stat.test: Statistical Test

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

Statistical Test

Description

This function asks you a sequence of questions in order to discern which statistical test to employ. It then directs you to the proper test and gathers information in order to deliver a result! This can execute z-tests, t-tests, two-sample t-tests, matched-pairs t-tests, one sample proportion tests, two-sample proportion tests, chi-squared tests, and chi-squared godness-of-fit tests.

Usage

stat.test()

Examples

****************
Proportion Tests
****************

> stat.test()
Are you considering a population mean (or means), a population proportion (or proportions), or a table of values?
  Possible answers are 'xbar', 'phat', or 'table'.
phat
Do you have a single population or are you comparing populations?
  Possible answers are 'single' and 'comparing'.
single
How many trials were there in your experiment?
  10
How many successes were there?
  5
The statistics for your dataset are:
  phat = 0.5
s = sqrt(0.5*(1-0.5)/10) = 0.1581139

What is the theoretical proportion you are testing against (called p_0)?
  (If you only want a confidence interval, type 'NA')
.2
What is your desired confidence level?
  .9
The probability of getting this result or more extreme for phat
if the proportion really is 0.2 is
p =  0.0327935

The 90% confidence interval for the population proportion is
0.187086  < p <  0.812914


You can get this result by typing:
  binom.test(x = 5, n = 10, p = 0.2, alternative = 'two.sided', conf.level = 0.9)






> stat.test()
Are you considering a population mean (or means), a population proportion (or proportions), or a table of values?
  Possible answers are 'xbar', 'phat', or 'table'.
phat
Do you have a single population or are you comparing populations?
  Possible answers are 'single' and 'comparing'.
comparing
How many trials were there in your first sample?
  15
How many successes were there in your first sample?
  10
How many trials were there in your second sample?
  20
How many successes were there in your second sample?
  10
The statistics for your dataset are:
  phat1 = 0.6666667
phat2 = 0.5
s = sqrt(0.6666667*(1-0.6666667)/15+0.5*(1-0.5)/20) = 0.1652719
What is your desired confidence level?
  .95
The probability of getting this result or more extreme for phat2 - phat1
if there really is no difference is
p =  0.521582

The 95% confidence interval for the difference in proportions is
-0.5489271  < p2 - p1 <  0.2155937


You can get this result by typing:
  prop.test(c(10,10), c(20,15), alternative = 'two.sided', conf.level = 0.95)

*******
t-Tests
*******

> stat.test()
Are you considering a population mean (or means), a population proportion (or proportions), or a table of values?
  Possible answers are 'xbar', 'phat', or 'table'.
xbar
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)






> stat.test()
Are you considering a population mean (or means), a population proportion (or proportions), or a table of values?
  Possible answers are 'xbar', 'phat', or 'table'.
xbar
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)






> x = c(1, 2, 3, 4, 5, 6, 7)
> y = c(2.5,  5.1,  6.4,  8.4, 10.8, 13.4, 15.3)
> stat.test()
Are you considering a population mean (or means), a population proportion (or proportions), or a table of values?
  Possible answers are 'xbar', 'phat', or 'table'.
xbar
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)






> stat.test()
Are you considering a population mean (or means), a population proportion (or proportions), or a table of values?
  Possible answers are 'xbar', 'phat', or 'table'.
xbar
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)












*****************
Chi-Squared Tests
*****************

> stat.test()
Are you considering a population mean (or means), a population proportion (or proportions), or a table of values?
  Possible answers are 'xbar', 'phat', or 'table'.
table
Are you comparing two distributions or checking goodness of fit?
  Possible answers are 'comparing' and 'goodness'.
comparing
How many rows are there in your table?
  3
How many columns are there in your table?
  2
What is the entry in row 1 and column 1?
  10
What is the entry in row 2 and column 1?
  9
What is the entry in row 3 and column 1?
  8
What is the entry in row 1 and column 2?
  5
What is the entry in row 2 and column 2?
  6
What is the entry in row 3 and column 2?
  19
The expected data were:
  [,1]      [,2]
[1,]  7.105263  7.894737
[2,]  7.105263  7.894737
[3,] 12.789474 14.210526

but you observed:
  [,1] [,2]
[1,]   10    5
[2,]    9    6
[3,]    8   19

Your chi-squared-statistic is:
  X^2  = 6.60856

The degrees of freedom are:
  df  = 2

The probability of getting this result or more extreme
if there really is no relationship is
p =  0.03672565

You can get this result by:

  Inputting the data in the table in a list that goes column-by-column:
  data  = c(10,9,8,5,6,19)

Then converting that into a matrix:
  A  = matrix(data,nrow = 3)

Then using that to run the test:
  chisq.test(A)






> stat.test()
Are you considering a population mean (or means), a population proportion (or proportions), or a table of values?
  Possible answers are 'xbar', 'phat', or 'table'.
table
Are you comparing two distributions or checking goodness of fit?
  Possible answers are 'comparing' and 'goodness'.
goodness
How many categories are there in your distribution?
  6
What is entry number 1 in your sample?
  10
What is entry number 2 in your sample?
  8
What is entry number 3 in your sample?
  14
What is entry number 4 in your sample?
  9
What is entry number 5 in your sample?
  5
What is entry number 6 in your sample?
  16
Is your hypothesis that all categories are equally likely?
  yes
The expected data were:
  [1] 10.33333 10.33333 10.33333 10.33333 10.33333 10.33333

but you observed:
  [1] 10  8 14  9  5 16

Your chi-squared-statistic is:
  X^2  = 7.870968

The degrees of freedom are:
  df  = 5

The probability of getting this result or more extreme if the distribution
is really the theoretical one
p =  0.1634917

You can get this result by:

  Inputting the sample data in a list:
  data  = c(10,8,14,9,5,16)

and also recording the theoretical data:
  prob  = c(0.166666666666667,0.166666666666667,0.166666666666667,0.166666666666667,0.166666666666667,0.166666666666667)

Then using that to run the test:
  chisq.test(data,p = prob)

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