Introduction to Statistics

Átírás

1 Introduction to Statistics Petra Petrovics

2 Statistics Statistics: is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. Practical activity to analyze data Set of data as a result of statistical activity Method Analyzing data Drawing conclusion

3 Central Statistical Office (HCSO) Independent administrative organization Operating under the direct supervision of the government Main tasks: Designing and conducting surveys, Recording Processing and storing data Data analyses- and dissemination, Protection of individual data.

4 Statistics Descriptive Statistics Study of how data can be summarized effectively to describe the important aspects of large data sets It turns data into information Data collection & analyzation Statistical Inference It is used when tentative conclusions about a population are drawn on the basis of a sample

5 Statistical Population All members of a specified group (N) It is a set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population. Discrete population Continuous population (interval)

6 Statistical Variables = Characteristic of a unit. (1) (2) Quantitative Qualitative Temporal Geographical Common Differential

7 Quantitative vs. Qualitative Quantitative data measures either how much or how many of something, i.e. a set of observations where any single observation is a number that represents an amount or a count. Qualitative data provide labels, or names, for categories of like items, i.e. a set of observations where any single observation is a word or code that represents a class or category. ~ categorical variable

8 Types of Quantitative Variables Continuous variables are those variables that have theoretically an infinite number of gradations between two measurements. For example, body weight of individuals, milk yield of cows or buffaloes etc. Most of the variables in biology are of continuous type. Discrete variables do not have continuous gradations but there is a definite gap between two measurements, i.e. they can not be measured in fractions. For example, number of eggs laid by hens, number of children in a family etc.

9 Scales of Measurement from weakest to strongest - nominal scale - ordinal scale - interval scale - ratio scale

10 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

11 2. Ordinal Scale Data elements may be ordered according to their relative size or quality, the numbers assigned to objects or events represent the rank order (1 st, 2 nd, 3 rd etc.) e.g. top lists of companies

12 3. Interval Scale Meaning of distances between any two observations The "zero point" is arbitrary Negative values can be used Ratios between numbers on the scale are not meaningful, so operations such as multiplication and division cannot be carried out directly e.g. temperature with the Celsius scale

13 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

14 Statistical Rows & Columns Classes Frequencies

15 Data Set 1. Mass of numerical data discrete values E.g: 11.8, 3.6, 16.6, 13.5, 3.6, 8.3, 8.9, 9.1, 7.7, 2.3, 12.1, 6.1, 10.2, 8.0, 11.4, 6.8, 9.6, 19.5, 15.3, 12.3, 8.5, 15.9, 18.7, 11.7, 6.2, 11.2, 10.4, 7.2, 5.5, Frequency distribution: method of organising & presenting data Score value Interval of score values: classes Statistical table records the number of observations in each class

16 Frequency table with score values Class Intervals Approximate class width: largest value - smallest value number of classes Number of class intervals: 2 k > N Gazdaságtudományi Kar Class Limits Frequency Class Limits Class Frequency Width Total Total 30

17 Statistical rows Types of Statistical Rows The main and partial Classifying population Same measures Comparative Generally: cannot add data Same types of data Descriptive Different types and measures of data Qualitative, Quantitative, Temporal, Geographical

18 Descriptive Rows Name Data Territory (Thousand qkm) 93,0 Population (Million people) 10,04 GDP (Billion Euro) 105,8 CPI (%) 106,1

19 Comparative Rows Year Hungarian Population (Thousand person) Temporal: Time series - Point of date - Discrete population summarize Temporal: Time series - Period - Continuous population We can summarize Year Number of marriage

20 Comparative Rows Geographical Country GDP (%) Hungary 4.2 Romania 5.7 Slovakia 4.6 Slovenia 3.4 Hungary, 2005 Year Expected lifetime (year) Men 68,6 Women 76,9 Source: Statistical Yearbook 2005 Qualitative

21 Classifying Rows Qualitative Temporal Geographical Product Period Turnover (Th HUF) Country A B C Total

22 Types of Quantitative Rows E.g: Water consumption in X village Water consumption (m 3 ) Number of houses f g (%) g (%) S (m 3 ) Z (%) Total Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency

23 Frequency (f): The number of times a value of the data occurs. Cumulative Frequency (f ): The sum of the frequencies for all values that are less than or equal to the given value. Water consumption (m 3 ) Number of houses f Total 50 - f k i 1 f i N

24 Relative Frequency (g): The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes. Cumulative Relative Frequency (g ): The term applies to an ordered set of observations from smallest to largest. The Cumulative Relative Frequency is the sum of the relative frequencies for all values that are less than or equal to the given value. Water consumption (m 3 ) g (%) g (%) Total g i fi (%) 100 (i 1,...,k) N

25 Sum of Values (S) x Water consumption Number of houses S (m 3 i i i ) (f) (m 3 ) * * * * *5 250 Total X i lower X i X i 2 x i : discrete value or middle of the class k i 1 S i f 1 X 1 S i 1... fk X k fi X i k f upper

26 Water consumption (m 3 ) Relative Sum of Values (Z) S (m 3 ) Z (%) Total S= Z i Si (%) 100 (i 1,...,k) S Z Z 1 i k i 1 Z i 1(100%)

27 Types of Statistical Tables Descriptive / Comparative Row Descriptive / Comparative Row Simple Table Classifying Row Classifying Row Descriptive / Comparative Row Classifying Table Classifying Row Combined Table

28 Statistical Table Statistical table: set of data arranged in rows and columns; It is important to have: title & source & measurements Signs: if we do not know the data: if there is not any data: 0

29 Name Data Territory (thousand qkm) 93,0 Population (million people) 10,04 GDP (billion euro) 105,8 CPI (%) 106,1 Source: HCSO (KSH) title measurements Data about Hungary (2008) source 1 dimension

30 Territory price index in Hungary (2008) Employed people Unemployed people Territory price index (Thousand people) Central Hungary 1245,5 80,5 Central Transdanubia 441,5 40,5 Western Transdanubia 408,2 36,5 Southern Transdanubia 337,4 42,3 Northern Hungary 397,6 69,9 Northern Great Plain 492,1 78,7 Southern Great Plain 474,8 53,3 Total 3797,1 401,7 Source: HCSO (KSH) 2 dimensions

31 Graphs

32 The Graphic Presentation of Data It allows to visualize important characteristics. Principals: Perspicuous Homogenous Aim oriented Simple Reconstructable Scaled

33 The Graphic Presentation of Time Series I Number of Accidents in Hungary Source: HCSO Line chart connects a series of data points together with a line

34 The Graphic Presentation of Time Series Natural Gas Consumption II Area chart to represent cumulated totals using numbers or percentages (stacked) over time; emphasizes a change in values

35 The Graphic Presentation of Time Series Change in the number of Employments III Source: Statistical Yearbook, Bar chart (Stacked) In case of time periods (x-axis: interval)

36 The Graphic Presentation of Quantitative Rows Source: Statistical Yearbook, Population Pyramide

37 The Graphic Presentation of Quantitative Rows Based on Word95.sav Scatterdot: Distribution of data points along one or two dimensions

38 The Graphic Presentation of Frequency Histogram bar chart grouped into a frequency distribution shows the quantity of points that fall within various numeric ranges Distribution

39 The Graphic Presentation of Frequency Frequency Polygon Distribution Connects data points through straight lines or higher order graphs x-axis: midpoint of each interval y-axis: absolute frequency Cumulative Distribution Frequency Tends to flatten out

40 The Graphic Presentation According Pie Chart: to Qualitative Variables 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

41 The Graphic Presentation According to Territory Variables Cartogram: map, showing quantitative information Pictogram

42 Thanks for your attention!