 Part 1. Introduction to MM4XL
 Part 2. MM4XL Tools
 1. Strategic Tools
 BCG Matrix
 Brand Mapping
 Brand Switch
 Decision Tree
 Forecast Manager
 McKinsey Matrix
 Profile Manager
 Quality Manager
 Risk Analyst
 Risk Analyst Expert in a Few Minutes
 Introduction to Decision Analysis
 Introducing Risk Analyst with an example
 1. How to run Risk Analyst
 2. Simulation Never heard of it
 3. Examples
 4. Functions
 1. Property Functions
 2. Utility Functions
 3. Distribution Functions
 mmBETA (Scale, Shape)
 mmBETAGEN (Scale, Shape, [Optional: Lower], [Optional: Upper])
 mmBINOMIAL (Trials, Successes)
 mmCHI2 (Degrees)
 mmDISCRETE (InputRange, Probabilities)
 mmERF (Mean)
 mmERLANG (Scale, Shape)
 mmEXPON (Mean)
 mmEXTVAL (ModalValue, StDeviation)
 mmGAMMA (Scale, Shape)
 mmGAUSSINV (Mean, Scale)
 mmGEO (Trials)
 mmHYPERGEO (Sample, Defects, BatchSize)
 mmINTUNI (Lower, Upper)
 mmLOGISTIC (Mean, StDeviation)
 mmLOGNORMAL (Mean, StDeviation)
 mmNEGBIN (Failures, Successes)
 mmNORMAL (Mean, StDeviation)
 mmPARETO (Location, ModalValue)
 mmPARETO2 (Location, ModalValue)
 mmPERT (Lower, ModalValue, Upper)
 mmPOISSON (Mean)
 mmRANDBETWEEN (Lower, Upper)
 mmRAYLEIGH (ModalValue)
 mmSTUDENT (Degrees)
 mmTRI (Lower, ModalValue, Upper)
 mmUNIFORM (Lower, Upper)
 mmWEIBULL (Life, Shape)
 Probability functions
 Technicalities
 Sources
 2. Analytical Tools
 Business Formulas
 mmBASS, Bass Diffusion Model
 mmBEI, Brand Equity Index
 mmBEP, BreakEven Point
 mmBEPR, BreakEven Point with Fixed Rate of Return
 mmBUYRATE, Purchase Rate Model
 mmCAGR, Compound Annual Growth
 mmCHIp, Chi Squared Test
 mmCODING, Coding of variables
 1. Customer Satisfaction
 2. Database Functions
 mmDHMS, Number to Time
 mmEI, Evolution Index
 mmEXPECT, Expected values
 3. Forecast Errors
 mmGROWTH
 mmGROWTHBACK
 mmGRP, Gross Rating Points
 mmHERF, Herfindahl Index
 mmINTERPOLE, Linear Interpolation
 mmLEARN, Learning Curve
 mmMSAR, Market Share to Advertising Ratio
 4. Opportunity Index
 5. Performance Ranking
 6. Project Management
 mmPREMIUM, Price Premium
 mmPRESS, Product Performance Index
 7. Price Indexes
 8. Queuing Theory
 mmRANGE
 mmREBUY, Repeat Purchase Rate
 mmREBUYS, Estimated Number of RePurchases
 mmRELATIVE
 mmSAMPLE, Sample Size
 mmSAMPLEMIN, Minimum Sample for Significant Values
 mmSEASON, Seasonality Indexes
 mmSHARE
 mmSIGNIF, Significance Test
 mmVARc, Coefficient of Variation
 Cluster Analysis
 CrossTab
 Descriptive Analyst
 Gravitation Analysis
 Proportion Analyst
 Sample Manager
 Segmentation Tree
 Variation Analyst
 3. Charts and Maps
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 Part 1. Introduction to MM4XL
 Part 2. MM4XL Tools
 1. Strategic Tools
 BCG Matrix
 Brand Mapping
 Brand Switch
 Decision Tree
 Forecast Manager
 McKinsey Matrix
 Profile Manager
 Quality Manager
 Risk Analyst
 1. How to run Risk Analyst
 2. Simulation Never heard of it
 3. Examples
 4. Functions
 1. Property Functions
 2. Utility Functions
 3. Distribution Functions
 mmBETA (Scale, Shape)
 mmBETAGEN (Scale, Shape, [Optional: Lower], [Optional: Upper])
 mmBINOMIAL (Trials, Successes)
 mmCHI2 (Degrees)
 mmDISCRETE (InputRange, Probabilities)
 mmERF (Mean)
 mmERLANG (Scale, Shape)
 mmEXPON (Mean)
 mmEXTVAL (ModalValue, StDeviation)
 mmGAMMA (Scale, Shape)
 mmGAUSSINV (Mean, Scale)
 mmGEO (Trials)
 mmHYPERGEO (Sample, Defects, BatchSize)
 mmINTUNI (Lower, Upper)
 mmLOGISTIC (Mean, StDeviation)
 mmLOGNORMAL (Mean, StDeviation)
 mmNEGBIN (Failures, Successes)
 mmNORMAL (Mean, StDeviation)
 mmPARETO (Location, ModalValue)
 mmPARETO2 (Location, ModalValue)
 mmPERT (Lower, ModalValue, Upper)
 mmPOISSON (Mean)
 mmRANDBETWEEN (Lower, Upper)
 mmRAYLEIGH (ModalValue)
 mmSTUDENT (Degrees)
 mmTRI (Lower, ModalValue, Upper)
 mmUNIFORM (Lower, Upper)
 mmWEIBULL (Life, Shape)
 Probability functions
 Risk Analyst Expert in a Few Minutes
 Introduction to Decision Analysis
 Introducing Risk Analyst with an example
 Technicalities
 Sources
 2. Analytical Tools
 Business Formulas
 1. Customer Satisfaction
 2. Database Functions
 3. Forecast Errors
 4. Opportunity Index
 5. Performance Ranking
 6. Project Management
 7. Price Indexes
 8. Queuing Theory
 mmBASS, Bass Diffusion Model
 mmBEI, Brand Equity Index
 mmBEP, BreakEven Point
 mmBEPR, BreakEven Point with Fixed Rate of Return
 mmBUYRATE, Purchase Rate Model
 mmCAGR, Compound Annual Growth
 mmCHIp, Chi Squared Test
 mmCODING, Coding of variables
 mmDHMS, Number to Time
 mmEI, Evolution Index
 mmEXPECT, Expected values
 mmGROWTH
 mmGROWTHBACK
 mmGRP, Gross Rating Points
 mmHERF, Herfindahl Index
 mmINTERPOLE, Linear Interpolation
 mmLEARN, Learning Curve
 mmMSAR, Market Share to Advertising Ratio
 mmPREMIUM, Price Premium
 mmPRESS, Product Performance Index
 mmRANGE
 mmREBUY, Repeat Purchase Rate
 mmREBUYS, Estimated Number of RePurchases
 mmRELATIVE
 mmSAMPLE, Sample Size
 mmSAMPLEMIN, Minimum Sample for Significant Values
 mmSEASON, Seasonality Indexes
 mmSHARE
 mmSIGNIF, Significance Test
 mmVARc, Coefficient of Variation
 Cluster Analysis
 CrossTab
 Descriptive Analyst
 Gravitation Analysis
 Proportion Analyst
 Sample Manager
 Segmentation Tree
 Variation Analyst
 3. Charts and Maps
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Part 2. MM4XL Tools > 2. Analytical Tools > Variation Analyst > Technicalities
Group Variation Analyst Technicalities It is frequently of interest to compare differences in results among several groups. When the outcome measurements across the groups are continuous, and certain assumptions are met, a methodology known as Analysis of Variance, or ANOVA, may be employed to compare the means of the groups. The term Analysis of Variance may be misleading since the objective of the analysis is to compare means. However, through an analysis of the variation in the data we will be able to draw conclusions about possible differences in the group means. Group Variation Analyst computes the onefactor ANOVA Ftest for difference for pairs of group means rather than for all groups at once. The assumptions to be met in order for the ANOVA to produce reliable results are three:  Error terms must be random and independent. That is, the difference (or error) for one observation should not be related to the difference for any other observation. Most often this assumption is violated when data are collected over a period of time, because measurements made at adjacent time points may be more alike than those made at very different time, for instance when measuring air temperature.
 Values in each group must be normally distributed. As long as the distributions are not extremely different from a normal distribution (bell shaped curve), the level of significance of the ANOVA test is fairly robust, particularly for large samples.
 Homogeneity of variance. This means that the variance within each group must be equal (very close) for all groups. This assumption is often violated when analyzing groups with different sample sizes. Thus, for computational effectiveness, robustness, and power, there should be groups of equal sample size whenever possible.
If the normality and homogeneity assumptions are violated, an appropriate data transformation may be used for normalizing data and reducing the difference in variances. In ANOVA the null hypothesis is that no difference exists in the means of the groups. The test splits the total variation in Within and Between group variation and it computes the test statistics F. The Fvalue follows an Fdistribution, and for a given level of confidence we may reject the null hypothesis if the Fvalue exceeds the Fcritical, which is the upper tail of the Fdistribution. Unequal Sample Size Although we have written that there should be groups of equal sample size whenever possible, we can still obtain a suitable test statistic when the sample sizes are not all equal. Specifically, we use the following formula as a test statistic and reject the null hypothesis when the computed value exceeds Fcritical. See Madsen pg 530 for details. Other ANOVA methods The analysisofvariance method we have discussed so far is the onefactor model. Two or more factors can also be tested, and MarketingStat is willing to develop further methods as our clients make the request. 