Business Statistics CONTENTS Key questions Roadmaps for - - PowerPoint PPT Presentation

CHOOSING THE RIGHT TEST

Business Statistics

Key questions Roadmaps for statistical tests A decision tree Old exam question Further study CONTENTS

▪ number of variables

▪ 1, 2, more than 2

▪ number of subpopulations

▪ 1, 2, more than 2

▪ types of data

▪ numerical, categorical

▪ parameter to test

▪ centrality, dispersion, proportion, ...

▪ characteristics of the population

▪ normal, symmetric, ...

▪ paired/independent variables ▪ association vs. comparison KEY QUESTIONS

Some tests can be conceived in different ways ▪ Example:

▪ ANOVA: comparing 𝜈 of >2 numerical variables 𝑌1, 𝑌2, 𝑌3, ... ▪ or: association between categorical 𝑌 and numerical 𝑍

▪ Here we focus on the most usual approach KEY QUESTIONS

One sample ▪ centrality 𝐼0: 𝜈 = 𝜈0 or 𝐼0: 𝑁 = 𝑁0

▪ CLT-conditions and 𝜏 known: 𝑨-test ▪ CLT-conditions and 𝜏 unknown: 𝑢-test ▪ symmetric distribution: Wilcoxon signed ranks test ▪ sign test

▪ dispersion 𝐼0: 𝜏2 = 𝜏0

2

▪ normal population: 𝜓2-test

▪ proportion 𝐼0: 𝜌 = 𝜌0

▪ binomial test ▪ 𝑜𝜌 ≥ 5 and 𝑜 1 − 𝜌 ≥ 5: normal approximation

ROADMAPS FOR STATISTICAL TESTS

CLT-conditions: 𝑜 < 15: normal population 15 ≤ 𝑜 < 30: symmetric population 𝑜 ≥ 30: no restrictions

Two related (dependent) samples ▪ comparison of “similar” variables:

▪ convert into one-sample situation ▪ e.g., 𝐸 = 𝑌𝑏𝑔𝑢𝑓𝑠 − 𝑌𝑐𝑓𝑔𝑝𝑠𝑓 and 𝐼𝑝: 𝜈𝐸 = 0

▪ association between two “dissimilar” variables:

▪ two numerical variables: ▪ normal populations: correlation (𝑢-test) ▪ rank correlation (𝑨-test) ▪ normal error term: simple regression (𝐺-test and 𝑢-test)

ROADMAPS FOR STATISTICAL TESTS

Two independent subpopulations ▪ centrality 𝐼0: 𝜈1 = 𝜈2 or 𝐼0: 𝑁1 = 𝑁2

▪ CLT-conditions and 𝜏1 and 𝜏2 known: 𝑨-test ▪ CLT-conditions and 𝜏1 = 𝜏2 unknown: 𝑢-test ▪ CLT-conditions and 𝜏1 and 𝜏2 unknown but not necessarily equal: 𝑢-test ▪ distribution equally-shaped: Wilcoxon-Mann-Whitney test

▪ dispersion 𝐼0: 𝜏1

2 = 𝜏2 2

▪ normal populations: 𝐺-test ▪ Levene’s test

▪ proportion 𝐼0: 𝜌1 = 𝜌2

▪ 𝑨-test

ROADMAPS FOR STATISTICAL TESTS

More than two independent subpopulations ▪ centrality 𝐼0: 𝜈1 = 𝜈2 = 𝜈3 or 𝐼0: 𝑁1 = 𝑁2 = 𝑁3

▪ normal populations and equal variances: ANOVA ▪ equally-shaped distributions and group sizes>5: Kruskal-Wallis test

▪ independence of two categorical variables

▪ expected count ≥ 5: 𝜓2-test on contingency table

▪ dispersion 𝐼0: 𝜏1

2 = 𝜏2 2 = 𝜏3 2

▪ Levene’s test

ROADMAPS FOR STATISTICAL TESTS

More than two related samples ▪ dependence of one numerical variable on several other numerical variables:

▪ normal error term and linear relation: multiple regression (𝐺-test and 𝑢-test)

▪ dependence of one numerical variable on several other categorical variables:

▪ normal error term: multiple regression with dummy variables (𝐺- test and 𝑢-test)

ROADMAPS FOR STATISTICAL TESTS

Which test to use when:

• a. comparing the mean of the income of men and women?
• b. comparing the variance of the income of men and women?
• c. the relation between the color of a car and its probability of

being involved in an accident?

• d. the relation between the color of a car and the gender of its
• wner?
• e. the relation between the mean of the income and ethnicity

(black, white, Asian)?

• f. the relation between income and IQ?

EXERCISE 1

A DECISION TREE

A DECISION TREE

A DECISION TREE

A DECISION TREE

A DECISION TREE

21 May 2015, Q2d OLD EXAM QUESTION

Doane & Seward 5/E missing Tutorial exercises week 6 choosing 1 choosing 2 FURTHER STUDY