Question(s) on interrupted time series

BCL Summer 2025

• The (naïve) 2-sample independent z-test/t-test

• The Mann-Whitney U tes(Wilcoxon rank-sum test)

• The 2-sample paired t-test

• The Wilcoxon signed-rank test

ex1 <- read.csv("ex1.csv",header = T)
head(ex1,n = 10)

   Obs Year Month Infection.Rate Trt
1    1 2011     1       6.823340 Pre
2    2 2011     2       7.661713 Pre
3    3 2011     3       6.071718 Pre
4    4 2011     4       6.907877 Pre
5    5 2011     5       7.053463 Pre
6    6 2011     6       7.075412 Pre
7    7 2011     7       5.808710 Pre
8    8 2011     8       4.429035 Pre
9    9 2011     9       7.966634 Pre
10  10 2011    10       5.677933 Pre

file:ex1.csv

t.test(Infection.Rate[Trt=="Pre"],Infection.Rate[Trt=="Post"],paired = F)

    Welch Two Sample t-test

data:  Infection.Rate[Trt == "Pre"] and Infection.Rate[Trt == "Post"]
t = -0.6961, df = 97.888, p-value = 0.488
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.9752373  0.4687357
sample estimates:
mean of x mean of y 
 4.381114  4.634365 

wilcox.test(Infection.Rate[Trt=="Pre"],Infection.Rate[Trt=="Post"],paired = F)

    Wilcoxon rank sum test with continuity correction

data:  Infection.Rate[Trt == "Pre"] and Infection.Rate[Trt == "Post"]
W = 1164, p-value = 0.5556
alternative hypothesis: true location shift is not equal to 0

So whether parametric or nonparametric, we have non-significance.

ex2 <- read.csv("ex2.csv",header = T)
head(ex2,n = 10)

   Obs Year Month Infection.Rate Trt
1    1 2011     1      10.520862 Pre
2    2 2011     2      12.008921 Pre
3    3 2011     3       9.380510 Pre
4    4 2011     4      10.848942 Pre
5    5 2011     5       9.037392 Pre
6    6 2011     6      10.915647 Pre
7    7 2011     7      10.082868 Pre
8    8 2011     8       9.074189 Pre
9    9 2011     9      10.621038 Pre
10  10 2011    10      10.161518 Pre

file:ex2.csv

t.test(Infection.Rate[Trt=="Pre"],Infection.Rate[Trt=="Post"],paired = F)

    Welch Two Sample t-test

data:  Infection.Rate[Trt == "Pre"] and Infection.Rate[Trt == "Post"]
t = 13.707, df = 97.997, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 4.167357 5.578359
sample estimates:
mean of x mean of y 
 8.490436  3.617578 

wilcox.test(Infection.Rate[Trt=="Pre"],Infection.Rate[Trt=="Post"],paired = F)

    Wilcoxon rank sum test with continuity correction

data:  Infection.Rate[Trt == "Pre"] and Infection.Rate[Trt == "Post"]
W = 2435, p-value = 3.195e-16
alternative hypothesis: true location shift is not equal to 0

So whether parametric or nonparametric, we have statistical significance.

If these data points are for some disease infection counts, we think there is no interesting story for Ex.1?