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PowerPoint Presentation 1 Chapter 1 What is statistics? 1 Lecture 1 What is statistics? • We are constantly being bombarded with statistics and statistical information For example – customer surveys –.
Lecture Chapter What is statistics? What is statistics? • We are constantly being bombarded with statistics and statistical information For example: – customer surveys – economic predictions – marketing information – political polls (proportion of people voting for candidate A or policy B) • How can we make sense out of all this data? What is statistics? Statistics Information Data “Statistics is a way to get information from data” Data: Facts, especially numerical facts, collected together for reference or information Information: Knowledge communicated concerning some particular fact “Statistics is a tool for creating new understanding from a set of numbers” Definitions: Oxford English Dictionary Key statistical concepts Population tổng thể, quần thề • A population is the group of all items of interest to a statistics practitioner • Frequently very large; sometimes infinite Example 1.4, page 4: An Australian automobile club and a new life insurance policy The population is all current million or so members of an automobile club Sample vật mẫu • A sample is a set of data drawn from the population • Potentially very large, but less than the population Example 1.4 (contd.): A sample of 500 members of the club selected Key statistical concepts Parameter tham số • A descriptive measure of a population Example 1.4 (Contd.): the proportion of all members who would purchase the new life insurance policy Statistic giá trị thống kê • A descriptive measure of a sample Example 1.4 (Contd.): the proportion of 500 selected members who would purchase the new life insurance policy Key statistical concepts Population Sample Subset Parameter Statistic • Populations have parameters • Samples have statistics • Examples of parameters / populations and statistics / samples?? Descriptive statistics • Methods of organizing, summarizing, and presenting data in a convenient and informative way These methods include: – graphical techniques (Chapters and 4), and – numerical techniques (Chapter 5) • The actual method used depends on what information you would like to extract Are you interested in: – measure(s) of central location and/or – measure(s) of variability (dispersion)? Descriptive statistics helps to answer these questions Inferential statistics • Descriptive statistics describes the data set that is being analysed, but does not allow us to draw any conclusions or make any inferences about the data Hence we need another branch of statistics: inferential statistics • Inferential statistics is also a set of methods, but it is used to draw conclusions or inferences about characteristics of populations based on data from a sample Statistical inference • Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample Population Sample Inference Parameter Statistic What can we infer about a population’s parameters based on a sample’s statistics? Statistical inference • We use the sample statistics to make inferences about the population parameters • Therefore, we can make an estimate, prediction, or decision about a population based on sample data • Thus, we can apply what we know about a sample to the larger population from which it was drawn Example 1.4 (contd.): Suppose 60 out of 500 selected members want to purchase the new life insurance policy (12%) a statistical inference may be made: about 12 % (or at least 10%) of all one million members would purchase the new policy Statistical inference • Rationale – Large populations make investigating each member impractical and expensive – It is easier and cheaper to take a sample and make estimates about the population from the sample • However – Such conclusions and estimates are not always going to be correct – For this reason, we build into the statistical inference 'measures of reliability', namely confidence level and significance level Statistical applications in economics & business • Statistical analysis plays an important role in virtually all aspects of business and economics • Throughout this course, we will see applications of statistics in: – – – – – – accounting economics finance human resources management marketing and operations management (See also cases on pages 7, 8, 9) Chapter Types of data, data collection and sampling 2.1 Types of data Optional reading: 2.2 Method of collecting data 2.3 & 2.4 Sampling and sampling plans 2.5 Sampling and non-sampling errors 13 Re-cap Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful information is produced Statistics Data Information Its methods make use of graphical techniques and numerical descriptive measures (such as averages) to summarize and present the data 14 Some useful definitions A variable is some characteristic of a population or sample E.g marks of IB2020A on the math exam (example, page 19) Typically denoted with a capital letter: X, Y, Z… The values of the variable are the range of possible values for a variable E.g student marks 0, 1, 2, …., 100 Data are the observed values of a variable E.g student marks: {67, 74, 71, 83, 93, 55, 48} 15 2.1 Types of data Data (at least for purposes of statistics) fall into three main groups: • Numerical (interval or quantitative) data • Nominal (categorical or qualitative) data kiệu đinh tính • Ordinal (ranked) data 16 Types of data Numerical data age income (pages 19, 20, 21) Nominal data person married Ordinal data exam grade HD 75 000 yes D 68 000 no C no P F data, computer brand all we weight gain With nominal With ordinal data, all we Food quality IBM can calculate is1 the +10 Excellent can use is computations that Dell proportion of data +5 involving theGood ordering Compaq falls into each category Satisfactory process IBM Poor IBM Dell Compaq other total 25 11 50 50% 22% 16% 12% 55 42 17 Calculations for Types of Data As mentioned above, • All calculations are permitted on numerical data • No calculations are allowed for nominal data, except counting the number of observations in each category and calculating their proportions • Only calculations involving a ranking process are allowed for ordinal data 18 Chapter Graphical descriptive techniques – Nominal data 3.1 Graphical techniques to describe nominal data Optional reading 3.2 Selecting the appropriate chart 3.3 Graphical techniques to describe ordinal data 3.4 Describing the relationship between nominal variables 13 3.1 Graphical techniques to describe nominal data The only allowable calculation on nominal data is to count the frequency of each value of the variable We can summarize the data in a table that presents the categories and their counts called a frequency distribution A relative frequency distribution lists the categories and the proportion with which each occurs 20 10 Example 3.1, page 45 • To determine the approximate market share of various women’s magazines in New Zealand, a women’s magazine readership survey was conducted using a sample of 300 readers • Data was collected and the count of the occurrences (frequencies) was recorded for each magazine • The frequencies were presented in a bar chart • Then the frequencies were converted to proportions and the results were presented in a pie chart 21 Example 3.1 (contd.) = Australian Women’s Weekly (NZ Edition); = NZ Women’s Weekly; = NZ Woman’s Day ; = NZ New Idea; = Next; and = That’s Life Magazine Frequency Percentage Australian Women's Weekly (1) 59 19.7 NZ Women's Weekly (2) 58 19.3 NZ Women's Day (3) 88 29.3 NZ New Idea (4) 39 13.0 Next (5) 35 11.7 That's Life (6) 21 7.0 300 100 Total 22 11 Example 3.1 (contd.): Excel representation Women's magazine readership, NZ, 2015 100 88 90 80 70 59 60 58 50 39 40 35 30 21 20 10 Australian Women's Weekly NZ Women's Weekly NZ Women's Day NZ New Idea Next That's Life 23 The size of each slice in a pie chart is proportional to the percentage corresponding to the category it represents Women's magazine readership, NZ, 2015 That's Life 7.0% Next 11.7% Australian Women's Weekly 19.7% (19.3)(3600)/100 = 69.60 NZ New Idea 13.0% NZ Women's Weekly 19.3% NZ Women's Day 29.3% 24 12 3.4 Describing the relationship between two nominal variables Now we will investigate the relationship between two nominal variables using either tabular or graphical techniques A cross-classification table is used to describe the relationship between two nominal variables A cross-classification table lists the frequency of each combination of the values of the two variables… 25 Example 3.7, page 67 • In a major Australian city there are four competing newspapers: N1, N2, N3 and N4 • To help design advertising campaigns, the advertising managers of the newspapers need to know which segments of the newspaper market are reading their papers • A survey was conducted to analyze the relationship between newspapers read and occupation 26 13 Example 3.7 (contd.) A sample of newspaper readers was asked to report which newspaper they read: N1, N2, N3, N4, and to indicate whether they were blue-collar worker (1), white-collar worker (2), or professional (3) By counting the number of times each of the 12 combinations occurs, we produced the Table 3.9 27 Example 3.7 (contd.) Interpretation: The relative frequencies in the rows and are similar, but there are large differences between rows and 2, and between rows and 28 14 Example 3.7 (contd.) Use the data from the cross-classification table to create bar charts - Professionals tend to Bar Chart 60 50 51 40 43 N1 38 37 30 N2 33 N3 29 27 20 18 10 22 21 N4 20 15 Blue colla White colla Professtional Occupation read newspaper N2 more than twice as often as newspaper N3 - Blue collar workers tend to read different newspapers from both white collar workers and professionals and that white collar and professionals are quite similar in their newspaper choice 29 Summary: Chapter page 40, Chapter page 73 Home assignment: - Section 2.1 Exercises pages 23 -24: 2.3, 2.5, 2.8 - Section 3.1 Exercises pages 60 - 61: 3.2, 3.3, 3.4 - Section 3.4 Exercises pages 71 - 72: 3.29, 3.30 30 15