management assignment

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Agenda Week 07

• W: basic data analysis

• F: core statistical analysis I

• Pop-up quizzes to earn bonus points – 5-10 minutes at the beginning of class

– Two chances to miss / drop a quiz

– Review important content before next class or do the “homework” will be helpful!

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Basic Data Analysis

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First things to do when you get data?

1. Become familiar with the data (variables and values)

2. Conduct descriptive analysis

3. Further understand the data using cross-tabulations

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Descriptive Analysis

• Summarize the basic characteristics of a variable such as:

• How frequently each value/response occurs – Frequency distribution (one-way frequency table)

• What the central or typical value is – Central tendency (mean, median, mode)

• Dispersion / variability of the variable – Range of the value (max - min)

– Deviation from the mean (standard deviation, variance)

• Choose appropriate statistics based on measurement type (nominal, ordinal, interval, ratio)

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Measurement Types (Revisit)

Ratio

Price

$3.25

$2.80

$1.85

$3.30

$2.25

$4.50

$3.75

Nominal (Identity)

ID Cereal

1 Heart to Heart

2 Cheerios

3 Rice Chex

4 Honey Bunches of Oats

5 Corn Flakes

6 Smart Start

7 Banana Nut Crunch

Ordinal (Order)

Rank 1 Rank 2

1 7

6 47

3 15

5 31

7 53

4 22

2 13

Interval (Distance)

Rating 1 Rating 2

9 5

1 -3

8 4

6 2

1 -3

7 3

8 4

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Frequency Distribution • Frequency table:

Number of respondents choosing each answer to a survey question – Frequency & percent

• Histogram: graphical way of showing frequency distribution – Frequency & percent

amount percentage

Under $50 5

50-99 10

100-149 20

150-199 30

200-249 25

About $250 10

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Central tendency • What the central or typical value is

• Mode: value occurs the most – There could be more than one mode

– {3,3,5,5,6,7}, 3 and 5 are the mode

• Median: the value separating the higher half of the data from the lower half – {3,3,5,6,7}, 5 is the median

– {3,3,4,5,6,7}, 4.5 is the median

• Mean: arithmetic average – {3,3,5,6,7}, 4.8 is the mean

• Nominal: mode

• Ordinal: mode, median

• Interval & ratio (metric data): mode, median, mean

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Dispersion • Range: difference between the largest value and the

smallest value

• Variance: mean squared deviation from the mean

– Technical detail: variance ∑

where

is individual value

is sample mean

• n is sample size

• Standard deviation: square root of variance

– Technical detail: ∑ 

• When the data points are clustered around the mean, the variance as well as s.d. are small

• Appropriate for interval and ratio variables

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Meaningful Statistics Summary

Measure Type Meaningful Descriptive Statistics

Example Analysis on Sample of Responses

Nominal scale Frequencies, Mode % of Sample that is Male

Ordinal scale Above + Median Median Ranking of Product

Interval scale Above + Range, mean, standard deviation

Mean Attribute Rating

Ratio scale Above + % Change % Increase in Sales

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Examples Typical “Generic” Questions

Typical Statistical approaches

What is the customers profile? Frequencies, histogram

What are the most common categories? Frequencies, histogram, mode

Which are the most and least critical service dimensions as perceived by customers?

Compute average rating for each service dimension

Is there any outliers? Histogram or range

How to measure the central tendency for a categorical variable?

Nominal: mode Ordinal: mode and median

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Cross-Tabulations

• If want to investigate the relationship between two or more categorical variables (nominal or ordinal) – Is tablet usage (light, heavy) related to gender

(male, female)?

– Is shopper type (1 store, 2 stores, 3 or more) related to income (low, middle, high)?

• Cross-tabs: combined frequency table

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Male Female Light 20 30 50 Heavy 35 35 70

55 65

Cross-Tabs • Crosstab of tablet usage and gender

• Conventional way is to put independent variable / predictor (e.g., demographics and lifestyle characteristics) in columns, and dependent variable / outcome (attitudes and behavior) in rows • so that each column represents a category of the

independent variable,

• and each row represents a category of outcome variable

Row variables

Column variables

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Cross-Tabs • Proportions are easier to understand than counts.

Proportions should be constructed at each category of the independent variable, across the dependent variable. – for a given category of independent variable, the proportions

should sum up to 100%

Male Female

Light 20 30 50

Heavy 35 35 70

55 65

Male Female

Light 20/55 30/65 50

Heavy 35/55 35/65 70

55 65

Male Female

Light 36% 46%

Heavy 64% 54%

100% 100%

• Seems to indicate that males are more likely to be heavy users of tablets (be cautious about causal interpretation!)

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Core Statistical Analysis I

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Inferential Statistics

• Unlike descriptive statistics which are used to describe characteristics of a sample, inferential statistics are used to make inferences about a population from a sample of that population – Based on a random sample of 1000

supermarkets, what is your estimate of market share of Faye Greek yogurt in all supermarkets in the U.S.? Did Faye reach its goal? Did it increase compared to last year?

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Why Making Inference?

• Why not study the entire population? – Time-consuming and expensive to do census

– Not all units in the population can be identified

– Not feasible to conduct test on the whole population

Population:

Total collection of objects or people to be studied

Sample:

Subset of a population

Make inference

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Sample Statistics and Population Parameters (Revisit)

• Sample statistics are measures computed from the sample data

• Population parameters are characteristics of the population

• Generally we do not know these population parameters so we use the corresponding sample statistics as estimates

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Uncertainty in Making Inference • However, these sample statistics are not exactly the

value of the population parameter – Sample market share is 5.2%, what is the true market

share? Remember confidence interval?

• So we need to take into account the inaccuracy of the sample statistics when we want to make a judgement about the population parameter – Sample market share is 5.2%, 95% confidence interval is

5.1% to 5.3%, did Faye reach its targeted market share of 5%?

• Hence the whole process of doing hypothesis testing

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Hypothesis Testing

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Null Hypothesis

Test-statistic P-value