Presentation on theme: "Introduction to Statistics"— Presentation transcript:
1 Introduction to Statistics Chapter 1Introduction to Statistics1-1 Overview1- 2 Types of Data1- 3 Abuses of Statistics1- 4 Design of Experiments
2 Statistics (Definition) OverviewStatistics (Definition)A collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data
3 Definitions Population Sample The complete collection of all data to be studied.SampleThe subcollection data drawn from the population.
4 Example Identify the population and sample in the study A quality-control manager randomly selects 50 bottles of Coca-Cola to assess the calibration of the filing machine.Emphasize 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.
5 Definitions Statistics Descriptive Statistics Broken into 2 areas Inferencial Statistics
6 Definitions Descriptive Statistics Inferencial Statistics Describes data usually through the use of graphs, charts and pictures. Simple calculations like mean, range, mode, etc., may also be used.Inferencial StatisticsUses sample data to make inferences (drawconclusions) about an entire 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.Test Question
7 1-2 Types of Data Parameter vs. Statistic Quantitative Data vs. Qualitative DataDiscrete Data vs. Continuous Data
8 Definitions Parameter population parameter a numerical measurement describing some characteristic of a populationpopulationparameter
9 Definitions Statistic sample statistic a numerical measurement describing some characteristic of a samplesamplestatistic
10 Examples Parameter Statistic 51% of the entire population of the US is FemaleStatisticBased on a sample from the US population is was determined that 35% consider themselves overweight.
11 Definitions Quantitative data Numbers representing counts or measurementsQualitative (or categorical or attribute) dataCan be separated into different categories that are distinguished by some nonnumeric characteristics
12 Examples Quantitative data The number of FLC students with blue eyesQualitative (or categorical or attribute) dataThe eye color of FLC students
13 DefinitionsWe further describe quantitative data by distinguishing between discrete and continuous dataDiscreteQuantitative DataContinuous
14 Definitions 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 or interval 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
15 ExamplesDiscreteThe number of eggs that hens lay; for example, 3 eggs a day.ContinuousThe amounts of milk that cows produce; for example, gallons a day.
16 Definitions Univariate Data Bivariate Data Involves the use of one variable (X)Does not deal with causes and relationshipBivariate DataInvolves the use of two variables (X and Y)Deals with causes and relationshipsUnderstanding 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.
17 Example Univariate Data Bivariate Data How many first year students attend FLC?Bivariate DataIs there a relationship between then number of females in Computer Programming and their scores in Mathematics?Understanding 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.
18 Important Characteristics of Data 1. Center: A representative or average value that indicates where the middle of the data set is located2. Variation: A measure of the amount that the values vary among themselves or how data is dispersed3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed)4. Outliers: Sample values that lie very far away from the vast majority of other sample values5. Time: Changing characteristics of the data over timeMost important characteristics necessary to describe, explore, and compare data sets.page 34 of text
19 Uses of StatisticsAlmost all fields of study benefit from the application of statistical methodsSociology, Genetics, Insurance, Biology, Polling, Retirement Planning, automobile fatality rates, and many more too numerous to mention.page 11 of text
20 1-3 Abuses of Statistics Bad Samples Small Samples Loaded Questions Misleading GraphsPictographsPrecise NumbersDistorted PercentagesPartial PicturesDeliberate Distortions
21 Abuses of Statistics Bad Samples Inappropriate methods to collect data. BIAS (on test) Example: using phone books to sample data.Small Samples (will have example on exam)We will talk about same size later in the course. Even large samples can be bad samples.Loaded QuestionsSurvey questions can be worked to elicit a desired response
22 Abuses of Statistics Bad Samples Small Samples Loaded Questions Misleading GraphsPictographsPrecise NumbersDistorted PercentagesPartial PicturesDeliberate Distortions
23 Salaries of People with Bachelor’s Degrees and with High School Diplomas $40,500$40,500$40,000$40,00035,00030,000$24,40030,00020,000$24,400page 11 of textGraphs whose vertical scales do not start at 0 will give a misleading representation of the differences in heights of the bars.25,00010,00020,000Bachelor High SchoolDegree DiplomaBachelor High SchoolDegree Diploma(a)(test question)(b)
24 We should analyze the numerical information given in the graph instead of being mislead by its general shape.
25 Abuses of Statistics Bad Samples Small Samples Loaded Questions Misleading GraphsPictographsPrecise NumbersDistorted PercentagesPartial PicturesDeliberate Distortions
26 Double the length, width, and height of a cube, and the volume increases by a factor of eight What is actually intended here? 2 times or 8 times?page 14 of text
27 Abuses of Statistics Bad Samples Small Samples Loaded Questions Misleading GraphsPictographsPrecise NumbersDistorted PercentagesPartial PicturesDeliberate Distortions
28 Abuses of Statistics Precise Numbers There are 103,215,027 households in the US. This is actually an estimate and it would be best to say there are about 103 million households.Distorted Percentages100% improvement doesn’t mean perfect.Deliberate DistortionsLies, Lies, all Lies
29 Abuses of Statistics Bad Samples Small Samples Loaded Questions Misleading GraphsPictographsPrecise NumbersDistorted PercentagesPartial PicturesDeliberate Distortions
30 Abuses of Statistics Partial Pictures “Ninety percent of all our cars sold in this country in the last 10 years are still on the road.”Problem: What if the 90% were sold in the last 3 years?
32 Definition Experiment Event apply some treatment (Action) observe its effects on the subject(s) (Observe)Example: Experiment: Toss a coinEvent: Observe a tail
33 Designing an Experiment Identify your objectiveCollect sample dataUse a random procedure that avoids biasAnalyze the data and form conclusions
34 Methods of Sampling Random (type discussed in this class) Systematic ConvenienceStratifiedClusterreview of the 5 different types of sampling
35 Definitions Random Sample Simple Random Sample (of size n) members of the population are selected in such a way that each has an equal chance of being selected (if not then sample is biased)Simple Random Sample (of size n)subjects selected in such a way that every possible sample of size n has the same chance of being chosen
36 Random Sampling - selection so that each has an equal chance of being selected page 19 of text
37 Systematic Sampling Select some starting point and then select every K th element in the population
38 use results that are easy to get Convenience Samplinguse results that are easy to get
39 subdivide the population into at Stratified Samplingsubdivide the population into atleast two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)
40 Cluster Sampling - divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clustersStudents will most often confuse stratified sampling with cluster sampling. Both break the population into strata or sections. With stratified a few are selected from each strata. With cluster, choose a few of the strata and choose all the member from the chosen strata.
41 Definitions Sampling Error Nonsampling Error the difference between a sample result and the true population result; such an error results from chance sample fluctuations.Nonsampling Errorsample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly).page 23 of text
42 Using Formulas Factorial Notation Order of Operations 8! = 8x7x6x5x4x3x2x1Order of Operations( )POWERSMULT. & DIV.ADD & SUBT.READ LIKE A BOOKKeep number in calculator as long a possiblepage 23 of text
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