Statistics Notes Chapter 1 - 9.doc

24 Pages

Operations Management and Information System
Course Code
OMIS 2010
Alan Marshall

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Chapter 1 Descriptive Statistics Deals with methods of organizing, summarizing, and presenting data in a convenient and informative way Forms: graphical techniques for easy extraction of useful information (Histogram) Numerical techniques to describe different features of data Actual technique depends on the specific information that we would like to extract Measure of central location (Mode, mean, median) Measure of variability (Range) Inferential Statistics Is a body of methods used to draw conclusions or inferences about characteristics of population based on sample data Asample that is only a small fraction of the size of the population can lead to correct inferences only a certain percentages of the time 1.1 Key Statistical Concepts Population Is the group of all items of interest to a statistics practitioner Descriptive measure: parameter represents the information we need (in most applications) Sample Set of data drawn from a studied population Descriptive measure: Statistic Used to make inferences about parameter Statistical Inference Process of making an estimate, prediction, or decision about a population based on sample data Populations = almost always VERY large, impractical to investigate each member Easier and cheaper to take sample from population and draw conclusions or make estimates Not always correct Thus statistical inference measure of reliability Confidence level: proportion of times that an estimating procedure will be correct Significance level: Measures how frequently the conclusion will be wrong Chapter 2 2.1 Types of Data and Information Variable: Some characteristic of a population or sample Varies from person to person, thus the name Values of the variable: Possible observations of the variable Data: Observed values of a variable (Plural form of datum) Three types Interval: Real numbers, referred to as quantitative or numerical Nominal: Categories, also called qualitative or categorical Ordinal:Appear to be nominal, but order of their values has meaning, and thus must be maintained. Magnitude no important, as long as they are in order Difference between ordinal and interval: Intervals or differences between values of interval are consistent and meaningful (can calculate or interpret), while the intervals or differences between ordinal values hold no meaning (cannot calculate or interpret) Calculations for Types of Data Interval Data All calculations are permitted Nominal Data Cannot perform any calculations Calculations based on codes used to store this type of data are meaningless Can only count or compute percentages of the occurrences of each category Ordinal Data Most important aspect = order of the values Only permissible calculations are those involving a ranking process Hierarchy of Data Placed in order of permissible calculations Higher-level data types may be treated as lower-level ones Conversion leads to loss of information Do not convert data unless necessary CANNOT treat lower-level data as higher-level Summary Interval Values are real numbers All calculations are valid Data may be treated as ordinal or nominal Ordinal Values must represent the ranked order of the data Calculations based on an ordering process are valid Data may be treated as nominal but not as interval Nominal Values are the arbitrary numbers that represent categories Only calculations based on the frequencies or percentages of occurrences are valid Data may not be treated as ordinal or interval Interval, Ordinal, and Nominal Variables Variables are given the same name as the type of data which they constitute 2.2 Describing a Set of Nominal Data Frequency Distribution: Summarized data in a table, which presents the categories and their counts Relative Frequency Distribution: Lists the categories and the proportion with which each occurs Bar Chart and Pie chart are used to present a picture of the data Bar chart = frequencies Pie chart = relative frequencies Used to enhance the readersability to grasp the substance of the data Describing Ordinal Data No specific graphical techniques When describing, treat as if nominal Only criterion = the bars in bar charts should be arranged in ascending or descending ordinal values, in pie charts the wedges are typically arranged clockwise Factors That Identify Where to Use Frequency and Relative Frequency Tables, Bar and Pie Charts Objective: Describe a single set of data Data type: Nominal or ordinal 2.3 Describing the Relationship between Two Nominal Variables and Comparing Two or More Nominal Data Sets Univariate: Techniques applied to single sets of data Bivariate: Techniques that depict relationship between variables Cross-classification table: Used to describe the relationship between two nominal variables (Table 2.5) Avariation of bar chart is used to describe the information graphically (Page 35) Same technique used to compare two or more sets of nominal data Tabular Methods of Describing the Relationship between Two Nominal Variables Must remember permitted only to determine the frequency of the values (Table 2.5) Comparing Two or More Sets of Nominal Data Consider one category as defining population (variables are different populations) Then compare the bar charts or individual bars Data Formats Several ways to store data to produce a table or a bar/pie chart 1. Data in two columns (Example 2.4) First column categories for first variable, second column categories for second variable Each row represents one observation of the two variables Number of observations in each column is the same Cross-classification Table can be created from this 2. The data are stored in two or more columns, with each column representing the same variable in a different sample or population Cross-classification Table can be created from this 3. Cross-classification Table is already given Factors That Identify When to Use a Cross-Classification Table Objective: Describe the relationship between two variables and compare two or more sets of data Data type: Nominal
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