introduction to statistics - university of...

• Gazdaságtudományi Kar• Gazdaságelméleti és Módszertani Intézet

Petra Petrovics

Introduction to Statistics


Statistics

Statistics: is a mathematical sciencepertaining to the collection, analysis,interpretation or explanation, andpresentation of data.

• Practical activity – to analyze data

• Set of data – as a result of statistical activity

• Method

• Analyzing data

• Drawing conclusion


Data Gathering• Trends and reports overview

• Observations

• Interview

• Focus group

• Survey

• Photo interview


Statistical Inference

• Study of how data can besummarized effectively todescribe the importantaspects of large data sets

• It turns data intoinformation

• Data collection &analyzation

• It is used when tentativeconclusions about apopulation are drawn onthe basis of a sample

Statistics

Descriptive Statistics


Statistical Population

• All members of a specified group (N)

• It is a set of entities concerning whichstatistical inferences are to be drawn, oftenbased on a random sample taken from thepopulation.

– Discrete population

– Continuous population (interval)


Statistical Variables= Characteristic of a unit.

(1)• Quantitative • Qualitative• Temporal• Geographical

(2)• Common• Differential


Quantitative vs. Qualitative• Quantitative data measures either how

much or how many of something, i.e. aset of observations where any singleobservation is a number that representsan amount or a count.

• Qualitative data provide labels, ornames, for categories of like items, i.e. aset of observations where any singleobservation is a word or code thatrepresents a class or category.

~ categorical variable


Types of Quantitative Variables• Continuous variables are those variables that have

theoretically an infinite number of gradationsbetween two measurements.For example, body weight of individuals, milk yield of cows orbuffaloes etc. Most of the variables in biology are of continuoustype.

• Discrete variables do not have continuous gradationsbut there is a definite gap between twomeasurements, i.e. they can not be measured infractions.For example, number of eggs laid by hens, number of children

in a family etc.


Scales of Measurement

from weakest to strongest

- nominal scale

- ordinal scale

- interval scale

- ratio scale


1. Nominal Scale• Numbers are labels of groups or classes

• Simple codes assigned to objects as labels

• For qualitative data, e.g. professional classification, geographic classification

• e.g. - blonde: 1, brown: 2, red: 3, black: 4

(a person with red hair does not possess more "hairness" than a person with blonde hair)

- female: 1, male: 2


2. Ordinal Scale

• Data elements may be ordered accordingto their relative size or quality, thenumbers assigned to objects or eventsrepresent the rank order (1st, 2nd, 3rd etc.)

• e.g. top lists of companies


3. Interval Scale

• Meaning of distances between any twoobservations

• The "zero point" is arbitrary

• Negative values can be used

• Ratios between numbers on the scale are notmeaningful, so operations such asmultiplication and division cannot be carriedout directly

• e.g. temperature with the Celsius scale


4. Ratio Scale

• Strongest scale of measurement

• Distances between observations and also the ratios of distances have a meaning

• Contains a meaningful zero

• e.g. mass, length, time

a salary of $50,000 is twice as large as a salary of $25,000


Graphs


The Graphic Presentation of Data

• It allows to visualize important characteristics.

• Principals:

− Perspicuous− Homogenous− Aim oriented− Simple− Reconstructable− Scaled


The Graphic Presentation of Time Series I

Source: HCSO

Number of Accidents in Hungary

Line chartconnects a series of data points together with a line


The Graphic Presentation of Time Series II

Area chartto represent cumulated totals using numbers or percentages (stacked) over time; emphasizes a change in values

Natural Gas Consumption


The Graphic Presentation of Time Series III

Source: Statistical Yearbook, 2005.

Change in the number of Employments

Bar chart (Stacked)In case of time periods (x-axis: interval)


The Graphic Presentation of Quantitative Rows

Population Pyramide

Source: Statistical Yearbook, 2005.


The Graphic Presentation of Quantitative Rows

Scatterdot: Distribution of data points along one or two dimensions

Based on Word95.sav


The Graphic Presentation of FrequencyDistribution

Histogram

• bar chart• grouped into a

frequency distribution• shows the quantity of

points that fall withinvarious numeric ranges


The Graphic Presentation of FrequencyDistribution

Frequency Polygon

• Connects data points throughstraight lines or higher order graphs

• x-axis: midpoint of each interval• y-axis: absolute frequency

Cumulative FrequencyDistribution

Tends to flatten out


The Graphic Presentation Accordingto Qualitative Variables

Pie Chart:

• Proportional relationships at a point in time• Shows percentage values as a slice of a pie• Compare part of a whole at a given point in time


The Graphic Presentation Accordingto Territory Variables

Cartogram: map, showing quantitative information

Pictogram


Thanks for your attention!

introduction to statistics - university of...

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