Pearson r

Pearson's rank correlation coefficient allows you to identify easily the strength of linear correlation within a data set of two variables, and whether the correlation is positive or negative (whether the slope of the corresponding line is positive or negative). A variant of Pearson’s r which is used with rank data is called Spearman’s Rho (rs). If we computed Pearson's r on the ranked data, it would give Spearman's Rho.

Introduction: Pearson r - the mean of the z-score products for X and Y pairs, where X stands for one variable and Y stands for the other. The range of the Pearson r is from +1 to -1. A positive value for r indicates a direct relationship between the variables, a negative value indicates an inverse relationship. Anything close to r = 0 indicates no relationship between the variables.

 

Pearson r Formula

  Note: This program is in TI-BASIC and can be entered into the calculator by the calculator keyboard. Do not enter the outline, line numbers or comments, they are for reference only. The example programs below are for testing the program. If you get the values listed, the program was entered correctly. If not, check the listing and correct it. The program has been checked and tested.

  Note: -> is the [STO->] on the calculator keyboard.

  Note: click on the underline text in Outline to go to that line number

    Program Memory = 760

 

Pearson r Outline:

Line 1. Clear Screen

Line 2 - 8. Instructions

Line 12 - 18. Lbl D: Data Input

Line 22 - 23. Input List ₁

Line 24 - 25. Input List ₃

Line 27 - 32. Calculator formula

Line 34 - 39. Disp List ₁

Line 40 - 43. Disp List ₃

Line 47 - 52. Pearson r Formula

Line 61 - 64. formula

Line 69 - 72. Formula calculations

Line 74 - 81. Output    r =

Line 79 - 83. Input   regression prediction terms

Line 86 - 87. calculations    Y predicted from X

Line 90 - 93. Output

  Pearson r Examples

  Reference

  Reference Links

 

PEARSON r

 

Pearson r Example 1:

List ₁: 77, 74, 73, 72, 70, 70, 69, 68, 67, 67, 66, 64, 63, 60

List ₂: 47.1, 45.5, 46.2, 46.1, 42.8, 38.3, 45.4, 36.5, 42.1, 37.2, 34.1, 35.1, 33.1, 33.0

Data: n = 14,  Σx = 960,  Σx² = 66,102   Σy = 562.5  Σy² = 22,976.13  Σxy = 38,852.5

Answers: n = 14,  Σx = 960,  Σx² = 66,102   Σy = 562.5  Σy² = 22,976.13  Σxy = 38,852.5  r = .88  Y = 1.03X - 30.45

 

Pearson r Example 2:

List ₁: 100, 40, 95, 90, 92, 85, 55, 60, 98, 20

List ₂: 0, 95, 5, 20, 30, 40, 50, 70, 0, 100

Data: n = 10,  Σx = 735,  Σx² = 61,043   Σy = 410  Σy² = 29,350  Σxy = 21,185

Answers: n = 10,  Σx = 735,  Σx² = 61,043   Σy = 410  Σy² = 29,350  Σxy = 21,185  r = -.95  Y = .89X + .38

 

Reference:

TI Basic Commands or Statements:

  augment( listA, listB)   Returns a list, which is list B appended to the end of list A

  ClrHome  clears home screen

  dim(  returns the dimension (number of elements) of list

  Disp  displays text or value specified

  End  identifies end of For(, If-Then-Else, Repeat, or While loop

  expr(  converts string to an expression

  Fix  sets fixed-decimal mode for number of decimal places

  Float  sets floating decimal mode. Displays decimal with no trailing zeros

  For( variable,begin,end[increment])    Executes commands through End, incrementing variable from begin by increment until End.

  Goto  goes to label specified. Goto requires a line label be implemented as a destination

  If; Then; Else  Executes commands from Then to Else If condition true: or from Else to End if condition false

  Input  prompts for value to store to variable. Requires user input through keypad.

  Lbl  creates a label of one or two characters

  Menu  generates a menu of up to seven items

  min( valueA, valueB)  Returns smaller of value A and Value B

  output( row, column)  displays text or value beginning at specified row and column

  round( value [,# decimals])   returns a number rounded to # decimals (=<9)

  seq( expression, variable, begin, end[, increment])   Returns list created by evaluating expression with regard to variable, from begin to end by increment

  SortA( listname)   Sorts elements of listname in ascending (count up) order

  Str# (# is number)   String: A sequence of characters is called a string

  sum(  returns the sum of elements in list

  While condition  Executes commands while condition is true until end

 

Statistics Reference:

Information or Links:

Statistical Inference on the TI-83

This site contains typical problems and solutions on the general statistics topics of probability distributions, confidence intervals, hypothesis testing, analysis of variance, and correlation analysis.

http://www.wku.edu/~david.neal/statistics/

Using the TI-83 graphing calculator tutorial

  General Info - Algebra 1 - Statistics 1 - Algebra 2 - Trigonometry - Statistics 2 - PreCalculus - Calculus

http://mathbits.com/mathbits/TISection/Openpage.htm

TI-83 Video Tutorials
This series of tutorials for the TI-83 (or TI-83 Plus)Currently, only the chapters on single population confidence intervals, population hypothesis test, linear regression, Chi-Square and ANOVA are completed.

http://student.ccbcmd.edu/elmo/math141s/TIVideo/TIWebpage.htm

United TI Forums - TI Basic

  TI-Basic - Use this forum to post questions and discuss the TI-BASIC programming language.

http://www.unitedti.org/index.php?showforum=4

Hints for Statistics Using a TI-83

http://www.math.wustl.edu/~sawyer/handouts/StatTI83.html#sampmean

  If you want the TI-83 to calculate the Pearson correlation coefficient r (which is the same as the Model R2 = r2 for the linear regression), you must turn "Diagnostics'' ON by entering 2nd 0 (for CATALOG), space down to DiagnosticOn, press ENTER, and then ENTER again if you see DiagnosticOn on a different screen

Quick-and-Dirty Guide to the TI-83, TI-83+, TI-84, and TI-84+

http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/ti.html

  The TI-83 "Plus", TI-84, and TI-84 "Plus" are almost identical, so this guide will serve just as well for them.

Getting y^ from Any x in a Regression on the TI-83/84/89

http://www.tc3.edu/instruct/sbrown/ti83/yhat.htm

  The regression line represents the model that best fits the data. This page shows you three methods, which all yield the same answer

Intro to Programming TI-83/83+ BASIC

http://odin.prohosting.com/mjs2k/tutorials/index.htm

  Here you will find several tutorials to help you learn how to write programs on your TI-83, TI-83+ calculator(s). NO PROGRAMMING EXPERIENCE IS NECESSARY

Statistical Inference on the TI-83+

http://www.wku.edu/~david.neal/statistics/

  This site contains typical problems and solutions on the general statistics topics of probability distributions, confidence intervals, hypothesis testing, analysis of variance, and correlation analysis. Detailed survey sampling projects are also included.

http://www.hsu.edu/default.aspx?id=3617

  TI-83/84 programs

http://101science.com/Ticalcpgms.htm

  Links to TI-83 Programs you can download to your calculator

http://www.angelfire.com/pro/fkizer/Instructions/tishrtusrguide83.htm

  Brief Users Guide for the TI-83 Plus

Interactive TI-83 Plus Tutorial

  TI-83 Plus Tutorial by Mathematics Department, SCSU.

TI-83/84/89/92 Procedures and Help

  This page points you to step-by-step procedures for several tasks on the TI-83

Business Statistics

  Calculating Statistics Using the TI-83 or Using Excel

DevHardware TI-83/84 forums

  Programming forum discussing coding and everything related to the well-known TI-83/84 graphing calculators

Math 320 (Statistics) Excel and Calculator Notes

  specific procedures for Excel or a TI-83

Pearson's r calculator

  Online calculator for Pearson r

 

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