MATB 344 Applied Statistics Introduction to newbies in
MATB 344 Applied Statistics Introduction to newbies in Statistics
What is Statistics? • Statistics is encountered in our daily life. Unavoidable. • Involves gathering, analysis and presentation of data 2
What does a Statistician do? • Collects numbers or data • Systematically organizes or arranges the data • Analyzes the data…extracts relevant information to provide a complete numerical description • Infers general conclusions about the problem using this numerical description 3
Uses of Statistics • Satistics - a branch of mathematics that have applications in daily life • Statistics – like a “new language” to you. • Usage: – a theoretical discipline in its own right – a tool for researchers in other fields – a general tool to draw general conclusions in a large variety of applications 4
• In Politics – Forecasting and predicting winners of elections – Where to concentrate campaign appearances, advertising and $$… • In Industry – To market product… – Eg: to predict the average length of life of a light bulb – Cannot test all the bulbs, so choose some sample to obtain the statistics. 5
CASE 1: OPINION POLLS THE WAR ON TERRORISM Do you think that the United States war on terrorism will spread to countries other than Afghanistan? YES 64% NO 34% Do you think that the United States should be directly involved in negotiating peace agreements in other parts of the world? YES 62% NO 31% How do we get the poll? Ask everyone? Is it possible? 6
Common Problem in Statistics • We are interested in the conclusion and prediction about the whole body of measurements, eg: Malaysian citizens. • The set of the whole body of measurements of interest is called POPULATION. • But we cannot survey on them all. • Sometimes, a the whole body of measurements is large and cannot be totally enumerated. • Solution: Use a smaller set of measurement to represent the whole body of measurements. • The smaller set of measurements that will (hopefully) be representative of the larger set is called the SAMPLE. 7
Examples • To predict the average length of life of a light bulb - to enumerate the population is destructive. We cannot take all light bulb and test. - So, select a smaller number of light bulb as a sample • To forecast the winner of an election - population of the whole country is too big and people do change their mind - So, select a group of people in certain location to be the sample. 8
What’s common in “Sample” and “Population” • We distinguish between set of objects on which we take measurements and the measurements themselves. - Experimental Units: The items or objects on which measurements are taken - Sample (or Population): the set of measurements taken on the experimental units. 9
Examples • Light bulbs – Experimental unit = bulb • Opinion polls – Experimental unit = person 10
Descriptive Statistics • Used to describe sets of measurements. • Example : Bar charts, pie charts, line charts etc. • Suitable for entire population. • DESCRIPTIVE STATISTICS consists of procedures used to summarize and describe the set of measurements. 11
Inferential Statistics • Used to describe / make inferences about a population based on statistics of the sample. • Used when we cannot enumerate the whole population • INFERENTIAL STATISTICS: Procedures used to draw conclusions or inferences about the population from information contained in the sample. 12
Objective of Inferential Statistics • To make inferences about a population – draw conclusions – make prediction – make decision from information contained in a sample. • The statistician’s job is to find the best way to do this. 13
But, … Our conclusions could be incorrect… consider this internet opinion poll… Who makes the best burgers? Votes Percent Mc. Donalds 123 Votes 13% Burger King 384 Votes 39% Wendy’s 304 Votes 31% All three have equally good burgers 72 Votes 7% None of these have good burgers 98 Votes 10% • How can be sure that the poll result is reliable? • We need a measure of reliability. 14
Summary: Steps in Inferential Statistics • Define the objective of the experiment and the population of interest • Determine the design of the experiment and the sampling plan to be used • Collect and analyze the data • Make inferences about the population from information in the sample • Determine the goodness or reliability of the inference. 15
Summary: Steps in Inferential Statistics • Define the objective of the experiment and the population of interest Example : In Presidential • Determine the design of the experiment and the sampling. Election plan to be used Objectivethe : To determine Who • Collect and analyze data will get the most votes • Make inferences about the population from Population: information in the sample. Set of all votes (from allgoodness registeredorvoters) • Determine the reliability of the inference. Sample : Sample voters from each states in USA. 16
Summary: Steps in Inferential Statistics • Define the objective of the experiment and the population of interest • Determine the design of the experiment and the sampling plan to be used • Collect and analyze • the. To data decide how to select • Make inferences aboutsample. the population from information in the sample • How big a sample to • Determine the goodness or reliability of the select. inference. • How much will it cost if the sample is selected. 17
Summary: Steps in Inferential Statistics • Define the objective of the experiment and the population of interest • Determine the design of the experiment and the sampling plan to be used • Collect and analyze the data • Make inferences about the population from • in Collect information from the sample information the sample Use appropriate method of • Determine • the goodness or reliability ofanalysis the inference. 18
Summary: Steps in Inferential Statistics • Define the objective of the experiment and the • Use information from the analysis to population of interest make inference • Determine the design of the experiment and the • Many methods but only one is the sampling plan to be used most accurate. Choose the best. • Collect and analyze the data • Make inferences about the population from information in the sample • Determine the goodness or reliability of the inference. 19
Summary: Steps in Inferential Statistics • Define the objective of the experiment and the population of interest • Inference might be wrong because • Determine the not design of theatexperiment we’re looking the whole and the samplingpopulation. plan to be used • Collect analyze data of reliability • and Need to havethe measure • Make inferences about the population from information in the sample • Determine the goodness or reliability of the inference. 20
Conclusion: Learn to View Statistics Critically • Why? Because Statistics can lie. • According to people against statistics - there are three kinds of lies…. . – Lies – Damn Lies – Statistics • Be positive!!! You need to make statistics work for you, not lie for you! 21
How to make statistics work for you and give reliable inference? • Use software tools to help perform the procedures. • List of Softwares: – MINITAB – SPSS – Microsoft EXCEL – Java applets. 22
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