Introduction to Statistics

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# Introduction to Statistics - PowerPoint PPT Presentation

Introduction to Statistics. Night 1 – Thursday April 5, 2012. Statistics - Definition. Statistics describes a set of tools and techniques that is used for describing, organizing, and interpreting information or data. Types of Statistics.

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### Introduction to Statistics

Night 1 – Thursday April 5, 2012

Statistics - Definition
• Statistics describes a set of tools and techniques that is used for describing, organizing, and interpreting information or data.
Types of Statistics
• Descriptive – to organize and describe the characteristics of a collection of data.
• Observation - Data or data set
• Measures of Central Tendency
• Measures of Dispersion
• Inferential – to make inferences from a smaller group of data to a possibly larger one.
• Sample
• Population
• ANOVA, Regression, Correlation, etc.

Next

Types of Sampling Methodology
• Probability sampling
• Simple Random sampling
• Systematic sampling
• Stratified sampling
• Stratified Random sampling
• Nonprobability sampling
• Convenience sampling
• Judgment sampling
• Quota sampling
Sampling Methodology Tests
• Reliability
• Cronbach Alpha
• Validity
• Measuring what you are supposed to measure
• Normality
• Normal distribution of data
Types of Variables
• Qualitative /Categorical variables (categories)
• Nominal – outcome or data that can fit into only ONE class or category
• Ordinal – outcome or data that is fit in an order or ranks
• Quantitative variables (real numbers)
• Discrete – outcome or data that is taken from a finite set
• Continuous – outcome or data that can assume any value along any underlying continuum
Descriptive Statistics
• Measures of Central Tendency
• Describe the “characteristics” of a distribution
• Mean
• Median
• Mode
• Measures of Dispersion
• Shows how the “distributions” differ from each other
• Range
• Standard Deviation
• Variance
Measures of Central Tendency
• Mean
• Sum of all values in a group, divided by the number of values in the group
• Median
• The midpoint in a set of scores
• Mode
• The value that occurs most frequently

Next

MHR Students’ Ages

47 48

49 27

47 33

30 44

34 31

28 31

50 33

38 29

40

Back

MHR Students’ Ages

27 38

28 40

29 44

30 47

31 47

31 48

33 49

33 50

34

Back

When do you use what???
• Qualitative data (categorical, nominal) use = MODE
• Quantitative data (discrete, continuous) use = MEAN, MEDIAN
• Use MEAN for continuous data (that do not include extreme scores)
• Use MEDIAN for data with extreme scores
• Use MODE with categorical data (data that fits into only one category)
Measures of Dispersion
• Is there variability in the data?
• Range
• Highest number – lowest number
• Standard Deviation – Average amount of variability in a set of scores

Next

Data Sets
• Data set 1
• 7, 6, 3, 3, 1
• Mean = 4
• Data set 2
• 3, 4, 4, 5, 4
• Mean = 4
• Data set
• 4, 4, 4, 4, 4
• Mean = 4

Back

Quiz scores MHR Systems Management
• Data set 1
• 5, 5, 5, 4, 4, 3, 4, 4, 5, 5, 4, 3, 5, 5, 4, 5
• Data set 2
• 5, 1, 3, 1, 4, 5, 3, 2, 1, 1, 2, 5, 4, 5, 3, 1

Back

Quiz scores MHR Systems Management
• Data set 1
• 5, 5, 5, 4, 4, 3, 4, 4, 5, 5, 4, 3, 5, 5, 4, 5
• 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5
• Data set 2
• 5, 1, 3, 1, 4, 5, 3, 2, 1, 1, 2, 5, 4, 5, 3, 1
• 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5

Back

Data Distribution
• Central Tendency = Average Value or Mean
• Variability
• Skewness
• Positively Skewed
• No Skewness
• Negatively Skewed

Next

Mean Distribution

70

80

90

100

130

110

120

Back

So, this explains why the values are not confined to [-1, 1]. It is, however, an interesting fact that 68% of the values are always within one standard deviation of the mean. So, as an interesting test for yourself write a program to draw a large number of values from a normal distribution with mean 0 and variance 1 and count the number that are within one standard deviation of the mean. You should get a number close to 68% (68.2689492137% to be a little more precise).

Variability Distribution

Back

So, this explains why the values are not confined to [-1, 1]. It is, however, an interesting fact that 68% of the values are always within one standard deviation of the mean. So, as an interesting test for yourself write a program to draw a large number of values from a normal distribution with mean 0 and variance 1 and count the number that are within one standard deviation of the mean. You should get a number close to 68% (68.2689492137% to be a little more precise).

Skewed Distribution

Back

Problem 3 Frequency Distributions
• Arrange the data in order
• Select the number of classes to be used (5-12)
• Determine the range
• Divide the range by the number of classes and you get the class width
• Round it up and then start the frequency with the smallest number and increasing it by the class width
Project Research Plan Part I

OPTION 1

INTERVENTION

Your solution DID solve the problem

OBJECTIVES

OPTION 2

PROPOSED INTERVENTION

Your solution WILL solve the problem

OBJECTIVES & HYPOTHESES

PROBLEM

OPTION 3

PROPOSED INTERVENTION

Your alternatives WILL solve the problem

OBJECTIVES & HYPOTHESES

Project Research Plan Part I

OPTION 1

INTERVENTION

Your solution DID solve the problem

OBJECTIVES

Intervention

(New Process/Training Manual/New Technology)

Measurable Objectives

(10% reduction in waiting time/50% reduction in errors)

Project Research Plan Part I

OPTION 2

INTERVENTION

Your solution WILL solve the problem

OBJECTIVES

HYPOTHESIS

Intervention

(New Process/Training Manual/New Technology)

Hypothesis

(There is a 25% negative level of patient satisfaction at this office)

Measurable Objectives

(10% reduction in waiting time/50% reduction in errors)

Project Research Plan Part I

OPTION 3

INTERVENTION

Your solution WILL solve the problem

OBJECTIVES

HYPOTHESIS (Alternatives)

Intervention

(New Process/Training Manual/New Technology)

Hypothesis

(There is a 10% negative level of patient satisfaction at this office/50% of patients feel the waiting times are unreasonable)

Measurable Objectives

(25% increase in the level of patient satisfaction)