Slide 1

STATISTICS

To be able to read and understand various statistical studies performed in their fieldsrequires a knowledge of the vocabulary, symbols, concepts, and statistical procedures To conduct research in their fieldsrequires ability to design experiments which involves collection, analysis, and summary of dataTo become better consumers and citizensWhy Should We Study Statistics?

PopulationBasic Terminology

POPULATION:

Complete collection of all elements or units (usually people, objects, transactions, or events) that we are interested in studying

In terms of data, a population is the collection of all outcomes, responses, measurement, or counts that are of interest.

CENSUS: A complete enumeration (or accounting) of the population (i.e. collecting data from every element (or unit) in the population).

PARAMETER: A numeric value associated with a population. (e.g. - the average height of ALL students in this class, given that the class has been defined as a population)

Sample Basic Terminology

SAMPLE: Taken from a population a sample is a subset from which information is collected. Example: 25 cans of corn (sample) randomly obtained from a full days production (population)

STATISTIC: A numeric value associated with a sample. Example: the average height of 10 individuals randomly selected from the class (defined population).

INFERENCE: An estimate, prediction, or some other generalization about a population based on information contained in a sample. Example: Based upon a randomly selected sample of 25 flights at JKF International Airport (the sample; individual flights are units) taken from all flights on Dec. 24, 2009 (defined population), we can state with a degree of confidence the mean delay for the population of the days flights was 35 minutes (sample statistic in context being inferred to the population).

Cluster Sample

Simple Random sampling

Stratified sampling

Systematic sample

In SummaryTo include ALL units, you are looking at:POPULATIONCENSUSPARAMETERSTo work with a subset of all units, you are looking at:SAMPLESTATISTICSINFERENCES to a populationParameterPopulationStatisticSample

VARIABLES AND NATURE

OF DATA

Language of StatisticsVariable: a characteristic or attribute that can assume different values

Variables whose values are determined by chance are called random variablesData: values (measurements or observations) that variables can assume Data is the information collected the group of information forms a data setEach value in the set is a data point or datum

Two kinds of variables

Qualitative Data can be separated into different categories (values) that are distinguished by some nonnumeric characteristic. Qualitative data are also referred to as categorical or attribute data. \

Examples include gender, eye color, and car brandsNote that the values of this type of variable are differentiated by words rather than numeric values. Example: Eye Color values include blue, brown, hazel, etc.

Quantitative Data are number-based and represent counts or measurements. This type of data may be subdivided into two categories...

Discrete Data - result when the number of possible values is either a finite or a countably infinite number.Examples: Siblings, Cars, and Coins in a jar (think of whole number counts here; even if you cannot count them all). Continuous Data - result from infinitely many possible values corresponding to some continuous scale that covers a range of values without gaps, interruptions, or jumps. Continuous data can assume any value, including fractional parts.Examples: Height, Weight, Time

Discrete

Continuous

Variable ClassificationsQualitative VariablesQuantitative VariablesCan be placed into distinct categories, according to some characteristic or attribute (typically non-numeric) Examples: Eye ColorGenderReligious PreferenceYes/No

NumericalCan be ordered or rankedExamples: HeightsWeightsPulse RateAgeBody TemperaturesCredit Hours

Measurement of Data

Nominal characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme. Qualitative data.Examples: Gender, Yes/No, Political Party affiliation, names of students.

Ordinal characterized by data that can be arranged in some order, but the differences between data values either cannot be determined or are meaningless. These variables may be either qualitative (categorical) data or quantitative (numerical) data.Examples: Military Rank, Position in a race, Attitude scales.

Interval 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. Quantitative data.Examples: Temperature (F or C); longitude; Calendar Years.

Ratio is the interval level modified to include the natural zero starting point. At this level, differences and ratios are both meaningful. Quantitative data.Examples: Height, Weight, Time, Age.

NominalOrdinal Examples: GenderZip CodesPolitical AffiliationReligion

Examples: Letter grades (A, B, C, D, F)Judging contest (1st, 2nd , 3rd )Ratings (Above Avg, Avg, Below Avg, Poor)

Interval RatioExamples: Temperature (0 does not mean no heat at all)IQ Scores (0 does not imply no intelligence)

Examples: Height WeightAreaNumber of phone calls receivedSalary