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
- Entering Formulas
- Exploring the R1C1 Cell Reference Style
- Referring to More Than a Single Cell
- Understanding Operator Precedence
- Using Exponents in Formulas
- Exploring Functions
- Formatting Your Spreadsheets
- Defining Custom Format Styles
- Leveraging Copy, Cut, Paste, and Paste Special
- Using Cell Names (Like Programming Variables)
- Validating Data
- Taking Advantage of Macros
- Adding Comments and Equation Notes
- Getting Help

Getting Acquainted with Visual Basic for Applications

- Introduction
- Navigating the VBA Editor
- Writing Functions and Subroutines
- Working with Data Types
- Defining Variables
- Defining Constants
- Using Arrays
- Commenting Code
- Spanning Long Statements over Multiple Lines
- Using Conditional Statements
- Using Loops
- Debugging VBA Code
- Exploring VBAs Built-in Functions
- Exploring Excel Objects
- Creating Your Own Objects in VBA
- VBA Help

Collecting and Cleaning Up Data

- Introduction
- Importing Data from Text Files
- Importing Data from Delimited Text Files
- Importing Data Using Drag-and-Drop
- Importing Data from Access Databases
- Importing Data from Web Pages
- Parsing Data
- Removing Weird Characters from Imported Text
- Converting Units
- Sorting Data
- Filtering Data
- Looking Up Values in Tables
- Retrieving Data from XML Files

Charting

- Introduction
- Creating Simple Charts
- Exploring Chart Styles
- Formatting Charts
- Customizing Chart Axes
- Setting Log or Semilog Scales
- Using Multiple Axes
- Changing the Type of an Existing Chart
- Combining Chart Types
- Building 3D Surface Plots
- Preparing Contour Plots
- Annotating Charts
- Saving Custom Chart Types
- Copying Charts to Word
- 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
- Centering Data
- Detrending a Time Series
- Estimating Seasonal Indices
- Deseasonalization of a Time Series
- Forecasting
- 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
- Getting to the Root of Things
- Rounding and Truncating Numbers
- Converting Between Number Systems
- Manipulating Matrices
- Building Support for Vectors
- Using Spreadsheet Functions in VBA Code
- Dealing with Complex Numbers

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
- Solving Linear Systems
- 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

Excel Scientific and Engineering Cookbook (Cookbooks (OReilly))

ISBN: 0596008791

EAN: 2147483647

EAN: 2147483647

Year: N/A

Pages: 206

Pages: 206

Authors: David M Bourg

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