Inference for Categorical Data: Determining Statistical Signficance of the Survivor and Case Fatality Rates for Historical YF Cases

Hypothesis Testing

In each YF Epidemic, the null hypothesis is that the proportion of case mortality rates for Caucasians was the same as the proportion of case mortality death rates for those of non-Caucasians in the epidemic. The alternative hypothesis is that the proportion of case mortality rates for Caucasians was different than the proportion of case mortality death rates for those of non-Caucasians in the epidemic.

1808 St. Mary's, Georgia YF Epidemic

# Difference in the proportions of case mortality rates
SMC <- 0.48275862
SMNC <- 0.06666667

SMpropdiff <- SMC - SMNC

# Pooled estimate
SMpooledest <- sqrt((42 + 3)/132)

# SE using the pooled estimate
SMSE <- sqrt(((SMpooledest * (1 - SMpooledest))/87) + ((SMpooledest * (1 - SMpooledest))/45))

# Z-Score
SMZscore <- SMpropdiff/SMSE

In this hypothesis test, the Z score is 4.59723, so the results of a proportion difference are statistically significant (even when the p-value is 0.001).

1855 Norfolk, Virginia YF Epidemic

# Difference in the proportions of case mortality rates
NVAC <- 0.4615385
NVANC <- 0.04

NVApropdiff <- NVAC - NVANC

# Pooled estimate
NVApooledest <- sqrt((66 + 2)/193)

# SE using the pooled estimate
NVASE <- sqrt(((NVApooledest * (1 - NVApooledest))/143) + ((NVApooledest * (1 - 
    NVApooledest))/50))

# Z-score
NVAZscore <- NVApropdiff/NVASE

In this hypothesis test, the Z score is 5.223765, so the results of a proportion difference are statistically significant (even when the p-value is 0.001).

1855 Portsmouth, Virginia YF Epidemic

# Difference in the proportions of case mortality rates
PVAC <- 0.419972
PVANC <- 0.05

PVApropdiff <- PVAC - PVANC

# Pooled estimate
PVApooledest <- sqrt((900 + 100)/4143)

# SE using the pooled estimate
PVASE <- sqrt(((PVApooledest * (1 - PVApooledest))/2143) + ((PVApooledest * 
    (1 - PVApooledest))/2000))

# Z-score
PVAZscore <- PVApropdiff/PVASE

In this hypothesis test, the Z score is 23.80309, so the results of a proportion difference are statistically significant (even when the p-value is 0.001).

1877: Port Royal, South Carolina, Sea Islands

# Difference in the proportions of case mortality rates
PSCC <- 0.25
PSCNC <- 0.01149425

PSCpropdiff <- PSCC - PSCNC

# Pooled estimate
PSCpooledest <- sqrt((25 + 1)/187)

# SE using the pooled estimate
PSCSE <- sqrt(((PSCpooledest * (1 - PSCpooledest))/100) + ((PSCpooledest * (1 - 
    PSCpooledest))/87))

# Z-score
PSCZscore <- PSCpropdiff/PSCSE

In this hypothesis test, the Z score is 3.364174, so the results of a proportion difference are statistically significant (even when the p-value is 0.001).

1878: Memphis, Tennessee

# Difference in the proportions of case mortality rates
MTNC <- 0.6699967
MTNNC <- 0.09

MTNpropdiff <- MTNC - MTNNC

# Pooled estimate
MTNpooledest <- sqrt((4024 + 990)/17006)

# SE using the pooled estimate
MTNSE <- sqrt(((MTNpooledest * (1 - MTNpooledest))/6006) + ((MTNpooledest * 
    (1 - PSCpooledest))/17006))

# Z-score
MTNZscore <- MTNpropdiff/MTNSE

In this hypothesis test, the Z score is 74.05432, so the results of a proportion difference are statistically significant (even when the p-value is 0.001).

1878 Holly Springs, MS Epidemic

# Difference in the proportions of case mortality rates
HSC <- 0.72039474
HSNC <- 0.07001647

HSpropdiff <- HSC - HSNC

# Pooled estimate
HSpooledest <- sqrt((219 + 85)/1518)

# SE using the pooled estimate
HSSE <- sqrt(((HSpooledest * (1 - HSpooledest))/304) + ((HSpooledest * (1 - 
    HSpooledest))/1214))

# Z-score
HSZscore <- HSpropdiff/HSSE

In this hypothesis test, the Z score is 20.39449, so the results of a proportion difference are statistically significant (even when the p-value is 0.001).