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ATAF/ATRN RESEARCH METHODS WORKSHOP

QUANTITATIVE METHODS - Basic Tools and Principles for Data Analysis

Presented by: Alex Oguso

June 3 -6, 2019

Kenya School of Monetary Studies (KSMS)

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OUTLINE Descriptive statistics

Inferential Statistics

Hypothesis Testing

Simple Regression model

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Descriptive Statistics – Definitions

Variable – a characteristic or attribute of a unit or subject that can assume different values. The values that a variable can assume are called data.

Dependent/explained/endogenous vs independent/explanatory/exogenous variables

Discrete variable – has a basic unit of measurement that cannot be subdivided e.g number of taxpayers in a country

Continuous variable – unit of measurement can be subdivided infinitely e.g amount of tax payments.

Parameter: value that describes a population

Statistic: a value that describes a sample

Parametric tests - Assume data follows a particular distribution e.g. normal distribution

Non-parametric test - Nonparametric techniques are usually based on ranks/ signs rather than actual data

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Descriptive Statistics

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Descriptive Statistics – Measures of Central Tendency

Mean – is the arithmetic average of all observations

Median – the middle value in the data (50% cases above/50% cases

below). Is insensitive to extreme cases (outliers)

Mode – the most frequently occurring observation

Quartiles/Percentiles - Split Ordered Data into 4 Quarters or percentages

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Descriptive Statistics – Measures of Dispersion

• Range – difference between the smallest and the largest observation in a dataset

• Variance – average deviation of observations from the mean. Based on

sum of squared deviations from the mean:

High variance means that most scores are far away from the mean.

Low variance indicates that most scores cluster tightly about the mean

• Standard Deviation – square root of variance:

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Descriptive Statistics – Measures of Symmetry

Skewness

When most of the scores in a distribution land on one side of the scale or the other; not symmetrical; typically have a tail on one of the scale or the other.

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Descriptive Statistics – Measures of Asymmetry

Kurtosis

• If a distribution is symmetric, the next question is about the central peak: is it

high and sharp, or short and broad?

• A high kurtosis distribution has a sharper "peak" and fatter "tails", while a low kurtosis distribution has a more rounded peak with wider "shoulder”

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Descriptive Statistics – Statistical Graphs

• Graphs for numerical data:

- Histograms

- Frequency polygons

- Pie Charts

• Graphs for categorical data

- Bar graphs

- Pie Charts

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Inferential Statistics

• Involves use of information from samples to make inferences about the population

• Population - the total collection of all cases that the researcher wishes to understand better.

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Hypothesis Testing

• A hypothesis is an assumption about the population parameter. Hypotheses are mutually exclusive & exhaustive

Hypothesis Testing Steps

(i) State Null and alternative hypotheses

(ii) Compute the Test statistic (e.g sample mean)

(iii) P-value and interpretation (can be one sided or two-side P-value)

(iv) Significance level (optional) – e.g 95% level of significance

Hypothesis Testing - Example

• Null Hypothesis, H0 = States the Assumption to be tested e.g. The Presumptive tax compliance rate in Nairobi is not higher than the Country’s average (H0: 𝒙 < 50%)

• Alternative Hypothesis, H1 = Is the opposite of the null hypothesis e.g. The Presumptive tax compliance rate in Nairobi is higher than the Country’s average (H1: 𝒙 > 50%)

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Hypothesis Testing…

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Hypothesis Testing – Errors in Making Decisions

Type I Error - reject Null Hypothesis yet it is true

Type II Error – fail to reject Null Hypothesis yet it is false

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Practical Session

Simple regression model:

1. Running a simple regression on Excel & Eviews

2. Hypothesis testing using the regression results

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Q & A Session

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References • Henk Van Elst, H. (2013). Foundations Of Descriptive And Inferential Statistics. Lecture notes for the

Bachelor degree programmes, Karlshochschule International University, Karlsruhe, Germany.

• Fedor-Freybergh, P.G. & Mikulecky, M. (2005). From the descriptive towards inferential statistics: Hundred years since conception of the Student‘s t-distribution. Neuroendocrinology Letters No.3 Vol.26, June 2005.