1 MATB344 Applied Statistics Introduction to newbies in Statistics

2 What is Statistics? Statistics is encountered in our daily life. Unavoidable.Statistics is encountered in our daily life. Unavoidable. Involves gathering, analysis and presentation of dataInvolves gathering, analysis and presentation of data

3 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

4 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

5 In PoliticsIn 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.

6 CASE 1: OPINION POLLS 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% YES 62%NO 31% 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% YES 62%NO 31% THE WAR ON TERRORISM How do we get the poll? Ask everyone? Is it possible?

7 Common Problem in Statistics We are interested in the conclusion and prediction about the whole body of measurements, eg: Malaysian citizens. POPULATION.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. SAMPLE.The smaller set of measurements that will (hopefully) be representative of the larger set is called the SAMPLE.

8 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.

9 What’s common in “Sample” and “Population” We distinguish between set of objects on which we take measurements and the measurements themselves. -Experimental Units: -Experimental Units: The items or objects on which measurements are taken -Sample (or Population): -Sample (or Population): the set of measurements taken on the experimental units.

10 Examples Light bulbs –Experimental unit = bulb Opinion polls –Experimental unit = person

11 Descriptive Statistics Used to describe sets of measurements. Example : Bar charts, pie charts, line charts etc. Suitable for entire population. DESCRIPTIVE STATISTICSDESCRIPTIVE STATISTICS consists of procedures used to summarize and describe the set of measurements.

12 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:INFERENTIAL STATISTICS: Procedures used to draw conclusions or inferences about the population from information contained in the sample.

13 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.

14 But, … How can be sure that the poll result is reliable? We need a measure of reliability. Who makes the best burgers?VotesPercent McDonalds123 Votes13% Burger King384 Votes39% Wendy’s304 Votes31% All three have equally good burgers72 Votes7% None of these have good burgers98 Votes10% Our conclusions could be incorrect… consider this internet opinion poll…

15 Summary: Steps in Inferential Statistics objective of the experimentDefine the objective of the experiment and the population of interest design of the experimentDetermine the design of the experiment and the sampling plan to be used CollectanalyzeCollect and analyze the data Make inferencesMake inferences about the population from information in the sample goodnessreliabilityDetermine the goodness or reliability of the inference.

16 Summary: Steps in Inferential Statistics objective of the experimentDefine the objective of the experiment and the population of interest design of the experimentDetermine the design of the experiment and the sampling plan to be used CollectanalyzeCollect and analyze the data Make inferencesMake inferences about the population from information in the sample goodnessreliabilityDetermine the goodness or reliability of the inference. Example : In Presidential Election Objective : To determine Who will get the most votes Population: Set of all votes (from all registered voters) Sample : Sample voters from each states in USA.

17 Summary: Steps in Inferential Statistics Define the objective of the experiment and the population of interest design of the experimentDetermine 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. To decide how to select sample. How big a sample to select. How much will it cost if the sample is selected.

18 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 CollectanalyzeCollect and analyze the data Make inferences about the population from information in the sample Determine the goodness or reliability of the inference. Collect information from the sample Use appropriate method of analysis

19 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 inferencesMake inferences about the population from information in the sample Determine the goodness or reliability of the inference. Use information from the analysis to make inference Many methods but only one is the most accurate. Choose the best.

20 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 goodnessreliabilityDetermine the goodness or reliability of the inference. Inference might be wrong because we’re not looking at the whole population. Need to have measure of reliability

21 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!

22 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.