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Lecture One What is Statistics? Lecturer Madgerie Jameson (Dr) Madgerie.Jameson@sta.uwi.edu

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Course Learning Objectives Differentiate between descriptive and inferential statistics Understand and distinguish the types of data Be able to compute mathematical equations Be familiar with notation and terminology Know how to summarize data appropriately Understand measures of central tendency and variability

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Definition of Statistics A set of tools and techniques that is used for describing, organising and interpreting information or data (Salkind, 2008, p.7). The methods used to collect, organise, summarise, analyse, interpret and draw collusions from a given data set.

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Why Educators Need to Know about Statistics To know how to: Properly present information Draw conclusions about populations based on sample information Interpret test data Incorporate testing data into classroom practice Provide evidence for best practices

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StatisticsDescriptiveInferential

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Descriptive Statistics Used to collect, organise, summarise and present a data set. It is usually presented graphically. For example the following table shows the names of 12 students and their M.Ed majors. You can use the descriptive data to find the most popular choice of subject and the average age of students enrolled in the course.

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StudentMajorAgeStudentMajorAge JoeyReading35BillCurriculum30 SarahCurriculum27JaneScience Ed45 AltheaYouth Guidance47JeffreyScience Ed27 NicoleScience Ed50PaulineReading40 MichaelCurriculum40LouiseReading34 ElizabethScience Ed27JordanScience Ed35

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Inferential Statistics Are used to make inferences from a given data set. Inferential statistics are often the next step after you have collected and summarised data. Inferential Statistics are used to 1. Make generalisations from the sample to the population using probabilities. 2. Perform hypothesis testing. 3. Determine relationships among groups. 4. Make predictions.

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Example You are asked to determine which of the following subjects is the most appealing among students at your school; Physics, Chemistry and Biology. After you have collected your data from the sample and perform the statistical analysis you can then infer the findings to the larger population.

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Population Population: Includes all objects of interest. That is the complete set of data elements. For example, In the previous example the population of students would be all the students enrolled in Physics, Chemistry and Biology ( 50 students) Parameter: Usually seen as the characteristics of the population and denoted with the Greek Letter [ mu (µ), sigma (σ)]

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Sample Sample: A sample is a portion of the population selected for further analysis, For example, you may decide to use 20 out of the 50 students for further analysis. Statistics: are associated with the sample and are usually denoted using the roman letters ( x, s).

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Population vs. Sample a b c d ef gh i jk l m n o p q rs t u v w x y z PopulationSample b c g i n o r u y Measures used to describe the population are called parameters Measures computed from sample data are called statistics

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Statistics are computed to estimate parameters. The computation is descriptive statistics. The estimation is inferential statistics.

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Example Assume there are 80 students in the research methods class. 20 of the 80 students major is Youth Guidance. Since 20 is 25% of 80, we can say 25% of the students enrolled in the M.Ed programme major in youth guidance. The 25% is a parameter ( not a statistic) of the class because it is based on the entire population of M.Ed students. If we assume that the M.Ed programme is a representative of the entire post graduate programme we treat the 20 students as a sample drawn from a larger population of post graduate students ( Dip Ed, M.Phil) then the 25% becomes a statistic.

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Population vs Sample Population: All post graduate students at UWI Sample: Students in your MEd. class

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Data Facts, observations and information that come from research. Data types Measurement Data are numeric (quantitative). Categorical data are non numeric ( qualitative).

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Types of Quantitative Data Discrete data Continuous data have a finite/limited number of possible values, for example., a subset of numbers {1,2, 3, 4, 5} that may correspond to {Strongly disagree... Strongly agree}. So when data represents counts they are discrete. have indefinite possibilities, for example, {1.4, 1.41. 1.414, 1.4142...}. The numbers are continuous with no gaps or interruptions. That is, any value on between the lowest and the highest point on the measurement scale. 64 is anything 63.5<=x<64.5

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Notation and Rounding Like any form of mathematics, statistics has it own form of notation, that is, a type of shorthand ( +, -, α, δ, σ) that are vital in statistics calculations. You need to pay careful attention to mathematical notation. You must also be mindful of computational accuracy. Take your calculator divide 1 hour by 7 ( 1 second ÷ 7). What answer did you get?

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Your calculator may show 0.142857143 hours. This is a value in billionths of an hour. Did your calculator give you more digits or fewer digits? Different calculators have different memory and display capacity. To address this anomaly you can round the quotient to tenths, hundredths, thousandths. For the purpose of course we will always round to the nearest hundredth ( to two decimal places) unless otherwise specified.

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Rounding Procedure Rounding to the nearest hundredth calculate your answer to at least three decimal places If the third digit is less than 5 ( 0, 1, 2,3,or 4), report the first two digits without change If the third digit is 5 or greater ( 5, 6, 7,8, or 9)report the first digit and increase the second digit by 1. Round.142857143 to the hundredth place you need to consider the third digit (2) because the digit is less than 5 you report the first two digits without change 0.14 Divide 2 by 3 on your calculator and round to the nearest hundredth. 0.66666666. Look at the third digit (6) it is greater than 5 you report the first digit and increase the second digit by 1 ( 0.67)

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Variables and Constants Constants - a defined value that does not change Variables - value can change with each observation Independent variable - manipulated Dependent variable - response

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Variables and Constants Convert degree Celsius to degree Fahrenheit EQ: F= (9/5) x + 32 where x = C Here, x= variable as x changes so does F 32 = constant

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Variable Definition: Characteristic or attribute that can assume different values Types of Variables Independent Variable: one that is manipulated, measured or selected by the researcher. Dependent variable: one that is not under the researchers control. It is observed and measured. Random variable: A variable whose values are determined by chance.

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Tips for doing well in statistics Doing well in any course at university demands a great deal of work. This is especially true in statistics. Doing well in this course will require a lot of study and organisation on your part. You have to be a self directed learner. Here are a number of things you can do to help you do well in the course.

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Statistics is Cumulative The information you learn in the statistics class is cumulative. Thorough comprehension of the topics covered at the beginning of the course is pivotal if you have to understand the topics presented later. If you miss only one lecture or you do not read the recommended chapters in the text it may may result in your inability to understand the rest of the course Keep up with the work, attend all lectures, do the recommended assignments, read the text consistently.

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Get help from your lecturer As a student you have a number of avenues to solicit help to enhance your learning. One of these avenues is your lecturer or tutor. Do not be afraid to approach your tutors or lecturer for help when you first notice that you need it. Clear up questions as they arise, ask questions in class when you do not understand a concept.

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Make friends with fellow students Students are another source of help. If you miss a lecture or do not understand a small point, a fellow student can often provide notes or information that will solve your problem. In turn helping other students will benefit you because as you shed light on specific concepts for your friends, you further clarify them for yourself. Take time to get to know you fellow students, exchange telephone numbers and email addresses and set study groups.

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Read the text The main text is extremely important. Always have your calculator, pen and paper ready when you are reading the chapters. Take time to read the outline to get an idea of the topics that will be discussed. Ensure that you work all numerical examples in the text. After you have finished the chapter try to summarise it and read the chapter summary to ensure that you got the point. Do not read the text like a novel.

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Practice, Practice, Practice! The best way to improve your skill is to practice. Work the examples Copy and re-work problems demonstrated in the lectures Work the problems at the end of the chapter. Work the problems for the tutorial Work additional problems in your study groups

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Get a feel of the statistics As you are learning statistics try to do more than cram the formulas. You must try to understand the concepts that are behind the formulas. For example, if you have the feel of statistics you will know the mean of the following set of numbers 25, 23, 24, and 25 cannot be less than 22 or more than 26. you will also know that a correlation coefficient cannot be more than+1.00 or less than -1.00. so if you compute a correlation of 12 you know that youve made an error. As you work more problems you will get a feel for statistics.

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Summary Statistics is a tool that helps us understand our world. This is done through the organisation of data that we have collected that permits us to make certain statements about how the features of the data can be related to other settings. Descriptive and inferential statistics work together. The type of statistics you use depends on the questions you want answered.

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Practice Time Why is it worth the effort to learn about statistics? What is the difference between statistics and statistic? Go through a recent copy of an educational journal. Identify an article that relies directly or indirectly on statistics. Briefly describe the article.

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References Berenson (2004) Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Phillips, JL (2000). How to think about statistics. New York Salkind, N. J. (2008) Statistics for people who (think they) hate Statistics. CA: Sage

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Chapter 1 Introduction and Data Collection

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