The ANOVA Test

Introduction

Analysis of variance (ANOVA) is a collection of statistical models and their associated procedures (such as "variation" among and between groups) used to analyze the differences among group means.

An ANOVA test is a way to find out if survey or experiment results are significant. In other words, they help you to figure out if you need to reject the null hypothesis or accept the alternate hypothesis. Basically, you’re testing groups to see if there’s a difference between them. Examples of when you might want to test different groups:

·         A group of psychiatric patients are trying three different therapies: counseling, medication and biofeedback. You want to see if one therapy is better than the others.

·         A manufacturer has two different processes to make light bulbs. They want to know if one process is better than the other.

·         Students from different colleges take the same exam. You want to see if one college outperforms the other.

What Does “One-Way” or “Two-Way Mean?

One-way or two-way refers to the number of independent variables (IVs) in your Analysis of Variance test. One-way has one independent variable (with 2 levels) and two-way has two independent variables (can have multiple levels). For example, a one-way Analysis of Variance could have one IV (brand of cereal) and a two-way Analysis of Variance has two IVs (brand of cereal, calories).

What are “Groups” or “Levels”?

Groups or levels are different groups in the same independent variable. In the above example, your levels for “brand of cereal” might be Lucky Charms, Raisin Bran, Cornflakes — a total of three levels. Your levels for “Calories” might be: sweetened, unsweetened — a total of two levels.

Let’s say you are studying if Alcoholics Anonymous and individual counseling combined is the most effective treatment for lowering alcohol consumption. You might split the study participants into three groups or levels: medication only, medication and counseling, and counseling only. Your dependent variable would be the number of alcoholic beverages consumed per day.

If your groups or levels have a hierarchical structure (each level has unique subgroups), then use a nested ANOVA for the analysis.

Types of Tests.

There are two main types: one-way and two-way. Two-way tests can be with or without replication.

·         One-way ANOVA between groups: used when you want to test two groups to see if there’s a difference between them.

·         Two way ANOVA without replication: used when you have one group and you’re double-testing that same group. For example, you’re testing one set of individuals before and after they take a medication to see if it works or not.

·         Two way ANOVA with replication: Two groups, and the members of those groups are doing more than one thing. For example, two groups of patients from different hospitals trying two different therapies.

One Way ANOVA

A one way ANOVA is used to compare two means from two independent (unrelated) groups using the F-distribution. The null hypothesis for the test is that the two means are equal. Therefore, a significant result means that the two means are unequal.

When to use a one way ANOVA

Situation 1: You have a group of individuals randomly split into smaller groups and completing different tasks. For example, you might be studying the effects of tea on weight loss and form three groups: green tea, black tea, and no tea.
Situation 2: Similar to situation 1, but in this case the individuals are split into groups based on an attribute they possess. For example, you might be studying leg strength of people according to weight. You could split participants into weight categories (obese, overweight and normal) and measure their leg strength on a weight machine.

Limitations of the One Way ANOVA

A one way ANOVA will tell you that at least two groups were different from each other. But it won’t tell you what groups were different. If your test returns a significant f-statistic, you may need to run an ad hoc test (like the Least Significant Difference test) to tell you exactly which groups had a difference in means.

Two Way ANOVA

A Two Way ANOVA is an extension of the One Way ANOVA. With a One Way, you have one independent variable affecting a dependent variable. With a Two Way ANOVA, there are two independents. Use a two way ANOVA when you have one measurement variable (i.e. a quantitative variable) and two nominal variables. In other words, if your experiment has a quantitative outcome and you have two categorical explanatory variables, a two way ANOVA is appropriate.

For example, you might want to find out if there is an interaction between income and gender for anxiety level at job interviews. The anxiety level is the outcome, or the variable that can be measured. Gender and Income are the two categorical variables. These categorical variables are also the independent variables, which are called factors in a Two Way ANOVA.

The factors can be split into levels. In the above example, income level could be split into three levels: low, middle and high income. Gender could be split into three levels: male, female, and transgender. Treatment groups are all possible combinations of the factors. In this example there would be 3 x 3 = 9 treatment groups.

Main Effect and Interaction Effect

The results from a Two Way ANOVA will calculate a main effect and an interaction effect. The main effect is similar to a One Way ANOVA: each factor’s effect is considered separately. With the interaction effect, all factors are considered at the same time. Interaction effects between factors are easier to test if there is more than one observation in each cell. For the above example, multiple stress scores could be entered into cells. If you do enter multiple observations into cells, the number in each cell must be equal.

·         Two null hypotheses are tested if you are placing one observation in each cell. For this example, those hypotheses would be:
H₀₁: All the income groups have equal mean stress.
H₀₂: All the gender groups have equal mean stress.

·         For multiple observations in cells, you would also be testing a third hypothesis:
H₀₃: The factors are independent or the interaction effect does not exist.

An F-statistic is computed for each hypothesis you are testing.

Assumptions for Two Way ANOVA

·         The population must be close to a normal distribution.

·         Samples must be independent.

·         Population variances must be equal.

·         Groups must have equal sample sizes.

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Branding Glossary(I - V) Part 2

I        Intangibles “Intangible” - incapable of being touched. (1) Intangible assets - trademarks, copyrights, patents, design rights, proprietary expertise, databases, etc. (2) Intangible brand attributes - brand names, logos, graphics, colors, shapes and smells. (See Service Brand.)

L        Launch The initial marketing of a new product in a particular market. The way in which the launch is carried out greatly affects the product’s profitability throughout its lifecycle.

M    Market Leader A company that has achieved a dominant position - either in scale (e.g., British Airways) or influence (e.g., Virgin) - within its field. This leading position often comes about because the company was the first to market a certain type of product and, with the protection of a patent, has managed to consolidate its position before direct competition was possible. Alternatively, a company may overtake a previous market leader through greater efficiency and skilful positioning.

Market Position A measure of the position of a company or product on a market. Defined as market share multiplied by share of mind.

Market Segment A group of customers who (a) share the same needs and values, (b) can be expected to respond in much the same way to a company’s offering, and (c) command enough purchasing power to be of strategic importance to the company.

Market Share A company’s share of total sales of a given category of product on a given market. Can be expressed either in terms of volume (how many units sold) or value (the worth of units sold).

Mass Marketing Simultaneous standardized marketing to a very large target market through mass media. Other names for this are market aggregation and undifferentiated marketing.

Masterbrand A brand name that dominates all products or services in a range or across a business. Sometimes used with sub-brands, sometimes used with alpha or numeric signifiers. (See also Monolithic Brand.) Audi, Durex, Nescafe and Lego, for example, are all used as masterbrands.

Monolithic Brand A single brand name that is used to “masterbrand” all products or services in a range. Individual products are nearly always identified by alpha or numeric signifiers. Companies like Mercedes and BMW favor such systems.

Multibrand Strategy /Multiple Branding Marketing of two or more mutually competing products under different brand names by the same company. The motive may be that the company wishes to create internal competition to promote efficiency, or to differentiate its offering to different market segments, or to get maximum mileage out of established brands that it has acquired. When a company has achieved a dominant market share, multibrand strategy may be its only option for increasing sales still further without sacrificing profitability. For example, Lever Brothers sells washing powders under the Persil, Omo and Surf names; Cadbury sells chocolates under the Dairy Milk, Bournville and Fruit & Nut names; Heinz sells canned convenience foods under the Baked Beans, Spaghetti Hoops and Alphabetti Spaghetti names.

N     Names There are three basic categories of brand (or corporate) name:

•      Descriptive name A name which describes the product or service for which it is intended, e.g., TALKING PAGES.

•      Associative name A name which alludes to an aspect or benefit of the product or service, often by means of an original or striking image or idea, e.g., VISA.

•      Freestanding name A name which has no link to the product or service but which might have meaning of its own, e.g., PENGUIN.

The following are also helpful:

•      Abstract name A name which is entirely invented and has no meaning of its own, e.g., ZENECA. Abstract names are a sub-set of freestanding names because they also have no link to the product of service.

•      Coined name Any name which is in some way invented. Coined names can be descriptive (CO-CREATE), associative (IMATION) and freestanding/abstract (ZENECA).

•      Niche Marketing Marketing adapted to the needs, wishes and expectations of small, precisely defined groups of individuals. A form of market segmentation, but aimed at

very small segments. Niche marketing characteristically uses selective media.

O     OEM market OEM stands for Original Equipment Manufacturers. The OEM market consists of companies that use another company’s product as a component in their own production. A manufacturer of ball bearings, for example, sells both to OEM customers who build the bearings into machines, and to end users who need the bearings as spare parts for machines that they have bought from the OEMs. Most manufacturing companies thus have an OEM market and a replacement market. The latter is usually called the MRO market or aftermarket.

Offering What a company offers for sale to customers. An offering includes the product and its design, features, quality, packaging, distribution, etc., together with associated services such as financing, warranties and installation. The name and brand of the product are also part of the offering.

P      Packaging Design The design of the pack format and graphics for a product brand.

Parent Brand A brand that acts as an endorsement to one or more sub-brands within a range.

Passing Off The name given to a legal action brought to protect the “reputation” of a particular trademark/brand/ get up. In essence, the action is designed to prevent others from trading on the reputation/goodwill of an existing trademark/brand/get up. The action is only available in those countries that recognize unregistered trademark rights (for example the UK and US). In some countries, it is called “unfair competition action.”

Perceptual Mapping Graphic Analysis and presentation of where actual and potential customers place a product or supplier in relation to other products and suppliers. Most perceptual maps show only two dimensions at a time, for example price on one axis and quality on the other. There also are methods of graphically analyzing and presenting measurement data in three or more dimensions.

Positioning Statement A written description of the position that a company wishes itself, its product or its brand to occupy in the minds of a defined target audience.

Power Branding A strategy in which every product in a company’s range has its own brand name which functions independently, unsupported by either the company’s corporate brand or its other product brands. Power branding is a resource-intensive strategy, since each brand must be commercially promoted and legally protected. This strategy is used mainly by manufacturers of consumer goods. Lever’s and Procter & Gamble’s detergents are good examples of power brands.

Product Brand A brand which is synonymous with a particular product offering, for example, Cheerios.

R      Rebrand When a brand owner revisits the brand with the purpose of updating or revising based on internal or external circumstances. Rebranding is often necessary after an M&A or if the brand has outgrown its identity/ marketplace.

Relative Market Share Your own company’s market share compared to those of your competitors. A large share confers advantages of scale in product development, manufacturing and marketing. It also puts you in a stronger position in the minds of customers, which has a positive influence on pricing.

Relaunch Reintroducing a product into a specific market. The term implies that the company has previously marketed the product but stopped marketing it. A relaunched product has usually undergone one or more changes. It may, for example, be technically modified, rebranded, distributed through different channels or repositioned.

Repositioning Communications activities to give an existing product a new position in customers’ minds and so expanding or otherwise altering its potential market. Many potentially valuable products lead an obscure existence because they were launched or positioned in an inadequate manner. It is almost always possible to enhance the value of such products by repositioning them.

Rollout The process by which a company introduces a new product or service to different geographical markets or consumer segments.

S

Selective Media Media that, unlike mass media, reach only small and identifiable groups of people, for example, members of a particular profession or industry or other groups defined by geographic, demographic or psychographic data (otherwise known as targeted media).

Service Brand A product consisting predominantly of intangible values. “A service is something that you can buy and sell, but not drop on your foot” (The Economist). In this sense, a service is something that you do for somebody, or a promise that you make to them.

Share of Mind There are many definitions of share of mind. At its most precise, share of mind measures how often consumers think about a particular brand as a percentage of all the times they think about all the brands in its category. More loosely, share of mind can be defined simply as positive perceptions of the brand obtained by market research. Whereas market share measures the width of a company’s market position, share of mind can be said to measure its depth.

Share of Voice The media spending of a particular brand when compared to others in its category.

Sub-brand A product or service brand that had its own name and visual identity to differentiate it from the parent brand.

T       Tangibles “Tangible” - capable of being touched. (1) Tangible assets - manufacturing plant, bricks and mortar, cash, investments, etc. (2) Tangible brand attributes - the product and its packaging. (3) Tangible brand values - useful qualities of the brand known to exist through experience and knowledge.

Target Market The market segment or group of customers that a company has decided to serve, and at which it consequently aims its marketing activities.

Top-of-Mind What is present in the uppermost level of consciousness; the manufacturer or brand that people in market surveys name first when asked to list products in a specific category. Top-of-mind is the highest degree of share of mind. To attain that position, a company normally needs to have a large share of voice in its category.

Trademark “Any sign capable of being represented graphically which is capable of distinguishing goods or services of one undertaking from those of another undertaking” (UK Trade Marks Act 1994).

Trademark Infringement A trademark registration is infringed by the unauthorized use of the registered trademark, or of one that is confusingly similar to it, on the registered goods or services, or in certain circumstances on similar or dissimilar goods and services.

Trendsetter Someone or thing that breaks a traditional mold or routine and gains a following because of it. iMac is an example of trendsetting in design as now office supplies come in the familiar colors and translucent packaging of an iMac.

U      User Segmentation Division of potential customers into market segments according to how and for what purpose they use a product. Do they use it for cleaning their teeth or for making cakes (baking powder)? For oiling their hair or for frying food? (True story concerning use of Brylcreem in Nigeria). As a decongestant chest rub or as an aphrodisiac? (True story concerning Ribby Rub in Caribbean).

V      Visual Identity What a brand looks like - including, among other things, its logo, typography, packaging and literature systems.

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Data analysis (Part 1) (Central tendancy - mean, median, mode, standard deviation)

Statistics is the science of collecting and analyzing numerical data. You could take a survey or collect information and then use measures like mean, median, mode and range to see what that data mean. Standard deviation is often the next calculation for describing what a set of numerical data is doing. Once you know how to find mean, you can find standard deviation.

Mean (The Average)

Mean is a measure of central tendency. It measures what the majority of the data are doing toward the middle of a set. The mean is often referred to as the average of a data set. As an example, an algebra class has 10 students. Their grades on the last test were 85, 90, 87, 93, 100, 53, 78, 85, 99 and 82. What is the average grade for the students? To find mean, simply add all the numbers in a data set and divide by the number of items in the set:

85 + 90 + 87 + 93 + 100 + 53 + 78 + 85 + 99 + 82 = 852 852 / 10 = 85.2

The average, or mean, test grade in the class is 85.2.

Mode (Which Occurs Most)

Mode is another measure of central tendency. The mode is just the number that occurs most frequently. It's easy to remember because mode and most sound alike. Using the algebra class example, what grade occurred most frequently among the students? To answer, put the values in order:

53, 78, 82, 85, 85, 87, 90, 93, 99, 100

The only grade that occurred more than once is 85. Since 85 occurred most, the mode is 85.

Median (The Middle, Range Is the Spread)

Median is another measure of central tendency. The median is simply the middle number of a set. Put the numbers in order and look for one in the middle. If there is no middle number, add the two in the center and divide by 2. In the algebra class example, what is the median grade? To answer, put the values in order:

53, 78, 82, 85, 85, 87, 90, 93, 99, 100

Since there are even numbers of test grades, there is no middle number. The two test grades in the middle are 85 and 87. Add them and divide by 2:

85 + 87 = 172 172 / 2 = 86

The median, or middle grade, is 86.

Range is a quick calculation. Range is simply the largest value minus the smallest. It shows you how spread out the numbers are. For these grades, subtract 53 from 100 to get the range of 47.

Find Variance before Standard Deviation

Standard deviation is the square root of the variance, so you must find the variance first. Variance is the average of the squared difference of each number from the mean. That may sound confusing, but it's pretty simple to do. Take each number in the set and subtract if from the mean. Then square it. Add those values together, and divide by the number of items in your set. Working with the algebra class grades again, subtracts each one from the mean:

85.2 - 53 = 32.2 85.2 - 78 = 7.2 85.2 - 82 = 3.2 85.2 - 85 = 0.2 85.2 - 85 = 0.2 85.2 - 87 = -1.8 85.2 - 90 = -4.8 85.2 - 93 = -7.8 85.2 - 99 = -13.8 85.2 - 100 = 14.8

Square each of those values, and then add them together:

1,036.84 + 51.84 + 10.24 + 0.04 + 0.04 + 3.24 + 23.04 + 60.84 + 190.44 + 219.04 = 1,595.6

Finally, divide that sum by the number of items in the set, in this case 10:

1,595.6 / 10 = 159.56

The variance for this data set is 159.56.

Standard Deviation (Measures Spread)

Standard deviation is the measure of how spread out the numbers is from the center of a data set. A small standard deviation means a lot of the numbers are grouped around the middle of the set. A large standard deviation means that the numbers are spread out with some very high and low numbers. With the algebra grades, use this equation:

square root (159.56) = 12.63

The standard deviation for this data set is 12.63.

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