Verifying the p-value. Comparison between Stats tester and R.
1. The Example data is entered by tapping the Example button of the Stats tester app.
2. When you tap the Calc button in the Stats tester, the p-value will be displayed at the end of the output window.
3. If you're using R language on a Mac or Windows PC : Copy the R code in the box, paste it to R screen of your PC to the right of the prompt (>), and press the return key. The p-value will appear at the end of the first line of the R result.
3. [One-Sample t-Test (to Specified Mean)]
Example
A : 1, 3, 2, 5, 6, 11
Specified Mean : 8
Stats tester
p = 0.073464 (2 tails)
R
Code:
A <- c(1,3,2,5,6,11)
mu <- 8
t.test(A, mu=8, alt="two.sided")
Result
p = 0.0734649 (2 tails)
4. [Two-Sample t-Test (Student's and Welch's t-Tests)]
Example
A : 1, 2, 3, 4, 5
B : 11, 13, 15, 17
Stats tester
Student p = 0.000097 (2 tails)
Welch p = 0.000846 (2 tails)
R
Code:
A <- c(1, 2, 3, 4, 5)
B <- c(11, 13, 15, 17)
t.test(A, B, alt="two.sided",var.equal=T) # (Student)
t.test(A, B, alt="two.sided",var.equal=F) # (Welch)
Result
Student p = 0.000097 (2 tails)
Welch p = 0.0008459 (2 tails)
5. [Paired-Sample t-test]
Example
A : 22, 20, 31, 25
B : 11, 15, 28, 20
Stats tester
p = 0.040519 (2 tails)
R
Code:
A <- c(22, 20, 31, 25)
B <- c(11, 15, 28, 20)
t.test(A, B, paired=T, alt="two.sided")
Result
p = 0.04052 (2 tails)
6. [One-Way Analysis of Variance (ANOVA)]
Example
A : 13, 12, 11, 11
B : 9, 8, 9, 7, 10
C : 12, 14, 11, 13
D : 13, 14, 13, 15
Stats tester
p = 0.000059
R
Code:
vx <-c(13, 12, 11, 11, 9, 8, 9, 7, 10, 12, 14, 11, 13, 13, 14, 13, 15 )
fx=factor(rep(c("A", "B", "C", "D"), c(4, 5, 4, 4)))
anova(aov(vx~fx))
Result
p = 5.874e-05
7. [Linear Regression and Test for Pearson Correlation Coefficient]
Example
A : 1, 4, 4, 6, 8
B : 5, 8, 7, 10, 11
Stats tester
p = 0.003436 (2 tails)
R
Code:
A <- c(1, 4, 4, 6, 8)
B <- c(5, 8, 7, 10,11)
cor.test(A, B, method="pearson")
Result
p = 0.003436 (2 tails)
8. [Shapiro-Wilk Test (Normality) and Q-Q Plot]
Example
A : 1, 2, 3, 3.9, 4.2, 4.5, 5, 5.4, 5.6 ,5.8, 6.2, 6.4, 6.6, 7, 7.5, 7.8, 8.1, 9, 10, 11
Stats tester
p = 0.999942
R
Code:
A <- c(1, 2, 3, 3.9, 4.2, 4.5, 5, 5.4, 5.6 ,5.8, 6.2, 6.4, 6.6, 7, 7.5, 7.8, 8.1, 9, 10, 11)
shapiro.test(A)
Result
p = 0.999942
9. [Chi-Square Test (2X2 Independence)]
Example
110, 90
88, 112
Stats tester
p = 0.035720 (Continuity corrected)
p = 0.027799 (Continuity not corrected)
R
Code:
table <- matrix(c(110, 90, 88, 112), ncol=2, byrow=T)
chisq.test(table, correct=T)
chisq.test(table, correct=F)
Result
p = 0.03572 (Continuity corrected)
p = 0.027799 (Continuity not corrected)