Data Analysis and Statistics

PERPI TrainingHotel Puri DenpasarMarch 30, 2017Version 2

by T.S. LimQuantitative Senior Research Director and PartnerLeap Research

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Agenda

1 What is Statistics?

2 Types of Variables and Levels of Measurement

3 Descriptive Statistics

4 Inferential Statistics

5 Independent and Dependent Samples

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References

Carr, Rodney. Practical Statistics. XLent Works. http://www.deakin.edu.au/~rodneyc/PracticalStatistics/, 2013

Gonick, Larry, and Woollcott Smith. The Cartoon Guide to Statistics (New York: HarperPerennial, 2015), Kindle edition

Lind, Douglas A., William G. Marchal, and Samuel A. Wathen. Statistical Techniques in Business & Economics. 15th ed. New York: McGraw-Hill/Irwin, 2012

Malhotra, Naresh K. Marketing Research: An Applied Orientation. Global Edition, 6th ed. Upper Saddle River: Pearson Education, 2010

Rumsey, Deborah. Statistics Essentials For Dummies. Hoboken: Wiley, 2010

What is Statistics?

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Statistics

The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions

2 categories: descriptive statistics and inferential statistics

DESCRIPTIVE STATISTICS: Methods of organizing, summarizing, and presenting data in an informative way

E.g., via various charts, tables, infographics INFERENTIAL STATISTICS: The methods used to

estimate a property of a population on the basis of a sample

E.g., T-Test, Z-Test, ANOVA, Regression Analysis, Factor Analysis, Cluster Analysis

Source: Lind, Marchal, and Wathen (2012)

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Ethics and Statistics

A guideline can be found in the paper “Statistics and Ethics: Some Advice for Young Statisticians,” in The American Statistician 57, no. 1 (2003)

The authors advise us to practice statistics with integrity and honesty, and urge us to “do the right thing” when collecting, organizing, summarizing, analyzing, and interpreting numerical information

The real contribution of statistics to society is a moral one. Financial analysts need to provide information that truly reflects a company’s performance so as not to mislead individual investors.

Information regarding product defects that may be harmful to people must be analyzed and reported with integrity and honesty

The authors of The American Statistician article further indicate that when we practice statistics, we need to maintain “an independent and principled point-of-view”

Source: Lind, Marchal, and Wathen (2012), page 14

In Marketing Research, we change the data values only when it’s clearly justifiable; e.g., data entry or coding error. We must never change the values just to increase / decrease the mean score.

Types of Variables and Levels of Measurement

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Types of Variables

Source: Lind, Marchal, and Wathen (2012)

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Ratio Level

Interval Level

Ordinal Level

Nominal Level

Four Levels of Measurement

It has all the characteristics of the interval level, and additionally the 0 point is meaningful and the ratio between two numbers is meaningful

It includes all the characteristics of the ordinal level, and additionally the difference between values is a constant size

Data are represented by sets of labels or names; they have relative values and hence they can be ranked or ordered

Observations of a qualitative variable can only be classified and counted

Data can be classified according to levels of measurement. The level of measurement of the data dictates the calculations that can be done to summarize and present the data. It will also determine the statistical tests that should be performed.

Source: Lind, Marchal, and Wathen (2012)

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Four Levels of MeasurementSummary

In Marketing Research, we usually assume that variables of non Nominal level to have at least Interval level

Source: Lind, Marchal, and Wathen (2012)

Descriptive Statistics

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Measures of Location

Measures of location that we discuss are measures of central tendency because they tend to describe the center of the distribution

If the entire sample is changed by adding a fixed constant to each observation, then the mean, mode and median change by the same fixed amount

Mean: The mean, or average value, is the most commonly used measure of central tendency

The measure is used to estimate the unknown population mean when the data have been collected using an interval or ratio scale

The data should display some central tendency, with most of the responses distributed around the mean

Note: Sample Mean is prone to the presence of outliers (very big or very small numbers) in the data

Source: Malhotra (2010)

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Measures of Location (Cont.)

Mode: The mode is the value that occurs most frequently It represents the highest peak of the distribution The mode is a good measure of location when the variable is inherently categorical or has otherwise

been grouped into categories

Median: The median of a sample is the middle value when the data are arranged in ascending or descending order

If the number of data points is even, the median is usually estimated as the midpoint between the two middle values by adding the two middle values and dividing their sum by 2

The median is the 50th percentile The median is an appropriate measure of central tendency for ordinal data Note: Sample Median is robust to the presence of outliers in the data. However, the mathematics

involved in dealing with median and ordinal level data in general is difficult.

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The Relative Positions of the Mean, Median, and Mode

Source: Lind, Marchal, and Wathen (2012)

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Measures Variability

The measures of variability, which are calculated on interval or ratio data, include the range, interquartile range, variance or standard deviation, and coefficient of variation

Range: The range measures the spread of the data It is simply the difference between the largest and smallest values in the sample

Interquartile Range (IQR): The interquartile range is the difference between the 75th and 25th percentiles

For a set of data points arranged in order of magnitude, the pth percentile is the value that has p% of the data points below it and (100 – p)% above it

If all the data points are multiplied by a constant, the interquartile range is multiplied by the same constant

Source: Malhotra (2010)

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Measures Variability (Cont.)

Variance: The difference between the mean and an observed value is called the deviation from the mean. The variance is the mean squared deviation from the mean.

The variance can never be negative When the data points are clustered around the mean, the variance is small. When the data points are

scattered, the variance is large. If all the data values are multiplied by a constant, the variance is multiplied by the square of the

constant

Standard Deviation: The standard deviation is the square root of the variance Thus, the standard deviation is expressed in the same units as the data, rather than in squared units

(like in the variance)

Coefficient of Variation: The coefficient of variation is the ratio of the standard deviation to the mean expressed as a percentage, and it is a unitless measure of relative variability

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FunnelRadar Combo

Column Line Bar

Example of Charts (1)

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Waterfall Histogram Pareto

Box & Whisker Treemap Sunburst

Example of Charts (2)

Inferential Statistics

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Estimating a Population Parameter: Making Your Best Guesstimate

We want to estimate a population parameter (a single number that describes a population) by using statistics (numbers that describe a sample of data)

Examples: Estimating Overall Liking score of a new product Estimating Customer Satisfaction Index Estimating the average units purchased per purchase occasion Estimating % agreement to a statement

Types of estimates: Point Estimate one single number only Interval Estimate an interval containing a range of numbers (called Confidence Interval)

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Simulation: One Proportion Inferencehttp://www.rossmanchance.com/applets/OneProp/OneProp.htm

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1St

anda

rd E

rror

Proportion

The highest Standard Error for Proportion is achieved at p = 0.5

When the Proportions are small or big, the Standard

Errors are small

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Simulation: Confidence Intervals for Meanshttp://www.rossmanchance.com/applets/ConfSim.html

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A General Procedure for Hypothesis Testing

HYPOTHESIS TESTING A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement

Examples: The heavy and light users of a brand differ

in terms of psychographics characteristics One hotel has a more upscale image than its

close competitor Concept A is rated higher than Concept B on

Overall Liking

Source: Malhotra (2010)

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Type I and Type II Errors in Hypothesis Testing

Alpha (α) is the probability of making a Type I error We want α to be as low as possible!

Beta (β) is the probability of making a Type II error.The power of a test is the probability (1 – β) of rejecting the null hypothesis when it is indeed false and hence should be rejected We want power to be as high as possible!

Unfortunately, α and β are interrelated. So, it’s necessary to balance the two types of errors.The level of α along with the sample size will determine the level of β for a particular research design.

In practice, we usually set α at 1%, 5%, or 10%.

The risk of both α and β can be controlled by increasing the sample size.For a given level of α, increasing the sample size will decrease β, and hence increasing the power of the test (1 – β).

Think of sample size as a magnifying glass.Sources: Lind, Marchal, and Wathen (2012). Malhotra (2010).

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Hypothesis Tests Related to Differences

Interval or Ratio Level Nominal or Ordinal Level

Source: Malhotra (2010)

Independent and Dependent Samples

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Two Independent Samples: Evaluating the Difference between Two Mean Scores

The data come from 2 unrelated samples, drawn randomly from different populationsThe 2 samples are not experimentally related. The measurement of one sample has no

effect on the values of the second sample.Note: In a monadic design, the samples are independentExamples

Comparing the Purchase Intent mean scores of Concept X vs. Concept Y Comparing the responses of Females vs. Males Comparing the reaction towards TVC A vs. TVC B

Online tools: http://www.evanmiller.org/ab-testing/t-test.html http://www.quantitativeskills.com/sisa/statistics/t-test.htm

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The data also come from 2 unrelated samples, but we focus on evaluating the proportionsExamples: comparing Top Box, Top 2 Boxes, Bottom Box, Bottom 2 Boxes, Brand

AssociationCaution: declaring 2 proportions as statistically significantly different when the actual

difference is small

An online tool: http://www.evanmiller.org/ab-testing/chi-squared.html

Two Independent Samples: Evaluating the Difference between Two Proportions

T2B Differences:Proto 1 (a) – Proto 2 (b) = 5%Proto 1 (a) – Proto 4 (d) = 4%

Product Attribute Proto 1 Proto 2 Proto 3 Proto 4 Competitor(a) (b) (c) (d) (e)

Respondents Base 247 242 241 246 244

Cleans hair very well T2B 93% 88% 92% 89% 92%bd

Means 4.43 4.45 4.47 4.51 4.46

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Some Basic Formulas

Source: Lind, Marchal, and Wathen (2012)

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The Case of More Than Two Independent Samples

Method: One-way ANOVA for a quantitative (numerical) variable E.g., Overall Liking, Purchase Intention, Product Attribute, Imagery attribute

Examples: In a blind product test, comparing the performances of 3 different facial moisturizer In a concept test, comparing the acceptance of 5 new powdered milk concepts In a U&A study, comparing the responses from SES Upper vs. Middle vs. Lower In a TVC pre-test, comparing the performances of 3 different new ads

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Simulation: One Way Analysis of Variancehttp://www.rossmanchance.com/applets/AnovaSim.html

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Two Dependent Samples

Paired data is formed from measurements of essentially the same quantitative variable (ordinal, internal, or ratio level) done on the same individuals

Examples: Concept score vs. Product score of a new mix (in a concept-product test project) Perceptions ‘Before’ and ‘After’ an exposure (e.g., a TVC) Perceptions ‘Before’ and ‘After’ attending a brand sponsored event

Statistical test for quantitative (numerical) variable: Pairwise T-Test for Means

Online tools: http://scistatcalc.blogspot.co.id/2013/10/paired-students-t-test.html http://vassarstats.net/tu.html

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The Case of More Than Two Dependent Samples

7.53

7.077.03

6.37

7.52 7.79

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Week 1 Week 2 Week 3

Usa

ge (g

ram

s)

Females Males

Total Usage Females : 21.63 grs / personTotal Usage Males : 21.68 grs / person

(***)

(***) vs. Week 1

(xxx)

(xxx) (xxx) vs. Week 1

Deodorant Usage in 3-Week Period The statistical method employed in this project was Repeated Measures ANOVA (in SPSS)

Please consult with your in-house Statistician if you face this kind of project

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Relationship Among Techniques: T-Test, ANOVA, ANCOVA, Regression

Interval or Ratio level

Source: Malhotra (2010)

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Some Practical Tips

Always focus on the research and business objectives when analyzing your data

Always prepare a DP Specs. Take your time to prepare a proper one. Get feedback from your DP if you’re not sure.

Once the data are ready, always check & recheck for errors. Compare the Excel tables to the SPSS raw data.

Before jumping to creating charts, do review the Excel tables from your DP. Look for patterns, interesting findings, anomalies. Try extracting and creating your preliminary story.

Plan the analysis early, even at the proposal stage. Envision the end results as early as possible. Consult with your in-house Statistician.

Phone: +62 818 906 875Email: ts.lim@leap-research.com

Leap ResearchSOHO Podomoro City, Unit 18-05

Jl. Letjen S. Parman Kav. 28Jakarta 11470

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QUESTIONSANY