2STATISTICS ELEMENTARY MARIO F. TRIOLA Chapter Introduction to StatisticsMARIO F. TRIOLAEIGHTHEDITION
3Introduction to Statistics Chapter 1Introduction to Statistics1-1 Overview1-2 The Nature of Data1-3 Uses and Abuses of Statistics1-4 Design of Experiments
4Statistics Two Meanings Specific numbers 1-1 Overview Method of analysis
5Statistics Specific number numerical measurement determined by a set of dataExample: Twenty-three percent of people polled believed that there are too many polls.
6Statistics Method of analysis a collection of methods for planning experiments, obtaining data, and then then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the datapage 4 of text
7Definitions Population the complete collection of all elements (scores, people, measurements, and so on) to be studied. The collection is complete in the sense that it includes all subjects to be studied.
8Definitions Census Sample the collection of data from every element in a populationSamplea subcollection of elements drawn from a populationEmphasize that a population is determined by the researcher, and a sample is a subcollection of that pre-determined group. For example, if I collect the ages from a section of elementary statistics students, that data would be a sample if I am interested in studying ages of all elementary statistics students. However, if I am studying only the ages of the specific section of elementary statistics, the data would be a population.
10Definitions Parameter a numerical measurement describing some characteristic of a populationpage 5 of text
11Definitions Parameter population parameter a numerical measurement describing some characteristic of a populationpopulationparameter
12Definitions Statistic a numerical measurement describing some characteristic of a sample
13Definitions Statistic sample statistic a numerical measurement describing some characteristic of a samplesamplestatistic
14Definitions Quantitative data numbers representing counts or measurementspage 6 of text
15Definitions Quantitative data numbers representing counts or measurementsQualitative (or categorical or attribute) datacan be separated into different categories that are distinguished by some nonnumeric characteristics
16DefinitionsQuantitative datathe incomes of college graduates
17Definitions Quantitative data the incomes of college graduatesQualitative (or categorical or attribute) datathe genders (male/female) of college graduates
18DefinitionsDiscretedata result when the number of possible values is either a finite number or a ‘countable’ number of possible values0, 1, 2, 3, . . .
19Definitions Discrete Continuous data result when the number of possible values is either a finite number or a ‘countable’ number of possible values0, 1, 2, 3, . . .Continuous(numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumpsUnderstanding the difference between discrete versus continuous data will be important in Chapters 4 and 5.When measuring data that is continuous, the result will be only as precise as the measuring device being used to measure.23
20DefinitionsDiscreteThe number of eggs that hens lay; for example, 3 eggs a day.
21DefinitionsDiscreteThe number of eggs that hens lay; for example, 3 eggs a day.ContinuousThe amounts of milk that cows produce; for example, gallons a day.
22Definitions nominal level of measurement characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme (such as low to high)Example: survey responses yes, no, undecidedpage 7 of text
23Definitions ordinal level of measurement involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaninglessExample: Course grades A, B, C, D, or FUnderstanding the differences between the levels of data will help students later in determining what type of statistical tests to use.Nominal and ordinal data should not be used for calculations (even when assigned ‘numbers’ for computerization) as differences and magnitudes of differences are meaningless.
24Definitions interval level of measurement like the ordinal level, with the additional property that the difference between any two data values is meaningful. However, there is no natural zero starting point (where none of the quantity is present)Example: Years 1000, 2000, 1776, and 1492Students usually have some difficulty understanding the difference between interval and ratio data. Fortunately, interval data occurs in very few instances.
25Definitions ratio level of measurement the interval level modified to include the natural zero starting point (where zero indicates that none of the quantity is present). For values at this level, differences and ratios are meaningful.Example: Prices of college textbooks
26Levels of Measurement Nominal - categories only Ordinal - categories with some orderInterval - differences but no natural starting pointRatio - differences and a natural starting pointreview of four levels of measurement
27Levels of Measurement Nominal - categories only Ordinal - categories with some orderInterval - differences but no natural starting pointRatio - differences and a natural starting point