Introduction: 2-Sample "t" Test - test the equality of the means of two populations (u1 and u2) based on independent samples when neither population standard deviation is known.
 
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    Related Articles:-   TTST2SMP

 
 Formula t test 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: for instructions line 2 through 7, do not use a line break or space between " and , but allow the code to wrap to the next line. Do not use more then 7 lines without a pause commant to display the text.
  Note: click on the underline text in Outline to go to that line number
 
Outline:
Line 1. Clear Screen
Line 2 - 8. Instructions
Line 12 - 18. Lbl D: Data Input
Line 22 - 25. Input List 1
Line 27 - 29. Input List 2
Line 31 - 35. Formula (List 1 & 2)
Line 36 - 38. Input List 4 (Data)
Line 40 - 42. Input List 5 (Freq)
Line 44 - 48. Formula (List 4 & 5)
Line 54 - 57. Disp List 1
Line 58 - 61. Disp List 2
Line 64 - 70. Formula
Line 72 - 73. Output
  Examples
  Reference
  Reference Links
 
 
prgmTTSTWFRQ
Line Command or Statement Comments
   1. ClrHome Clear Screen
   2. Disp "SELECT LIST OR" Instructions
   3. ,"DATA TO BEGIN -"         |
   4. ,"USE COMMAS BTWN"         |
   5. ,"NUMBERS IN LIST"         |
   6. ,"ENTER n1,x1, S1²"         |
   7. ,"n2, x2, S2², FOR"         |
   8. ,"DATA" End Instructions
   9. Pause 
  10. ClrHome 
 11. Menu("T TEST","LIST",L,"DATA",D) 
 12. Lbl D 
 13. Input "x1=",C X1
 14. Input "S1²=",X S1²
 15. Input "n1=",N N1
 16. Input "x2=",F X2
 17. Input "S2²=",Y S2²
 18. Input "n2=",M N2
 19. Goto C 
 20. Pause 
 21. ClrHome 
 22. Lbl L 
 23. Disp "DATA LIST-1 Data List 1
 24. Input "L1=",Str1 
 25. expr("{"+Str1->L1  
 26. ClrHome 
 27. Disp "FREQ LIST-2 Freq List 2
 28. Input "L2=",Str2 
 29. expr("{"+Str2->L2  
 30. ClrHome 
 31. sum(L2->N sample size (n1)
 32. sum(L1L2->A Σx1    sum(  calculator formula
 33. A/N->C calculates mean    x1
 34. sum(L1²L2->U Σx1² = sumX1squared
 35. (((U-((A)²)/N))/(N-1))->X calculates variance     S1²
 36. Disp "DATA LIST-4 Data List 4
 37. Input "L4=",Str4 
 38. expr("{"+Str4->L4 
 39. ClrHome 
 40. Disp "FREQ LIST-5 Freq List 5
 41. Input "L5=",Str5 
 42. expr("{"+Str5->L5  
 43. ClrHome 
 44. sum(L5->M sample size (n2)
 45. sum(L4L5->B Σx2    sum(  calculator formula
 46. B/M->F calculates mean    x2
 47. sum(L4²L5->V  Σx2² = sumX2squared
 48. (((V-((B)²)/M))/(M-1))->Y calculates variance     S2²
 49.Output(1,1,"n1=  
 50.Output(1,4,N n1=
 51.Output(4,1,"n2= 
 52.Output(4,4,M n2=
 53. Fix 4 
 54.Output(2,1,"x1=  
 55.Output(2,4,C  x1=
 56.Output(3,1,"S1²=  
 57.Output(3,5,X S1²=
 58.Output(5,1,"x2=  
 59.Output(5,4,F  x2=
 60.Output(6,1,"S2²=  
 61.Output(6,5,Y S2²=
 62. Float 
 63. Lbl C 
 64.  ((N-1)X)->G  (N1 - 1)S1²
 65. ((M-1)Y)->H  (N2 - 1)S2²
 66. ((N+M)-2)->S (N+M)-2
 67. (1/N)->K 1/N1
 68. (1/M)->L 1/N2
 69. (C-F)->R (C-F)
 70. R/√(((G+H)/S(K+L))->T 
 71. Fix 4 
 72. Output(8,1,"T= 
 73. Output(8,3,T 
 74. Float 
 75. Pause 
 76. ClrHome 
 
Example:
Two-sample t test for independent samples:
You can enter values by lists (L1 & L2) or summary Stats (mean [x], variance [S²], sample size [n]
 Example: summary Stats
  Input:  x1 = 27.6  x2 = 22.1 
  S1² = 25.4  S2² = 22.2
  n1 = 10  n2 = 10
  Output: t = 2.52  
 Example: data List
 Input:   L1 = 10, 9, 8, 7, 6, 5, 3, 2  
 Input:   L2 = 1, 2, 1, 3, 2, 1, 1, 1  
   n1 = 12 x1 = 6.58  S1² = 5.72  
   L4 = 14, 13, 12, 10, 8, 7, 5  
   L5 = 1, 3, 2, 1, 2, 2, 2  
   n2 = 13 x2 = 9.77  S2² = 10.53  
  Output:  t = -2.77  
 
Reference:
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
 
Information or Links:
Online t Test Calculator
http://www.graphpad.com/quickcalcs/ttest1.cfm
  Use a t test to compare a continuous variable (e.g., blood pressure, weight or enzyme activity). Use a contingency table to compare a categorical variable (e.g., pass vs. fail, viable vs. not viable).
Independent Groups t Test for means Online Calculator
http://www.dimensionresearch.com/resources/calculators/ttest.html
  This calculator is used to compare the means of two independent groups to determine if they are significantly different from one another.
Students t Test Online Calculator
http://www.physics.csbsju.edu/stats/t-test.html
Student's t-test or Paired Student's t-test
Statistics on the TI-83
http://www.cbu.edu/~wschrein/media/Stat/TI83Pman.pdf
Descriptive Statistics One and Two variable statistics with the TI-83 Plus. One-Way Anova, Chi-Square. Confidence Interval & Hypothesis Testing.
TI-83 Plus Engineering Applications Handbook
http://www.geocities.com/cvandy2/TI83_Plus_Handbook.html
This handbook is a result of combining my lecture notes with over 170 worked examples, with explanations, plus over 130 different applications of the TI-83 Plus calculator.
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
 
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