MUP-501-Chapter-2- Data and Analytics Intro

MUP-501-Chapter-2- Data and Analytics Intro

• 1.
  Chapter 2 The Roleof Statistics and the Data Analysis Process by Alexis J. Abella I, PhD
• 2.
  Statistics is thescientific discipline that provides methods to help us make sense of data. Statistical methods are used in business, medicine, agriculture, social sciences, natural sciences, and applied sciences, such as engineering.
• 3.
  Three Reasons toStudy Statistics Being Informed “How do we decide whether claims based on numerical information are reasonable?” Making Informed Judgments “Throughout your personal and professional life, you will need to understand statistical information and make informed decisions using this Evaluating Decisions That Affect Your Life
• 4.
  The Nature andRole of Variability Statistics is a science whose focus is on collecting, analyzing, and drawing conclusions from data. Suppose that every student took the same number of units, spent the same amount of money on textbooks this semester, and favored increasing student fees to support expanding library services. For this population, there is no variability in the number of units, amount spent on books, or student opinion on the fee increase.
• 5.
  The Nature andRole of Variability Example. Monitoring Water Quality
• 6.
  Statistics and theData Analysis Process Methods for organizing and summarizing data make up the branch of statistics called descriptive statistics. For example, the admissions director at a large university might be interested in learning why some applicants who were accepted for the fall 2006 term failed to enroll at the university. The population of interest to the director consists of all accepted applicants who did not enroll in the fall 2006 term. Because this population is large and it may be difficult to contact all the individuals, the director might decide to collect data from only 300 selected students. These 300 students constitute a sample.
• 7.
  Statistics and theData Analysis Process The entire collection of individuals or objects about which information is desired is called the population of interest. A sample is a subset of the population, selected for study in some prescribed manner.
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  Statistics and theData Analysis Process The second major branch of statistics, inferential statistics, involves generalizing from a sample to the population from which it was selected.
• 9.
  Sample size Sample sizeis a count the of individual samples or observations in any statistical setting, such as a scientific experiment or a public opinion survey. Sample size measures the number of individual samples measured or observations used in a survey or experiment.
• 10.
  Calculation of SampleSize To determine the sample size needed for an experiment or survey, researchers take a number of desired factors into account. First, the total size of the population being studied must be considered. Researchers will also need to consider the margin of error, the reliability that the data collected is generally accurate; and the confidence level, the probability that your margin of error is accurate.
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  Dangers of SmallSample Size Large sample sizes are needed for a statistic to be accurate and reliable, especially if its findings are to be extrapolated to a larger population or group of data.
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  How to DetermineSample Size Design your experiment Calculate the population size Specify the level of accuracy you want from your research. Calculate your ideal sample size.
• 13.
  Sample Size Estimationusing Yamane and Cochran The Yamane sample size states that: where is your Yamane sample size, is your underlying population size and is determined from the confidence you are seeking from your study. That is, if you want to be 95% sure about the results of your study then .
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  Example: Find thesample size the researcher wants to include in her study if the population size of her respondents 4,750 at 95% accuracy.
• 15.
  Sample Size Estimationusing Yamane and Cochran Cochran’s formula is considered especially appropriate in situations with large populations. A sample of any given size provides more information about a smaller population than a larger one, so there’s a ‘correction’ through which the number given by Cochran’s formula can be reduced if the whole population is relatively small.
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  Example: Suppose we aredoing a study on the inhabitants of a large town and want to find out how many households serve breakfast in the mornings. We don’t have much information on the subject to begin with, so we’re going to assume that half of the families serve breakfast: this gives us maximum variability. So, p = 0.5. Now let’s say we want 95% confidence, and at least 5 percent—plus or minus—precision. A 95 % confidence level gives us Z values of 1.96, per the normal tables, so we get: Z – 1.96 p – 50% (half of the families serve breakfast) = 0.5 q – (1 – 0.5) = 0.5
• 18.
  So, a randomsample of 384 households in our target population should be enough to give us the confidence levels we need.
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  The Cochran’s formula(if population is known): In our earlier example, if there were just 1000 households in the target population, we would calculate.
• 20.
  If no is385 and N is equal 1000, then n is: So, for this smaller population, all we need are 278 households in our sample: a substantially smaller sample size.