MATH1342MATH1342S08 – 7:00A-8:15A T/RS08 – 7:00A-8:15A T/R

BB218BB218SPRING 2014SPRING 2014

Daryl RuppDaryl Rupp

What proportion of southern Iowa homes What proportion of southern Iowa homes have soft water? A sample of 6 homes in 6 have soft water? A sample of 6 homes in 6 cities found 3 had soft water. What is the cities found 3 had soft water. What is the conclusion?conclusion? 1. 0.50 of the homes in southern Iowa have 1. 0.50 of the homes in southern Iowa have

soft water.soft water. 2. Approximately 0.50 of the homes in 2. Approximately 0.50 of the homes in

southern Iowa have soft water.southern Iowa have soft water. 3. We can not make a conclusion.3. We can not make a conclusion. 4. Between 0.33 an 0.67 of the homes have 4. Between 0.33 an 0.67 of the homes have

soft water,soft water, 5. There is an 80% 5. There is an 80% confidenceconfidence that between that between

0.33 and 0.67 of the homes have soft water.0.33 and 0.67 of the homes have soft water.NOTE: See Problem 10 of the homework for a NOTE: See Problem 10 of the homework for a

great examplegreat example

STATISTICSSTATISTICS

The science of collecting, organizing, The science of collecting, organizing, summarizing and analyzing data to summarizing and analyzing data to draw conclusions or answering draw conclusions or answering questions, with a given amount of questions, with a given amount of confidence concerning the answer.confidence concerning the answer.

In other words, it is the method or In other words, it is the method or process used in finding an answer to process used in finding an answer to a question, with a specific amount of a question, with a specific amount of confidence that the answer is confidence that the answer is correct.correct.

THE SCIENTIFIC METHODTHE SCIENTIFIC METHOD

1. Define the question & scope to be investigated1. Define the question & scope to be investigated 2. Gather information & resources to define 2. Gather information & resources to define

hypothesishypothesis 3. Perform experiment & gather data3. Perform experiment & gather data 4. Analyze date4. Analyze date 5. Interpret data and draw conclusion which may 5. Interpret data and draw conclusion which may

lead to a starting point for continued investigationlead to a starting point for continued investigation 6. Retest to verify results (usually done by others) 6. Retest to verify results (usually done by others)

or revise hypothesis and start new investigationor revise hypothesis and start new investigation

TWO TYPES OF STATSISTICSTWO TYPES OF STATSISTICS

DescriptiveDescriptive is about organizing and is about organizing and summarizing data in order to picture summarizing data in order to picture the nature of the population or sample the nature of the population or sample represented by the data. (Ch’s 2 – 3)represented by the data. (Ch’s 2 – 3)

InferentialInferential is the process or method of is the process or method of generalizing the results from a sample generalizing the results from a sample to the entire population and measuring to the entire population and measuring the reliability of that answer (Ch’s 9 – the reliability of that answer (Ch’s 9 – 11, 4)11, 4)

DEFINITIONSDEFINITIONS

POPULATION: The entire group of POPULATION: The entire group of individuals being investigated (size is N). individuals being investigated (size is N). Must be Must be preciselyprecisely defined. defined.

INDIVIDUAL: One member of the entire INDIVIDUAL: One member of the entire group or population.group or population.

SAMPLE: A subset of individuals of a SAMPLE: A subset of individuals of a given size (n) taken from the population.given size (n) taken from the population.

DEFINITIONSDEFINITIONS VARIABLE: A given aspect of an individual. This VARIABLE: A given aspect of an individual. This

would be the definition of the aspect. For would be the definition of the aspect. For example, if a population or sample consists of example, if a population or sample consists of people then the variable could be weight, people then the variable could be weight, height, color of eyes, gender, etc. What height, color of eyes, gender, etc. What aspects could be found for a individual country?aspects could be found for a individual country?

DATA: The possible observations or outcomes DATA: The possible observations or outcomes for a variable concerning individuals. This is a for a variable concerning individuals. This is a label or a count of a measurement.label or a count of a measurement.

CHARCTERISTIC: A summary of a numerical CHARCTERISTIC: A summary of a numerical variable of a population or sample such as variable of a population or sample such as mean, max, range or standard deviation. Label mean, max, range or standard deviation. Label data can not be summarized.data can not be summarized.

DEFINITIONSDEFINITIONS

DATA CONSISTS OF DATA CONSISTS OF ATTRIBUTES ATTRIBUTES (Labels):(Labels): Colors, Judgments, Grades Colors, Judgments, Grades (as is A, B, C, D, F), Names.(as is A, B, C, D, F), Names.

DATA CONSISTS OF DATA CONSISTS OF NUMBERSNUMBERS FROM FROM MEASUREMENTS OR COUNTSMEASUREMENTS OR COUNTS: : Weights, Polls, Surveys, Weights, Polls, Surveys, Temperatures, Lengths, Bowling Temperatures, Lengths, Bowling scores, Number of Home Runs.scores, Number of Home Runs.

DEFINITIONSDEFINITIONS Characteristics (numerical) that come Characteristics (numerical) that come

from the POPULATION are called from the POPULATION are called PARAMETERS.PARAMETERS.

Characteristics (numerical) that come Characteristics (numerical) that come from a SAMPLE are called STATISTICS.from a SAMPLE are called STATISTICS.

If the data comes from labels then not If the data comes from labels then not called either (as no numerical summary called either (as no numerical summary is possible for Qualitative data).is possible for Qualitative data).

DEFINITIONSDEFINITIONS

QUALITATIVE DATA comes from QUALITATIVE DATA comes from LABELS.LABELS.

QUANTITATIVE DATA comes from QUANTITATIVE DATA comes from NUMERICAL dataNUMERICAL data

DEFINITIONSDEFINITIONS

DISCRETE DATA comes from counts DISCRETE DATA comes from counts and are whole numbers (have no and are whole numbers (have no decimal parts).decimal parts).

CONTINUOUS DATA comes from CONTINUOUS DATA comes from measurements and are real numbers measurements and are real numbers (may have decimal parts)(may have decimal parts)

NOTE: LABELS are neitherNOTE: LABELS are neither

A SIDE NOTEA SIDE NOTE

Statistics is all about the number line.Statistics is all about the number line.

Draw a number line for the interval 0 to 5.Draw a number line for the interval 0 to 5. Draw a number line centered at o and going Draw a number line centered at o and going

6 units in each direction.6 units in each direction. Draw a number line for the interval – 3 to Draw a number line for the interval – 3 to

+3.+3. Draw a number line from – infinity to infinityDraw a number line from – infinity to infinity

DEFINITIONSDEFINITIONS

TWO METHODS OF OBTAINING DATA:TWO METHODS OF OBTAINING DATA:

OBSERVATION: Data from observing, only. OBSERVATION: Data from observing, only. Not interfering with the process in any Not interfering with the process in any way.way.

EXPERIMENTATION: Data from controlling EXPERIMENTATION: Data from controlling some factors of a process. Often involves some factors of a process. Often involves comparing results of two or more values of comparing results of two or more values of a control factor. Involves the interference a control factor. Involves the interference by the investigator.by the investigator.

LEVELS OF LEVELS OF MEASUREMENTMEASUREMENT(Defines how data can be analyzed)(Defines how data can be analyzed)

Nominal: Values of the variables are names Nominal: Values of the variables are names or labels; they can not be ranked or ordered or labels; they can not be ranked or ordered (like color of eyes).(like color of eyes).

Ordinal: Values of the variables are names or Ordinal: Values of the variables are names or labels but they can be ordered but no labels but they can be ordered but no numeric value so cannot find differences (like numeric value so cannot find differences (like letter grades)letter grades)

LEVELS OF MEASUREMENTLEVELS OF MEASUREMENT

Interval: Values of the variables have Interval: Values of the variables have the property of being ordered and can the property of being ordered and can be compared (find real differences) but be compared (find real differences) but have no absolute zero (like have no absolute zero (like temperature).temperature).

Ratio: Values of the variables are like Ratio: Values of the variables are like interval, but have absolute meaning – interval, but have absolute meaning – there is a 0 values that means that there is a 0 values that means that absence of value (like weight)absence of value (like weight)

SPECIAL NOTESPECIAL NOTE

The data you collect is not the The data you collect is not the answer or analysis to the question answer or analysis to the question you are investigating.you are investigating.

The data you collect is the result of The data you collect is the result of the question you ask or the the question you ask or the instructions you give.instructions you give.

ExamplesExamples

TYPES OF SAMPLINGTYPES OF SAMPLING

Sampling: Obtaining the data from a Sampling: Obtaining the data from a number (size n) of individuals from a number (size n) of individuals from a population (size N).population (size N).

Simple Random Sampling: Where Simple Random Sampling: Where every individual in the population has every individual in the population has an equal chance of being selected. an equal chance of being selected. The best and the goal of sampling The best and the goal of sampling methods.methods.

TYPES OF SAMPLINGTYPES OF SAMPLING

Stratified Sampling: Separating the Stratified Sampling: Separating the population into non overlapping population into non overlapping groups (strata) and then selecting groups (strata) and then selecting simple random samples from each simple random samples from each group.group.

Systematic Sampling: Obtained by Systematic Sampling: Obtained by selecting every kselecting every kthth member of the member of the population.population.

TYPES OF SAMPLINGTYPES OF SAMPLING Cluster Sampling: Dividing the Cluster Sampling: Dividing the

population into groups (or clusters) and population into groups (or clusters) and selecting all the individuals from that selecting all the individuals from that cluster.cluster.

Convenience Sampling: Individuals are Convenience Sampling: Individuals are selected on the ease of obtaining them selected on the ease of obtaining them and not randomly from the population.and not randomly from the population.

Voluntary Sampling (Type of Voluntary Sampling (Type of convenience): Worst possible.convenience): Worst possible.

See section 1.4 for complete discussion See section 1.4 for complete discussion of sampling methodsof sampling methods

BIAS IN SAMPLINGBIAS IN SAMPLING

Always Try to Avoid BiasAlways Try to Avoid Bias Two Types: Intentional and Two Types: Intentional and

UnintentionalUnintentional Sampling: Method tends to favor one Sampling: Method tends to favor one

section of population. One section is section of population. One section is under represented.under represented.

Non-response Bias: From Voluntary Non-response Bias: From Voluntary Sampling where individuals can Sampling where individuals can refuse to take part.refuse to take part.

BIAS IN SAMPLINGBIAS IN SAMPLING Response Bias: Answers do not reflect Response Bias: Answers do not reflect

true feelings of responder Caused by:true feelings of responder Caused by: Interviewer error, the way the question is Interviewer error, the way the question is

framed;framed; The choices and wording offered in survey;The choices and wording offered in survey; Order of questions or responsesOrder of questions or responses Plain old entry error.Plain old entry error.

See 1.5 for complete discussionSee 1.5 for complete discussion

Easy to DeceiveEasy to Deceive

Can be done graphically.Can be done graphically.

Can be done numerically by focusing Can be done numerically by focusing on numbers rather than relative on numbers rather than relative proportion.proportion.

Can be done by fudging numbers.Can be done by fudging numbers.

EXPERIMETAL TYPESEXPERIMETAL TYPES

CONTROL FACTORS: All processes have CONTROL FACTORS: All processes have random results, but the results can be random results, but the results can be somewhat limited through control somewhat limited through control factors. By changing these factors the factors. By changing these factors the results can be changed.results can be changed.

BLIND STUDIES: Can lead to Bias.BLIND STUDIES: Can lead to Bias. DOUBLE BLIND STUDIES: The best. DOUBLE BLIND STUDIES: The best.

Used in many medical studies. Can Used in many medical studies. Can involve the use of placebos or another involve the use of placebos or another medication.medication.

EXPERIMETAL TYPESEXPERIMETAL TYPES