Photo by Coffee Geek on Unsplash

Generate Random Data

x <- rnorm(1000,1000,20)
m <- 6
c <- 10
y <- m*x + c


simdf <- data.frame(x = x , y=y)
head(simdf)
## x y
## 1 1005.4237 6042.542
## 2 1009.2766 6065.660
## 3 1001.2252 6017.351
## 4 995.0024 5980.014
## 5 964.0087 5794.052
## 6 979.7846 5888.707
sampSize <- 100
sample1 <- simdf[sample(seq(1 , nrow(simdf) , 1) , sampSize ),]
sample2 <- simdf[sample(seq(1 , nrow(simdf) , 1) , sampSize ),]

head(sample1)
## x y
## 440 970.4631 5832.779
## 48 1011.4937 6078.962
## 199 1006.4098 6048.459
## 723 992.0803 5962.482
## 375 999.7168 6008.301
## 705 978.0303 5878.182
head(sample2)## x y
## 336 1024.1023 6154.614
## 476 1005.8980 6045.388
## 439 1024.4581 6156.749
## 157 972.8277 5846.966
## 30 993.1578 5968.947
## 233 994.1998 5975.199

Are these two samples from the same distribution?

s1mean <- mean(sample1$y)
s2mean <- mean(sample2$y)

print(s1mean)
## [1] 5997.703print(s2mean)## [1] 6009.034

Is the difference between the means actually statistically significant

Two sample T-test

## [1] “combined sd of the t distribution”## [1] 15.78279## t_stat t_crit degf
## 1 -0.7179117 1.652648 196.4361
t.test(sample1$y , sample2$y)##
## Welch Two Sample t-test
##
## data: sample1$y and sample2$y
## t = -0.71791, df = 196.44, p-value = 0.4737
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -42.45612 19.79481
## sample estimates:
## mean of x mean of y
## 5997.703 6009.034
data.frame(fstat = sd(sample1$y)²/sd(sample2$y)²
, fcrit = qf(0.95 , df1 = nrow(sample1) , df2 = nrow(sample2)))
## fstat fcrit
## 1 1.195933 1.39172
var.test(sample1$y , sample2$y)##
## F test to compare two variances
##
## data: sample1$y and sample2$y
## F = 1.1959, num df = 99, denom df = 99, p-value = 0.3749
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.8046737 1.7774364
## sample estimates:
## ratio of variances
## 1.195933

Conclusions

summary(aov(sample1$y ~ sample2$y))`## Df Sum Sq Mean Sq F value Pr(>F) 
## sample2$y 1 139428 139428 11.35 0.00108 **
## Residuals 98 1203617 12282
## — -
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1

School of Data Science @ University of North Carolina — Charlotte

School of Data Science @ University of North Carolina — Charlotte