Introduction to Applied Statistics

1. Introduction to Applied Statistics CHAPTER 1 BCT2053

2. CONTENT 1.1 Statistical Terminologies 1.2 Statistical Problem-Solving Methodology 1.3 Review of Descriptive Statistics 1.3.1 Measures of Central Tendency 1.3.2 Measures of Variation 1.3.2.1 Game of Darts 1.4 Exploratory Data Analysis 1.4.1 Stem and Leaf Plot 1.4.2 Boxplots

3. OBJECTIVE • By the end of this chapter, you should be able to • Define the meaning of statistics, population, sample, parameter, statistic, descriptive statistics and inferential statistics. • Understand and explain why a knowledge of statistics is needed • Outline the 6 basic steps in the statistical problem solving methodology. • Identifies various method to obtain samples. • Discuss the role of computers and data analysis software in statistical work. • Summarize data using measures of central tendency, such as the mean, median, mode, and midrange. • Describe data using measures of variation, such as the range, variance, and standard deviation. • Identify the position of a data value in a data set, using various measures of position, such as percentiles, deciles, and quartiles. • Analyze accuracy and precision of data using game of darts. • Draw and interpret a stem and leaf plot. • Draw and interpret a boxplot.

4. 1.1 OVERVIEW • Define the meaning of statistics, population, sample, parameter, statistic, descriptive statistics and inferential statistics. • Understand and explain why a knowledge of statistics is needed

5. What is Statistics? Most people become familiar with probability and statistics through radio, television, newspapers, and magazines. For example, the following statements were found in newspapers: • Ten of thousands parents in Malaysia have chosen StemLife as their trusted stem cell bank. • The death rate from lung cancer was 10 times for smokers compared to nonsmokers. • The average cost of a wedding is nearly RM10,000. • In USA, the median salary for men with a bachelor’s degree is $49,982, while the median salary for women with a bachelor’s degree is $35,408. • Globally, an estimated 500,000 children under the age of 15 live with Type 1 diabetes. • Women who eat fish once a week are 29% less likely to develop heart disease.

6. Statistics • is the sciences of conducting studies to collect, organize, summarize, analyze, present, interpret and draw conclusions from data. Any values (observations or measurements) that have been collected

7. The basic idea behind all statistical methods of data analysis is to make inferences about a population by studying small sample chosen from it Population The complete collection of measurements outcomes, object or individual under study Parameter A number that describes a population characteristics • Tangible • Always finite & after a population is sampled, the population size decrease by 1 • The total number of members is fixed & could be listed Conceptual Population that consists of all the value that might possibly have been observed & has an unlimited number of members Sample A subset of a population, containing the objects or outcomes that are actually observed • Statistic • A number that describes a sample characteristics

8. EXERCISE 1.1 • The freshman class at IT College has 317 students and an IQ pre-test is given to all of them in their first week. The dean of admission collected data on 27 of them and found their mean score on the IQ pre-test was 51. The mean for the entire freshman class was therefore estimated to approximately 51 on this test. A subsequent computer analysis of all freshmen showed the true mean to be 52. Based on the above problem, • What is the population? • Is the population tangible or conceptual? • What is the sample? • What number is a parameter? • What number is a statistic?

9. Descriptive statistics consists of the collection, organization, classification, summarization, and presentation ofdata obtain from the sample. Used to describe thecharacteristics of the sample Used to determine whether the sample represent the target population by comparing sample statistic and population parameter Descriptive & Inferential Statistics • Inferential statistics • consists ofgeneralizing from samples to populations, performing estimations hypothesis testing, determining relationships among variables, and making predictions. • Used to describe, infer, estimate, approximate the characteristics of the target population • Used when we want to draw a conclusionfor the data obtain from the sample

10. EXERCISE 1.1 • In each of these statements, tell whether descriptive or inferential statistics have been used. • Ten of thousands parents in Malaysia have chosen StemLife as their trusted stem cell bank. (Descriptive) • The death rate from lung cancer was 10 times for smokers compared to nonsmokers. (Inferential) • The average cost of a wedding is nearly RM10,000. • In USA, the median salary for men with a bachelor’s degree is $49,982, while the median salary for women with a bachelor’s degree is $35,408. • Globally, an estimated 500,000 children under the age of 15 live with Type 1 diabetes. • A researcher claim that a new drug will reduce the number of heart attacks in men over 70 years of age.

11. An overview of descriptive statistics and statistical inference

12. Need for Statistics • It is a fact that, you need a knowledge of statistics to help you: • Describe and understand numerical relationship between variables • There are a lot of data in this world so we need to identify the right variables. • Make better decision • Statistical methods allow people to make better decisions in the face of uncertainty.

13. Describing relationship between variables • A management consultant wants to compare a client’s investment return for this year with related figures from last year. He summarizes masses of revenue and cost data from both periods and based on his findings, presents his recommendations to his client. • A college admission director needs to find an effective way of selecting student applicants. He design a statistical study to see if there’s a significance relationship between SPM result and the gpa achieved by freshmen at his school. If there is a strong relationship, high SPM result will become an important criteria for acceptance.

14. Aiding in Decision Making • Suppose that the manager of “Big-Wig Executive Hair Stylist”, Alvin Tang, has advertised that 90% of the firm’s customers are satisfied with the company’s services. If Pamela, a consumer activist, feels that this is an exaggerated statement that might require legal action, she can use statistical inference techniques to decide whether or not to sue Alvin. • Students and professional people can also use the knowledge gained from studying statistics to become better consumers and citizens. For example, they can make intelligent decisions about what products to purchase based on consumer studies about government spending based on utilization studies, and so on.

15. 1.2: STATISTICAL PROBLEM SOLVING METHODOLOGY • Outline the 6 basic steps in the statistical problem • solving methodology. • Identifies various method to obtain samples. • Discuss the role of computers and data analysis • software in statistical work.

16. STATISTICAL PROBLEM SOLVING METHODOLOGY 6 Basic Steps • Identifying the problem or opportunity • Deciding on the method of data collection • Collecting the data • Classifying and summarizing the data • Presenting and analyzing the data • Making the decision

17. STEP 1Identifying the problem or opportunity • Must clearly understand & correctly define the objective/goal of the study • If not, time & effort are waste • Is the goal to study some population? • Is it to impose some treatment on the group & then test the response? • Can the study goal be achieved through simple counts or measurements of the group? • Must an experiment be performed on the group? • If sample are needed, how large?, how should they be taken? – the larger the better (more than 30)

18. Characteristics of Sample Size • The larger the sample, the smaller the magnitude of sampling errors. • Survey studies needed large sample because the returns of the survey is voluntary based. • Easy to divide into subgroups. • In mail response the percentage of response may be as low as 20%-30%, thus the bigger number of samples is required. • Subject availability and cost factors are legitimate considerations in determining appropriate sample size.

19. STEP 2Deciding on the Method of Data Collection • Data must be gathered that are accurate, as complete as possible & relevant to the problem • Data can be obtained in 3 ways • Data that are made available by others (internal, external, primary or secondary data) • Data resulting from an experiment (experimental study) • Data collected in an observational study (observation, survey, questionnaire, interview)

20. STEP 3Collecting the data • Nonprobability data • Is one in which the judgment of the experimenter, the method in which the data are collected or other factors could affect the results of the sample • 3 basic methods: Judgment samples, Voluntary samples and Convenience samples • Probability data • Is one in which the chance of selection of each item in the population is known before the sample is picked • 4 basic methods : random, systematic, stratified, and cluster.

21. A) Nonprobability Data Samples • Judgment samples • Base on opinion of one or more expert person • Ex: A political campaign manager intuitively picks certain voting districts as reliable places to measure the public opinion of his candidate • Voluntary samples • Question are posed to the public by publishing them over radio or tv (phone or sms) • Convenience samples • Take an ‘easy sample’ (most conveniently available) • Ex: A surveyor will stand in one location & ask passerby their questions

22. B) Probability Data Samples • Random samples • Selected using chance method or random methods • Example: • A lecturer wants to study the physical fitness levels of students at her university. There are 5,000 students enrolled at the university, and she wants to draw a sample of size 100 to take a physical fitness test. She obtains a list of all 5,000 students, numbered it from 1 to 5,000 and then randomly invites 100 students corresponding to those numbers to participate in the study.

23. B) Probability Data Samples • Systematic samples • Numbering each subject of the populations and data is selected every kth number. • Example: • A lecturer wants to study the physical fitness levels of students at her university. There are 5,000 students enrolled at the university, and she wants to draw a sample of size 100 to take a physical fitness test. She obtains a list of all 5,000 students, numbered it from 1 to 5,000 and randomly picks one of the first 50 voters (5000/100 = 50) on the list. If the pick number is 30, then the 30th student in the list should be invited first. Then she should invite the selected every 50th name on the list after this first random starts (the 80th student, the 130th student, etc) to produce 100 samples of students to participate in the study.

24. B) Probability Data Samples • Stratified samples • Dividing the population into groups according to some characteristics that is important to the study, then sampling from each group • Example: • A lecturer wants to study the physical fitness levels of students at her university. There are 5,000 students enrolled at the university, and she wants to draw a sample of size 100 to take a physical fitness test. Assume that, because of different lifestyles, the level of physical fitness is different between male and female students. To account for this variation in lifestyle, the population of student can easily be stratified into male and female students. Then she can either use random method or systematic methods to select the participants. As example she can use random sample to chose 50 male students and use systematic method to chose another 50 female students or otherwise.

25. B) Probability Data Samples • Cluster samples • Dividing the population into sections/clusters, then randomly select some of those cluster and then choose all members from those selected cluster • Using a cluster sampling can reduce cost and time. • Example: • A lecturer wants to study the physical fitness levels of students at her university. There are 5,000 students enrolled at the university, and she wants to draw a sample to take a physical fitness test. Assume that, because of different lifestyles, the level of physical fitness is different between freshmen, sophomores, juniors and seniorsstudents. To account for this variation in lifestyle, the population of student can easily be clustered into freshmen, sophomores, juniors and seniorsstudents. Then she can choose any one cluster such as freshmen and take all the freshmen students as the participant.

26. EXERCISE 1.2 • In each of these statements, identify the type of sample obtain. • A quality engineer wants to inspect rolls of wallpaper in order to obtain information on the rate at which flows in the printing are occurring. She decides to draw a sample of 50 rolls of wallpaper from a day’s production. Each hour for 5 hours, she takes the 10 most recently produced rolls and counts the number of flaws on each. • Suppose a researcher have a list of 1000 registered voters in a community and he want to pick a probability sample of 50. He use a random number table to pick one of the first 20 voters (1000/50 = 20) on our list. The table gave him the number of 16, so he select the 16th voter on the list as the first selected number. Then he pick every 20th name after this random start (the 36th voter, the 56th voter, etc) to produce a sample. • A researcher wanted to survey students in 100 homerooms in secondary school in a large school district. They randomly select 10 schools from all the secondary schools in the district. Then from a list of homerooms in the 10 schools they randomly select 100 homerooms.

27. EXERCISE 1.2 • In each of these statements, identify the type of sample obtain. • In a consumer surveys of large cities the procedure is to divide a map of the city into small blocks. Each blocks containing a cluster are surveyed. A number of clusters are selected for the sample, and all the households in a cluster are surveyed. • Using a cluster sampling can reduce cost and time. Less energy and money are expended if an interviewer stays within a specific area rather than traveling across stretches of the cities. • Suppose our population is a university student body. We want to estimate the average annual expenditures of a college student for non school items. Assume we know that, because of different lifestyles, juniors and seniors spend more than freshmen and sophomores, but there are fewer students in the upper classes than in the lower classes because of some dropout factor. To account for this variation in lifestyle and group size, the population of student can easily be stratified into freshmen, sophomores, junior and seniors. A sample can be stratum and each result weighted to provide an overall estimate of average non school expenditures.

28. STEP 4Classifying and Summarizing the Data • Organize or group the facts/sample raw data for study and investigation • Classifying- identifying items with like characteristics & arranging them into groups or classes. • Ex: Production data (product make, location, production process,…) • Data can be classified as Qualitative (categorical/Attributes) data and Quantitative (Numerical) data. • Summarization • Graphical & Descriptive statistics ( tables, charts, measure of central tendency, measure of variation, measure of position)

29. Data Classification • Data are the values that variables can assume • Variables is a characteristic or attribute that can assume different values. • Variables whose values are determined by chance are called random variables Variables can be classified By how they are categorized, counted or measured - Level of measurements of data As Quantitative and Qualitative

30. Qualitative (categorical/Attributes) 1*Data that refers only to name classification (done using numbers) 2* Can be placed into distinct categories according to some characteristic or attribute. Nominal Data (can’t be rank) Gender, race, citizenship. etc Types of Data Use code numbers (1, 2,…) Ordinal Data (can be rank) Feeling (dislike – like), color (dark – bright) , etc Likert scale Discrete Variables Assume values that can be counted and finite Ex : no of “something” Quantitative (Numerical) 1*Data that represent counts or measurements (can be count or measure) 2*Are numerical in nature and can be ordered or ranked. Continuous variables 1. Can assume all values between any two specific values & it obtained by measuring 2. Have boundaries and must be rounded because of the limits of measuring device Ex: weight, age, salary, height, temperature, etc

31. EXERCISE 1.2 • The Lemon Marketing Corporation has asked you for information about the car you drive. For each question, identify each of the types of data requested as either attribute data or numeric data. When numeric data is requested, identify the variable as discrete or continuous. • What is the weight of your car? • In what city was your car made? • How many people can be seated in your car? • What’s the distance traveled from your home to your school? • What’s the color of your car? • How many cars are in your household? • What’s the length of your car? • What’s the normal operating temperature (in degree Fahrenheit) of your car’s engine? • What gas mileage (miles per gallon) do you get in city driving? • Who made your car? • How many cylinders are there in your car’s engine? • How many miles have you put on your car’s current set of tyres?

32. Level of Measurements of Data Examples

33. EXERCISE 1.2 • The chart shows the number of job-related injuries for each of the transportation industries for 1998. I • What are the variables under study? • Categorize each variable as qualitative or quantitative. • Categories each quantitative variables as discrete or continuous. • Identify the level of measurement for each variable.

34. STEP 5Presenting and Analyzing the data • Summarized & analyzed information given by the • graphical statistics (graph and chart) • descriptive statistics (refer topic 1.3) • Identify the relationship of the information • Making any relevant statistical inferences • hypothesis testing • confidence interval • ANOVA • control charts, …

35. Types of Graph & Chart • The purpose of graphs in statistics is to convey the data to the viewer in pictorial form. • Graphs are useful in getting the audience’s attention in a publication or a presentation.

36. Types of Graph & Chart

37. Bell Shaped Has a single peak & tapers off at either end Approximately symmetry It is roughly the same on the both sides of a line running through the center J-Shaped Has a few data values on the left side & increase as one move to the right Uniform Basically flat/rectangular Reverse J-Shaped Opposite J-Shaped Has a few data values on the right side & increase as one move to the left Distribution Shapes for Histogram

38. Distribution Shapes for Histogram • Right Skewed • The peak is to the left • The data value taper off to the right • Bimodal • Have 2 peak at the same height • Left Skewed • The peak is to the right • The data value taper off to the left • U-Shaped • The shape is U

39. STEP 6Making the decision • The researchers can make a list of all the options and decisions which can achieve the objective and goal of the research, weighs the options and choose the best options which represents the ‘best’ solution to the problem. • The correctness of this choice depends on the analytical skill and the quality of the information.

40. Statistical Problem Solving Methodology No Yes Yes No

41. Role of the Computer in Statistics Two software tools commonly used for data Analysis: • Spreadsheets • Microsoft Excel & Lotus 1-2-3 • Statistical Packages • MINITAB, SAS, SPSS and SPlus

42. Data AnalysisAplication in EXCEL • Graph and chart • Formulas • Add in – AnalisisTool Park – Data Analysis

43. 1.3: REVIEW OF DESCRIPTIVE STATISTICS • Summarize data using measures of central tendency, such as • the mean, median, mode, and midrange. • Describe data using measures of variation, such as the range, variance, and standard deviation. • Identify the position of a data value in a data set, using various measures of position, such as percentiles, deciles, and quartiles.

44. Summary Statistics (Data Description) • Statistical methods can be used to summarize data. • Measures of average are also called measures of central tendencyand include the mean, median, mode, and midrange. • Measures that determine the spread of data values are called measures of variation or measures of dispersion and include the range, variance, and standard deviation. • Measures of position tell where a specific data value falls within the data set or its relative position in comparison with other data values. The most common measures of position are percentiles, deciles, and quartiles. • The measures of central tendency, variation, and position are part of what is called traditional statistics. This type of data is typically used to confirm conjectures about the data.

45. Casio fx-570MS Insert data MODE SD data M+ Shift 1 Shift 2 Clear data Shift CLR 1 Casio fx-570W Insert data MODE SD data M+ Shift 1 Shift 2 Shift 3 Shift 4 Clear data Shift AC/ON = TIPS: INSERT & CLEAR DATA by using Scientific Calculator ROUNDING RULE: The value of statistic/parameter should be rounded to one more decimal place than occurs in the raw data

46. 1.3.1 Measures of Central Tendency Mean the sum of the values divided by the total number of values. Population Mean Sample Mean Example: 9 2 1 4 3 3 7 5 8 6 ,

47. Properties of Mean • The mean is compute by using all the values of the data. • The mean varies less than the median or mode when samples are taken from the same population and all three measures are computed for these samples. • The mean is used in computing other statistics, such as variance. • The mean for the data set is unique, and not necessarily one of the data values. • The mean cannot be computed for an open-ended frequency distribution. • The mean is affected by extremely high or low values and may not be the appropriate average to use in these situations

48. 1.3.1 Measures of Central Tendency Median the middle number of n ordered data (smallest to largest) If n is odd If n is even Example: 9 2 1 3 3 7 5 8 6 MD = 5 Example: 9 2 1 4 3 3 7 5 8 6 MD = 4.5

49. Properties of Median • The median is used when one must find the center or middle value of a data set. • The median is used when one must determine whether the data values fall into the upper half or lower half of the distribution. • The median is used to find the average of an open-ended distribution. • The median is affected less than the mean by extremely high or extremely low values. • Try this data: 19 2 1 4 3 3 7 5 8 6

50. 1.3.1 Measures of Central Tendency Mode the most commonly occurring value in a data series • The mode is used when the most typical case is desired. • The mode is the easiest average to compute. • The mode can be used when the data are nominal, such as religious preference, gender, or political affiliation. • The mode is not always unique. A data set can have more than one mode, or the mode may not exist for a data set. Example: 9 2 1 4 3 3 7 5 8 6 Mode = 3