) # Minimum Bonferroni-corrected p-value from pairwise tests.

list(fisher_pg = fisher_pg, min_pairwise_p_bonf = min_pairwise_p_bonf, x = x, n = n)
} else {
return(NULL) # Return NULL if group sizes are invalid.
}
}

http://rio2016.5ch.net/test/read.cgi/math/1723152147/809

810: １３２人目の素数さん [sage] 2025/04/30(水) 08:07:51.54 ID:wedVH8wl

# Find data where the overall Fisher's exact test is not significant,
# but at least one pairwise Fisher's exact test (with Bonferroni correction) is significant.
res_no_overall_sig_pairwise_sig <- NULL
while (is.null(res_no_overall_sig_pairwise_sig) || res_no_overall_sig_pairwise_sig$fisher_pg > alpha || res_no_overall_sig_pairwise_sig$min_pairwise_p_bonf > alpha) {
res_no_overall_sig_pairwise_sig <- sim_fisher()
}
cat("Data where overall Fisher's test is not significant, but pairwise is:\n")
print(res_no_overall_sig_pairwise_sig)
cat("\n")

# Find data where the overall Fisher's exact test is significant,
# but all pairwise Fisher's exact tests (with Bonferroni correction) are not significant.
res_overall_sig_no_pairwise_sig <- NULL
while (is.null(res_overall_sig_no_pairwise_sig) || res_overall_sig_no_pairwise_sig$fisher_pg < alpha || res_overall_sig_no_pairwise_sig$min_pairwise_p_bonf < alpha) {
res_overall_sig_no_pairwise_sig <- sim_fisher()
}
cat("Data where overall Fisher's test is significant, but pairwise is not:\n")
print(res_overall_sig_no_pairwise_sig)

options(warn = 0)

http://rio2016.5ch.net/test/read.cgi/math/1723152147/810

811: １３２人目の素数さん [sage] 2025/04/30(水) 08:12:32.33 ID:wedVH8wl

options(warn = -1)
alpha <- 0.05

sim_chisq <- function(N = 100) {
# Function to simulate data for three groups and perform Chi-squared test (without Yates' correction).
# N: Total sample size.

# Determine sample sizes for each of the three groups.
A <- sample(1:(N - 2), 1) # Randomly select a size for group A, ensuring space for B and C.
remaining <- N - A
if (remaining > 1) {
B <- sample(1:(remaining - 1), 1) # Randomly select a size for group B, ensuring space for C.
C <- N - A - B # Calculate the size for group C.
ABC <- c(A, B, C) # Vector containing the sample sizes of the three groups.

# Randomly generate the number of successes for each group (must be between 0 and the group size).
abc <- sapply(ABC, function(x) if (x > 0) sample(0:x, 1) else 0)
x <- abc # Vector containing the number of successes for each group.
n <- ABC # Vector containing the total number of trials for each group.

# Create a contingency table for the overall Chi-squared test.
contig_all <- rbind(s = x, f = n - x) # Rows: successes (s), failures (f); Columns: groups.
chisq_pg <- chisq.test(contig_all, correct = FALSE)$p.value # Perform Chi-squared test (no correction) and get the p-value.

# Perform pairwise proportion tests with Bonferroni correction.
pairwise_prop_p_values <- as.vector(
pairwise.prop.test(x, n, correct = FALSE, p.adj = "bon")$p.value
) # Perform pairwise proportion tests (no correction) and get Bonferroni-adjusted p-values.
min_pairwise_p_bonf <- min(pairwise_prop_p_values, na.rm = TRUE) # Get the minimum of the adjusted pairwise p-values.

# Return a list containing the overall p-value, the minimum Bonferroni-corrected pairwise p-value, successes, and total trials.
list(chisq_pg = chisq_pg, min_pairwise_p_bonf = min_pairwise_p_bonf, x = x, n = n)
} else {
return(NULL) # Return NULL if the group sizes are invalid.
}
}

http://rio2016.5ch.net/test/read.cgi/math/1723152147/811

812: １３２人目の素数さん [sage] 2025/04/30(水) 08:12:39.62 ID:wedVH8wl

# Find data where the overall Chi-squared test is not significant (p > alpha),
# but at least one pairwise proportion test (with Bonferroni correction) is significant (p <= alpha).
res_no_overall_sig_pairwise_sig <- NULL
while (is.null(res_no_overall_sig_pairwise_sig) || res_no_overall_sig_pairwise_sig$chisq_pg > alpha || res_no_overall_sig_pairwise_sig$min_pairwise_p_bonf > alpha) {
res_no_overall_sig_pairwise_sig <- sim_chisq() # Keep simulating until the condition is met.
}
cat("Data where overall Chi-squared test is not significant, but pairwise proportion test is:\n")
print(res_no_overall_sig_pairwise_sig)
cat("\n")

# Find data where the overall Chi-squared test is significant (p <= alpha),
# but all pairwise proportion tests (with Bonferroni correction) are not significant (p > alpha).
res_overall_sig_no_pairwise_sig <- NULL
while (is.null(res_overall_sig_no_pairwise_sig) || res_overall_sig_no_pairwise_sig$chisq_pg < alpha || res_overall_sig_no_pairwise_sig$min_pairwise_p_bonf < alpha) {
res_overall_sig_no_pairwise_sig <- sim_chisq() # Keep simulating until the condition is met.
}
cat("Data where overall Chi-squared test is significant, but pairwise proportion test is not:\n")
print(res_overall_sig_no_pairwise_sig)

options(warn = 0)

http://rio2016.5ch.net/test/read.cgi/math/1723152147/812

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