t_test: t-test

In jrpriceUPS/Math160UPS: Suite of Functions for Math 160 Classes at the University of Puget Sound

t-test

Description

This function asks you a sequence of questions in order to execute a t-test. It finds a confidence interval and a p-value, produces a plot, and indicates how this could be queried directly from R.

Usage

t_test()

Examples

> x = c(1, 2, 3, 4, 5, 6, 7)
> t_test()
Do you have a single population or are you comparing populations?
  Possible answers are 'single' and 'comparing'.
single
Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
  Possible answers are 'whole' or 'stats'.
whole
What is the name of your variable?
  x
The statistics for your dataset are:
  xbar =  4
s =  2.160247
n =  7
df =  7 - 1 =  6

What is the theoretical mean you are testing against (called mu_0)?
  (If you only want a confidence interval, type 'NA')
3
What is your desired confidence level?
  .95
Your t-statistic is:
  t  = (4-3)/(2.160247/sqrt(7)) = 1.224745

The probability of getting this result or more extreme for xbar
if mu really is 3 is
p =  0.2665697

You can get this result by typing:
  2*(1-pt(1.22474487139159,6))


The 95% confidence interval for the population mean is
2.002105  < mu <  5.997895

You can get this result by finding:
  tstar = 1-qt((1-0.95)/2,6) = 2.446912

and then calculating:
  4 - 2.446912 x 2.160247/sqrt(7)  and  4 + 2.446912 x 2.160247/sqrt(7)


Or, since you have the whole dataset, you could just type:
  t.test(x,mu = 3,conf.level = 0.95)



> t_test()
Do you have a single population or are you comparing populations?
 Possible answers are 'single' and 'comparing'.
single
Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
 Possible answers are 'whole' or 'stats'.
stats
What is your sample mean?
 4
What is your sample standard deviation?
 2.16
What is your sample size?
 7
What is the theoretical mean you are testing against (called mu_0)?
 (If you only want a confidence interval, type 'NA')
3
What is your desired confidence level?
 .95
Your t-statistic is:
 t  = (4-3)/(2.16/sqrt(7)) = 1.224885

The probability of getting this result or more extreme for xbar
if mu really is 3 is
p =  0.2665206

You can get this result by typing:
 2*(1-pt(1.22488486623361,6))


The 95% confidence interval for the population mean is
2.002333  < mu <  5.997667

You can get this result by finding:
 tstar = 1-qt((1-0.95)/2,6) = 2.446912

and then calculating:
 4 - 2.446912 x 2.16/sqrt(7)  and  4 + 2.446912 x 2.16/sqrt(7)






> t_test()
Do you have a single population or are you comparing populations?
  Possible answers are 'single' and 'comparing'.
comparing
Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
  Possible answers are 'whole' or 'stats'.
whole
Is this a matched-pairs comparison in which the same subjects are measured twice?
  yes
What is the name of the variable for the first set of measurements?
  x
What is the name of the variable for the second set of measurements?
  y
The statistics for your datasets are:
  n =  7
xbar1 =  4
s1 =  2.160247

xbar2 =  8.842857
s2 =  4.595236

The statistics for the difference are:
  xbar =  4.842857
s =  2.445988
n =  7
df =  7 - 1 =  6

What is your desired confidence level?
  .95
Your t-statistic is:
  t  = 4.842857/(2.445988/sqrt(7)) = 5.238372

The probability of getting this result or more extreme for xbar2 - xbar1 if there really is no difference is
p =  0.001941435

You can get this result by typing:
  2*(1-pt(5.23837230565063,6))


The 95% confidence interval for the difference in population means is
2.580696  < mu2 - mu1 <  7.105019

You can get this result by finding:
  tstar = 1-qt((1-0.95)/2,6) = 2.446912

and then calculating:
  (8.84285714285714-4) - 2.446912 x 2.445988/sqrt(7)  and  (8.84285714285714-4) + 2.446912 x 2.445988/sqrt(7)


Or, since you have the whole dataset, you could just type:
  t.test(y,x, paired = TRUE, conf.level = 0.95)






> t_test()
Do you have a single population or are you comparing populations?
  Possible answers are 'single' and 'comparing'.
comparing
Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
  Possible answers are 'whole' or 'stats'.
whole
Is this a matched-pairs comparison in which the same subjects are measured twice?
  no
What is the name of the variable for the first set of measurements?
  x
What is the name of the variable for the second set of measurements?
  y
The statistics for your datasets are:
  n1 =  7
xbar1 =  4
s1 =  2.160247

n2 =  7
xbar2 =  8.842857
s2 =  4.595236

The statistics for the difference are:
  xbar =  4.842857
s = sqrt(2.160247^2/7 + 4.595236^2/7) = 1.919183
df = 8.5285

What is your desired confidence level?
  .95
Your t-statistic is:
  t  = (4.84285714285714)/(1.919183) = 2.523395

The probability of getting this result or more extreme for xbar2 - xbar1 if there really is no difference is
p =  0.03391985

You can get this result by typing:
  2*(1-pt(2.52339452856832,8.52849965837585))


The 95% confidence interval for the difference in population means is
0.4644978  < mu2 - mu1 <  9.221216

You can get this result by finding:
  tstar = 1-qt((1-0.95)/2,8.5285) = 2.281366

and then calculating:
  (8.84285714285714-4) - 2.281366 x 1.919183  and  (8.84285714285714-4) + 2.281366 x 1.919183


Or, since you have the whole dataset, you could just type:
  t.test(y,x, conf.level = 0.95)

jrpriceUPS/Math160UPS documentation built on April 28, 2024, 12:41 p.m.