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:-   TTSTWFRQ

 
 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 - 7. Instructions
Line 12 - 18. Lbl D: Data Input
Line 22 - 23. Input List 1
Line 26 - 27. Input List 2
Line 30 - 35. Calculator formulas
Line 36 - 39. Disp n1 & n2
Line 41 - 44. Disp List 1
Line 45 - 48. Disp List 2
Line 49 - 57. Formula
Line 59 - 60. Output
  Examples
  Reference
  Reference Links
 
 
 
prgmTTST2SMP
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 n,"x, S, FOR"        |
  7. ,"DATA" End Instructions
  8. Pause 
  9. ClrHome 
 10. Float 
 11. Menu("T TEST","LIST",L,"DATA",D) 
 12. Lbl D Input Data
 13. Input "x1=",C X1
 14. Input "S1=",X S1
 15. Input "n1=",N N1
 16. Input "x2=",F X2
 17. Input "S2=",Y S2
 18. Input "n2=",M N2
 19. Goto X  
 20. Lbl L 
 21. Disp "DATA LIST 
 22. Input "L1=",Str1 Input List 1
 23. expr("{"+Str1->L1 
 24. Pause 
 25. ClrHome 
 26. Input "L2=",Str2 Input List 2
 27. expr("{"+Str2->L2 
 28. Pause 
 29. ClrHome 
 30. dim(L1->N N1    calculator formula   dim(
 31. mean(L1->C X1    calculator formula   mean(
 32. variance(L1->X S1   calculator formula   variance(
 33. dim(L2->M N2    calculator formula   dim(
 34. mean(L2->F X2    calculator formula   mean(
 35. variance(L2->Y S2   calculator formula   variance(
 36. Output(1,1, "n1= 
 37. Output(1,5,N n1=
 38. Output(4,1,"n2= 
 39. Output(4,4,M n2=
 40. Fix 4 
 41. Output(2,1,"x1= Disp List 1
 42. Output(2,5,C x1=
 43. Output(3,6,"S1= 
 44. Output(3,6,X S1=
 45. Output(5,1,"x2 = Disp List 2
 46. Output(5,5,F x2 =
 47. Output(6,6,"S2= 
 48. Output(6,6,Y S2=
 49. Lbl X formula calculations & display
 50. Float 
 51. ((N-1)X)->G (N1 - 1)S1 ->G
 52. ((M-1)Y)->H (N2 - 1)S2 ->H
 53. ((N+M)-2)->S (N1 + N2 - 2)
 55. (1/N)->K 1/N1
 55. (1/M)->L 1/N2
 56. (C-F)->R (X1 - X2) -> R
 57. R/√(((G+H)/S(K+L))->T 
 58. Fix 4 
 59. Disp "T= Output
 60. Output(8,3,T T=
 61. Pause 
 62. ClrHome 
 63. End 
 
Example 1:

  Two-sample t test for independent samples:

You can enter values by lists (L1 & L2) or summary Stats (mean [x], variance [S], sample size [n]
 Example: summary Stats

  Input: x1 = 27.6 x2 = 22.1 
  S1 = 25.4 S2 =22.2
  n1 = 10 n2 = 10
  Output: t = 2.52 
 Display:  
  x1 = 27.6 
  S1 = 25.4 
  n1 = 10 
  x2 = 22.1 
  S2 = 22.2 
  n2 = 10 
   
  t = 2.5209 

 
Example 2:
 Example: data List
 Input:  L1 = 10, 9, 9, 8, 7, 7, 7, 6, 6, 5, 3, 2
  n1 = 12 x1 = 6.58 S1 = 5.72
  L2 = 14, 13, 13, 13, 12, 12, 10, 8, 8, 7, 7, 5, 5
  n2 = 13 x2 = 9.77 S2 = 10.53
  Output: t = -2.77 
 Display:  
  n1 = 12 
  x1 = 6.5833 
  S1 = 5.7197 
  n2 = 13 
  x2 = 9.7692 
  S2 = 10.5256 
   
  t = -2.7746 

 
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
 
Reference:
Information or Links:
  Online t Test Calculator
http://www.graphpad.com/quickcalcs/ttest1.cfm
  Independent Groups t Test for means Online Calculator
http://www.dimensionresearch.com/resources/calculators/ttest.html
  Students t Test Online Calculator
http://www.physics.csbsju.edu/stats/t-test.html  
  Statistics on the TI-83
http://www.cbu.edu/~wschrein/media/Stat/TI83Pman.pdf
TI-83 t test
  Student T-Test - One Small Sample
Statistics TI-83
  Hints for Statistics Using a TI-83
descriptive statsistics
  Sample Statistics on the TI-83/84
TI-83 help
  Graphing Calculator Help TI-83
TI-83 Statistical Tests
  Using the TI-83 to Perform a Statistical Test
 
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