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ANOVA Two-Way, Description, Solution

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6-5-24 Tests k ANOVA (Two-Way) u Description The nearby table shows measurement results for a metal product produced by a heat treatment process based on two treatment levels: time (A) and temperature (B). The experiments were repeated twice each under identical conditions. B (Heat Treatment Temperature) B1 B2 A (Time) A1 113 , 116 139 , 132 A2 133 , 131 126 , 122 Perform analysis of variance on the following null hypothesis, using a significance level of 5%. Ho : No change in strength due to time Ho : No change in strength due to heat treatment temperature Ho : No change in strength due to interaction of time and heat treatment temperature u Solution Use two-way ANOVA to test the above hypothesis. Input the above data as shown below. List1={1,1,1,1,2,2,2,2 } List2={1,1,2,2,1,1,2,2 } List3={113,116,139,132,133,131,126,122 } Define List 3 (the data for each group) as Dependent. Define List 1 and List 2 (the factor numbers for each data item in List 3) as Factor A and Factor B respectively. Executing the test produces the following results. • Time differential (A) level of significance P = 0.2458019517 The level of significance (p = 0.2458019517) is greater than the significance level (0.05), so the hypothesis is not rejected. • Temperature differential (B) level of significance P = 0.04222398836 The level of significance (p = 0.04222398836) is less than the significance level (0.05), so the hypothesis is rejected. • Interaction (A × B) level of significance P = 2.78169946e-3 The level of significance (p = 2.78169946e-3) is less than the significance level (0.05), so the hypothesis is rejected. The above test indicates that the time differential is not significant, the temperature differential is significant, and interaction is highly significant. 20050401

Section	Page
BEFORE USING THE CALCULATOR FOR THE FIRST TIME...	3
Quick-Start	5
Quick-Start	6
TURNING POWER ON AND OFF	6
USING MODES	6
BASIC CALCULATIONS	7
REPLAY FEATURE	8
FRACTION CALCULATIONS	9
EXPONENTS	10
GRAPH FUNCTIONS	11
DUAL GRAPH	13
DYNAMIC GRAPH	14
TABLE FUNCTION	16
Precautions when Using this Product	17
Precautions when Connecting to a Computer	17
Handling Precautions	18
Contents	20
Getting Acquainted — Read This First!	24
Chapter 1 Basic Operation	26
1-1 Keys	27
1-2 Display	30
1-3 Inputting and Editing Calculations	35
1-4 Option (OPTN) Menu	51
1-5 Variable Data (VARS) Menu	53
1-6 Program (PRGM) Menu	57
1-7 Using the Setup Screen	58
1-8 Using Screen Capture	63
1-9 When you keep having problems…	64
Chapter 2 Manual Calculations	66
2-1 Basic Calculations	67
2-2 Special Functions	73
2-3 Specifying the Angle Unit and Display Format	81
2-4 Function Calculations	83
2-5 Numerical Calculations	95
2-6 Complex Number Calculations	108
2-7 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers	113
2-8 Matrix Calculations	118
Chapter 3 List Function	140
3-1 Inputting and Editing a List	141
3-2 Manipulating List Data	149
3-3 Arithmetic Calculations Using Lists	157
3-4 Switching Between List Files	162
Chapter 4 Equation Calculations	163
4-1 Simultaneous Linear Equations	164
4-2 Quadratic and Cubic Equations	166
4-3 Solve Calculations	168
4-4 What to Do When an Error Occurs	170
Chapter 5 Graphing	171
5-1 Sample Graphs	172
5-2 Controlling What Appears on a Graph Screen	180
5-3 Drawing a Graph	190
5-4 Storing a Graph in Picture Memory	199
5-5 Drawing Two Graphs on the Same Screen	200
5-6 Manual Graphing	206
5-7 Using Tables	214
5-8 Dynamic Graphing	230
5-9 Graphing a Recursion Formula	238
5-10 Changing the Appearance of a Graph	248
5-11 Function Analysis	256
Chapter 6 Statistical Graphs and Calculations	278
6-1 Before Performing Statistical Calculations	279
6-2 Calculating and Graphing Single-Variable Statistical Data	283
6-3 Calculating and Graphing Paired-Variable Statistical Data	287
6-4 Performing Statistical Calculations	301
6-5 Tests	311
6-6 Confidence Interval	336
6-7 Distribution	347
Chapter 7 Financial Calculation (TVM)	369
7-1 Before Performing Financial Calculations	370
7-2 Simple Interest	372
7-3 Compound Interest	374
7-4 Cash Flow (Investment Appraisal)	378
7-5 Amortization	381
7-6 Interest Rate Conversion	384
7-7 Cost, Selling Price, Margin	385
7-8 Day/Date Calculations	386
Chapter 8 Programming	388
8-1 Basic Programming Steps	389
8-2 PRGM Mode Function Keys	391
8-3 Editing Program Contents	393
8-4 File Management	397
8-5 Command Reference	401
8-6 Using Calculator Functions in Programs	419
8-7 PRGM Mode Command List	431
8-8 Program Library	434
Chapter 9 Spreadsheet	444
9-1 Spreadsheet Overview	445
9-2 File Operations and Re-calculation	449
9-3 Basic Spreadsheet Screen Operations	452
9-4 Inputting and Editing Cell Data	456
9-5 S.SHT Mode Commands	477
9-6 Statistical Graphs	481
9-7 Using the CALC Function	487
9-8 Using Memory in the S.SHT Mode	491
Chapter 10 eActivity	496
10-1 eActivity Overview	497
10-2 Working with eActivity Files	505
10-3 Inputting and Editing eActivity File Data	508
10-4 Using Matrix Editor and List Editor	528
10-5 eActivity File Memory Usage Screen	530
Chapter 11 System Settings Menu	531
11-1 Using the System Settings Menu	532
11-2 System Settings	533
11-3 Version List	535
11-4 Reset	537
Chapter 12 Data Communications	539
12-1 Connecting Two Units	540
12-2 Connecting the Unit to a Personal Computer	541
12-3 Performing a Data Communication Operation	542
12-4 Data Communications Precautions	547
12-5 Image Transfer	550
12-6 Add-ins	553
12-7 MEMORY Mode	554
Appendix	571
1 Error Message Table	572
2 Input Ranges	576
3 Specifications	579
4 Key Index	581
5 P Button (In case of hang up)	584