INTRODUCTION TO STATISTICS

Yrd. Doç. Dr. Elif TUNA

Statistics: Statistics is the science that deals with the collection, analysis, and interpretation of numerical information.

This science can be divided into two areas: descriptive statistics and inferential statistics. In descriptive statistics ,techniques are provided for processing raw numerical data into usable forms. These techniques include methods for collecting, organising, summarising, describing and presenting numerical information.

Statistics

Statistics

Descriptive Statistics

Inferential Statistics

Inferential Statistics

Tools for Collecting Data

Survey Design Steps

Survey Design Steps

Types of Questions

Populations and Samples

Key Definitions

Population vs. Sample

Why Sample?

Sampling Techniques

Statistical Sampling

Simple Random Sampling

Stratified Random Sampling

Systematic Random Sampling

Cluster Sampling

DATA TYPES

Variable: In statistics, variables are measurable characteristics of things (persons, objects, places, etc) that vary within a group of such things. A quantitative variable is determined when the description of the characteristic of interest results in a numerical value. When a measurement is required to describe the characteristic of interest or it is necessary to perform a count to describe the characteristic, a quantitative variable is defined. A qualitative variable is determined when the description of the characteristic of interest results in a nonnumerical value. A qualitative variable may be classified into two or more categories. A discrete variable is a quantitative variable whose values are countable. Discrete variables usually result from counting. A continuous variable is a quantitative variable that can assume any numerical value over an interval or over several intervals.

Data Types

Data Types

Time Series Data

Ordered data values observed over time.

Cross Section Data

Data values observed at a fixed point in time

Panel Data

Combines time series and cross section data

Data Types

Data Measurement Levels

Nominal scale: Nominal-level measurement is the most basic level of measurement in which the things being measured are simply classified into unique categories. Categories on nominal scales are not ordered in any way (e.g. , from small to large) , and numbers are used only as labels for categories. The arithmetic operations of addition, subtraction, multiplication, and division are not performed for nominal data. Thus, car licence numbers are an example of a nominal scale. The minimum number of categories on a nominal scale is two (e.g., whether a coin lands heads or tails) and there can be as many categories as needed.

Data Measurement Levels

Ordinal Scale : Ordinal-level measurement is the next level above nominal. Now the categories are ordered: ranked according to the magnitude of the characteristic being measured. Each category can now be said to be greater than (>), or less than (<) its neighbor, depending on the amount of the characteristic it represents. Some examples of ordinal scales are : ranking the size of a set of objects on a three-number scale (1=small, 2=medium, 3=large) ; ranking the quality of movies on a five-number scale (from 1=very bad, to 5=excellent) ; and ranking the aggressiveness of children at play on a ten-number scale (1=unaggressive, to 10=very aggressive)

Data Measurement Levels

Interval Scale : Interval-level is the next higher level of measurement above ordinal level. Its scales include the properties of nominal and ordinal scales. Interval scales have arbitrary and not absolute zero points. One example of an interval scale is the Celsius (or centigrade) scale for temperature.

Data Measurement Levels

Ratio Scale : Ratio level is the highest level of measurement. Its scales include the properties of nominal and ordinal , and interval scales, and now in addition also have absolute zeros. This means that at the zero value on a ratio scale , the characteristic being measured has decreased to the point where it is not present or least it is not observable. Because numbers on such scales now represent distances from an absolute zero , it is legitimate to calculate ratios between measurements on the scale: to express one measurement as a multiple of another.

Data Measurement Levels