T Test 2 Samples - program listing in TI Basic for the TI-83/84 Graphing Calculator. Instructions and tutorial on statistics

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.

Instructions: Click on the Related Article (in blue) to go to that Article

Related Articles:- TTSTWFRQ

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, S², 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 "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 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	S₁² calculator formula variance(
33.	dim(L2->M	N₂ calculator formula dim(
34.	mean(L2->F	X₂ calculator formula mean(
35.	variance(L2->Y	S₂² 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,"S₁²=
44.	Output(3,6,X	S₁²=
45.	Output(5,1,"x₂ =	Disp List 2
46.	Output(5,5,F	x₂ =
47.	Output(6,6,"S₂²=
48.	Output(6,6,Y	S₂²=
49.	Lbl X	formula calculations & display
50.	Float
51.	((N-1)X)->G	(N₁ - 1)S₁² ->G
52.	((M-1)Y)->H	(N₂ - 1)S₂² ->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 [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

Display:
	x1 = 27.6
	S1² = 25.4
	n1 = 10
	x2 = 22.1
	S2² = 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

S1² = 5.72

L2 = 14, 13, 13, 13, 12, 12, 10, 8, 8, 7, 7, 5, 5

n2 = 13

x2 = 9.77

S2² = 10.53

Output:

t = -2.77

Display:
	n1 = 12
	x1 = 6.5833
	S1² = 5.7197
	n2 = 13
	x2 = 9.7692
	S2² = 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