Conducting ANOVA
Problem
You'd like to conduct an analysis of variance (ANOVA).
Solution
The Analysis ToolPak offers three flavors of ANOVA: single factor, two-factor with replication, and two-factor without replication. Select Tools images/U2192.jpg border=0> Data Analysis from the main menu bar to access these tools.
Discussion
By way of example, consider the hypothetical drug effectiveness data shown in Figure 5-19.
The data values represent some measure of merit, or effectiveness, for drugs A, B, and C, along with a control group. The Anova: Single Factor tool allows you to perform an analysis of variance for two or more groups, so we'll use that tool to test the hypothesis that there's no difference between the means of these groups.
After selecting the Anova: Single Factor tool from the Data Analysis dialog box, you should see the Anova: Single Factor dialog box like the one shown in Figure 5-20.
In the Input Range field, type or select the cell range containing all the data under consideration. Your dataset must be in contiguous columns for this tool. If you include the column labels as I did in this example, then be sure to check the "Labels in first row" option. You can set the Alpha parameter to whatever you'd like. In this case I left it at 5%.
Finally, choose your output options and press OK. Here, I chose to generate the output in the same worksheet, starting in cell E178. The results of this analysis are shown in Figure 5-21.
These results show descriptive statistics for each group, along with standard ANOVA information. ANOVA results are displayed for between groups and within groups. SS represents the sum of squared deviations from the mean. df represents degrees of freedom. MS is the mean square value. F is the F-Ratio. And finally, F crit is the critical F-value based on the F-distribution. In this example, the P-value is less than the supplied Alpha value, and the obtained F-value is greater than the critical F-value. These results imply that we should reject the null hypothesis that there's no significant difference between the means of these groups and conclude that there's some statistically significant difference.
Figure 5-19. Drug effectiveness
Figure 5-20. Anova: Single Factor dialog box
Figure 5-21. ANOVA results
See Also
To learn more about the Analysis ToolPak ANOVA tools, read the Excel help topic "About statistical analysis tools." Refer to any standard text that covers statistical tests, or tests of significance, to learn more about ANOVA and other statistical tests.
Using Excel
- Introduction
- Navigating the Interface
- Entering Data
- Setting Cell Data Types
- Selecting More Than a Single Cell
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- Exploring the R1C1 Cell Reference Style
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- Understanding Operator Precedence
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Getting Acquainted with Visual Basic for Applications
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Collecting and Cleaning Up Data
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Charting
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- Recipe 4-14. Displaying Error Bars
Statistical Analysis
- Introduction
- Computing Summary Statistics
- Plotting Frequency Distributions
- Calculating Confidence Intervals
- Correlating Data
- Ranking and Percentiles
- Performing Statistical Tests
- Conducting ANOVA
- Generating Random Numbers
- Sampling Data
Time Series Analysis
- Introduction
- Plotting Time Series Data
- Adding Trendlines
- Computing Moving Averages
- Smoothing Data Using Weighted Averages
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- Detrending a Time Series
- Estimating Seasonal Indices
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- Applying Discrete Fourier Transforms
Mathematical Functions
- Introduction
- Using Summation Functions
- Delving into Division
- Mastering Multiplication
- Exploring Exponential and Logarithmic Functions
- Using Trigonometry Functions
- Seeing Signs
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- Rounding and Truncating Numbers
- Converting Between Number Systems
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Curve Fitting and Regression
- Introduction
- Performing Linear Curve Fitting Using Excel Charts
- Constructing Your Own Linear Fit Using Spreadsheet Functions
- Using a Single Spreadsheet Function for Linear Curve Fitting
- Performing Multiple Linear Regression
- Generating Nonlinear Curve Fits Using Excel Charts
- Fitting Nonlinear Curves Using Solver
- Assessing Goodness of Fit
- Computing Confidence Intervals
Solving Equations
- Introduction
- Finding Roots Graphically
- Solving Nonlinear Equations Iteratively
- Automating Tedious Problems with VBA
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- Tackling Nonlinear Systems of Equations
- Using Classical Methods for Solving Equations
Numerical Integration and Differentiation
- Introduction
- Integrating a Definite Integral
- Implementing the Trapezoidal Rule in VBA
- Computing the Center of an Area Using Numerical Integration
- Calculating the Second Moment of an Area
- Dealing with Double Integrals
- Numerical Differentiation
Solving Ordinary Differential Equations
- Introduction
- Solving First-Order Initial Value Problems
- Applying the Runge-Kutta Method to Second-Order Initial Value Problems
- Tackling Coupled Equations
- Shooting Boundary Value Problems
Solving Partial Differential Equations
- Introduction
- Leveraging Excel to Directly Solve Finite Difference Equations
- Recruiting Solver to Iteratively Solve Finite Difference Equations
- Solving Initial Value Problems
- Using Excel to Help Solve Problems Formulated Using the Finite Element Method
Performing Optimization Analyses in Excel
- Introduction
- Using Excel for Traditional Linear Programming
- Exploring Resource Allocation Optimization Problems
- Getting More Realistic Results with Integer Constraints
- Tackling Troublesome Problems
- Optimizing Engineering Design Problems
- Understanding Solver Reports
- Programming a Genetic Algorithm for Optimization
Introduction to Financial Calculations
- Introduction
- Computing Present Value
- Calculating Future Value
- Figuring Out Required Rate of Return
- Doubling Your Money
- Determining Monthly Payments
- Considering Cash Flow Alternatives
- Achieving a Certain Future Value
- Assessing Net Present Worth
- Estimating Rate of Return
- Solving Inverse Problems
- Figuring a Break-Even Point
Index
EAN: 2147483647
Pages: 206
