Session 7 Introduction to Research and Evaluation

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Session 7 Introduction to Research and
Evaluation

• Topic 1 Research Questions and Hypothesis
  Testing
• And
• Topic 2 Introduction to Statistics

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For Tonight
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Today

• Review the contents of the proposal
• Topics tonight
• Finish the research questions
• Types of data review
• Hypothesis Testing
• Intro to Stats

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The phases of a research project

• Problem statement
• Purpose
• Hypothesis development / research question(s)
• Population / Sample type
• Results reporting (data)
• Statistical testing
• Conclusions Recommendations

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Parts of the Research Report

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• References
• Appendix

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Components of Chapter 1

• Introduction
• Background of the study
• Problem statement
• Significance of study
• Overview of methodology
• Delimitations of study
• Definitions of key terms
• Conclusion (optional)

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Characteristics of Components in Chapter 1

• Introduction 1 paragraph 3 pages
• Gets attention - gradually
• Brief vs. reflective opening
• Background 2-5 pages
• History of problem, etc.
• Professional vs. practical use
• Be careful of personal intrusions

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Characteristics of Components in Chapter 1

• Problem Statement ½ page
• States problem as clearly as possible
• Significance of study 1 pgh. to 1 page
• Answers Why did you bother to conduct the
  study?
• Be careful of promising too much

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Ways to Convey Significance

• Problem has intrinsic importance, affecting
  organizations or people
• Previous studies have produced mixed results
• Your study examines problem in different setting
• Meaningful results can be used by practitioners
• Unique population
• Different methods used

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Characteristics of Components

• Delimitations as needed
• Not flaws
• Establishes the boundaries can study be
  generalized?
• Consider
• sample
• Setting
• time period
• methods

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Stating the Problem

• Developing a hypothesis
• Methods estimation and hypothesis testing.
• Estimation, the sample is used to estimate a
  parameter and a confidence interval about the
  estimate is constructed.
• Parameter numerical quantity measuring some
  aspect
• Confidence Interval range of values that
  estimates a parameter for a high proportion of
  the time
• Hypothesis Testing the most common use
• Hypothesis an intelligent guess or assumption
  that guides the design of the study
• Null hypothesis there is no difference or there
  is no effect
• Alternative hypothesis there is a difference or
  there is an effect
• Hypotheses more than hypothesis, which are
  related to the population

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TYPES OF DATA
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Variables

• Two categories
• Independent
• Variables in an experiment or study which are not
  easily to be manipulated without changing the
  participants.
• Age, gender, year, classroom teacher, any
  personal background data, etc
• Dependent
• Variables which are changed in an experiment
• Hours of sleep, amount of food, time given to
  complete an activity, curriculum, instructional
  method, etc.

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Variables

• A variable any measured characteristic or
  attribute that differs for different subjects.
• Two types
• Quantitative sometimes called "categorical
  variables.
• measured on one of three scales
• Ordinal first second or third choice (most of
  the children preferred red popsicles, and grape
  was the second choice)
• Interval direct time periods between two events
  ( time it takes a child to respond to a question)
• Ratio scale compares the number of times one
  event happens in comparison to another event.
  (example the number of time a black card is
  pulled in comparison to the number of times a red
  card is pulled)
• Qualitative
• measured on a nominal scale.

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Types of Data

• Nominal Data  -- Data that describe the presence
  or absence of some characteristic or attribute
  data that name a characteristic without any
  regard to the value of the characteristic also
  referred to as categorical data. Male 1 Female
  2, blue, green, etc
• Ordinal Data -- Measurement based on the rank
  order of concepts or variables differences among
  ranks need not be equal.
• interval data -- Measurement based on numerical
  scores or values in which the distance between
  any two adjacent, or contiguous, data points is
  equal scale without a meaningful or true zero
• Ratio Data  -- Order and magnitude. Measurement
  for which intervals between data points are
  equal a true zero exists if the score is zero,
  there is a complete absence of the variable.

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• Four levels
• nominal assigning items to groups or categories
  
• Examples Classroom, color, size
• Ordinal ordered in the sense that higher numbers
  represent higher values
• Examples 1 freshmen, 2 sophomore
• Interval one unit on the scale represents the
  same magnitude on the trait or characteristic
  being measured across the whole range of the
  scale.
• Interval scales do not have a "true" zero point,
• it is not possible to make statements about how
  many times higher one score is than another.
• Ratio represents the same magnitude on the trait
  or characteristic being measured across the whole
  range of the scale.
• DO have true zero points

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Nominal level of measurement

• Assigns a number to represent a group (gender
  geography)
• Numbers represent qualitative differences
  (good-bad)
• No order to numbers
• Statistics -- mode, percentages, chi-square

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Ordinal level of measurement

• Things are rank-ordered -- gt, lt
• Numbers are not assigned arbitrarily
• Assume a continuum
• Examples -- classification (fr, soph, jr, sr),
  levels of education, Likert scales
• Statistics--median (preferred), mode, percentage,
  percentile rank, chi-square, rank correlation.

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Interval level of measurement

• Equal units of measurement
• Arbitrary zero point--does not indicate absence
  of the property
• Example -- degrees, Likert-type scales
  (treatment), numerical grades
• Statistics -- frequencies, percentages, mode,
  mean, SD, t test, F test, product moment
  correlation

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Ratio level of measurement

• Absolute zero
• Interval scale
• Examples -- distance, weight
• Statistics -- all statistical determinations

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Which are these?

• Never married
• Lower middle Class
• Divorced
• Age
• Separated
• Middle class
• Widowed
• Weight
• Religious Affiliations

• Height
• Political Affiliations
• Distance
• freshmen

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Which are these?

• Never married
• Lower middle Class
• Divorced
• Age
• Separated
• Middle class
• Widowed
• Weight
• Religious Affiliations

• Height
• Political Affiliations
• Distance
• freshmen
• Minutes

N
I/R
O
N
N
I/R
O
I/R
N
I/R
O
N
I/R
N
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Key Point

• Statistical Significance must be distinguished
  from practical significance
• Even a small difference in a large sample might
  be significant if the sample is large
• No p-value of a .0001 means that 1 in 10000 times
  the difference observed will occur by chance (no
  real difference between groups)

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Example Hypothesis

• There will be no significant difference in the
  EOC scores for schools that use CAERT and those
  that dont.
• The EOC exam scores for schools using Caert and
  those that dont will not be significantly
  different.
• The EOC exam scores for schools using Caert and
  those that dont will be significantly different.

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Statistics for Teachers
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StatisticsIf you can assign a number to it,
you can measure it Dr. W. Edward Demming

• Statistics
• refers to calculated quantities regardless of
  whether or not they are from a sample
• is defined as a numerical quantity
• Often used incorrectly to refer to a range of
  techniques and procedures for analyzing data,
  interpreting data, displaying data, and making
  decisions based on data. Because that is the
  basic learning outcomes of a statistics course.

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What is the mean medium and the mode in this
example?
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Descriptive statistics

• Descriptive statistics
• summarize a collection of data in a clear and
  understandable way.
• Example Scores of 500 children on all parts of a
  standardized test.
• Methods numerical and graphical.
• Numerical more precise- uses numbers as accurate
  measure
• mean the arithmetic average which is calculated
  by adding a the scores or totals and then
  dividing by the number of scores.
• standard deviation. These statistics convey
  information about the average degree of shyness
  and the degree to which people differ in shyness.
  
• Graphical better for identifying patterns
• stem and leaf display a graphical method of
  displaying data to show how several data are
  aligned on a graph
• box plot. Graphical method to show what data are
  included. The box stretches from the 25th
  percentile to the the 75th percentile
• historgrams.
• Since the numerical and graphical approaches
  compliment each other, it is wise to use both.

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Inferential statistics
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For choosing a statistical test variables fall
into 2 groups

• Continuous variables are numeric values that can
  be ordered sequentially, and that do not
  naturally fall into discrete ranges.
• Examples include  weight, number of seconds it
  takes to perform a task, number of words on a
  user interface
• Categorical variable values cannot be
  sequentially ordered or differentiated from each
  other using a mathematical method.
• Examples include  gender, ethnicity, software
  user interfaces

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Tools for Measuring

• Measurement is the assignment of numbers to
  objects or events in a systematic fashion.
• Four levels
• nominal assigning items to groups or categories
  
• Examples Classroom, color, size
• Ordinal ordered in the sense that higher numbers
  represent higher values
• Examples 1 freshmen, 2 sophomore
• Interval one unit on the scale represents the
  same magnitude on the trait or characteristic
  being measured across the whole range of the
  scale.
• Interval scales do not have a "true" zero point,
• it is not possible to make statements about how
  many times higher one score is than another.
• Ratio represents the same magnitude on the trait
  or characteristic being measured across the whole
  range of the scale.
• DO have true zero points

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Data Analysis

• Explaining and interpreting the data
• Data are plural
• You are looking at more than one number or group
  of numbers subject-verb agreement is important
  when writing.
• Central Tendency measures of the location of the
  middle or the center of the whole data base for a
  variable or group of variables
• Frequency the number of times a number appears
• Mean the arithmetic average
• Mode the number that appears most often
• Median the number in the middle when numbers are
  arranged by value
• Skew A distribution is skewed if one of its
  tails is longer than the other. Data may be
  skewed positively or negatively.
• Standard deviation the amount of variance
  between each sigma

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Inferential statistics

• Inferential statistics
• Infers or implies something about population from
  a sample.
• Population A total group
• Sample A few from the whole group
• Representative sample a sample that is equally
  propionate to the population
• Random Sample a sample that is chosen strictly
  by chance is not hand-picked
• Probability the percentage of change that an
  event will occur

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Parameters vs Statistics Parametric vs
Non-Parametric

• Definitions again
• Parameter is the true value in the population of
  interest (everyone)
• Statistics is a number you calculate from your
  sample data in order to estimate the parameter
• Example
• All the Ag Teachers of the state
• Only 25 teachers selected from the 285 that exist
  

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What can make the sample different from the true
value/result of the whole?

• Students taught by teachers using Caert will
  score higher on end of course exams than those
  who do not.
• True difference one group actually has a higher
  capacity to learn.
• Random Variations -- The two populations have
  identical means and the observed differences is a
  coincidence of sampling
• Sampling error (bias) Poorly selected samples
  not representing the population.

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Parameters or Parametric Data

• Parameter a numerical quantity measuring some
  aspect of a population of scores.
• Parameters are usually estimated by statistics
  computed in samples
• Quantity Parameter Greek letters are commonly
  accepted for writing formulas
• Statistical symbols are most common in reporting
  actual data analysis in reports or articles.

Greek letters are used to designate parameters
Quantity Parameter Statistic
Mean µ M
Standard deviation s s
Proportion p p
Correlation ? r
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Stats tests types of data each use

• 1 Sample t-test         1 Continuous Dependent
  Variable with normal distribution         0
  Independent Variables  
• 1 Sample Median         1 Continuous Dependent
  Variable with non-normal distribution         0
  Independent Variables 
• Binomial test         1 Bi-level Categorical
  Dependent Variable         0 Independent
  Variables 
• Chi-Square Goodness of Fit      1 Categorical
  Dependent Variable         0 Independent
  Variables         
• 2 Independent Sample t-test     1 Continuous
  Dependent Variable with normal distribution
• 1 (2 level) Categorical Independent Variable
•  Wilcoxon Signed Ranks Test     1 Continuous
  Dependent Variable with non-normal distribution
    
• 1 (2 level) Categorical Independent Variable
• Chi Square Test         1 Categorical
  Dependent Variable         1 (2-level)
  Categorical Independent Variable
• Fisher Exact Test         1 Categorical
  Dependent Variable         1 (2 level)
  Categorical Independent Variable
• Paired t-test     1 Continuous Dependent Variable
  with normal distribution,  1 (2 Level)
  Categorical Independent Variable
• One-way repeated measures ANOVA 1 Continuous
  Dependent Var w/normal distribution
• 1 (Multi-Level) Categorical Independent Variable
• Friedman Analysis of Variance by Ranks 1
  Continuous Dependent Var w/ non-normal
  distribution
• 1 (Multi-Level) Categorical Independent Variable
• One-way ANOVA         1 Continuous Dependent
  Variable with normal distribution
• 1 (Multi-level) Categorical Independent Variable
• Kruskal Wallis        1 Continuous Dependent
  Variable with non-normal distribution
• 1 (Multi-level) Categorical Independent Variable 

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Results
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Results

• At the end of the trial experience schools using
  Caert had EOC exam scores that were 18 that
  were higher than those schools that did not use
  Caert.
• Alpha set at plt.05
• Observed P value of .03

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Conclusion

• Interpretation Given that there is no true
  (other than scores) difference between schools
  using Caert and those that dont, the probability
  of observing a 3 (.03) or more difference due to
  chance is less than .05

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ANOVA

• A factorial ANOVA has two or more categorical
  independent variables (either with or without the
  interactions) and a single normally distributed
  interval dependent variable. 

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ANOVA

• In statistics, ANOVA is short for analysis of
  variance. Analysis of variance is a collection of
  statistical models, and their associated
  procedures, in which the observed variance is
  partitioned into components due to different
  explanatory variables.
• The initial techniques of the analysis of
  variance were developed by the statistician and
  geneticist R. A. Fisher in the 1920s and 1930s,
  and is sometimes known as Fisher's ANOVA or
  Fisher's analysis of variance, due to the use of
  Fisher's F-distribution as part of the test of
  statistical significance.

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Z test

• The Z-test is a statistical test used in
  inference which determines if the difference
  between a sample mean and the population mean is
  large enough to be statistically significant,
  that is, if it is unlikely to have occurred by
  chance.
• The Z-test is used primarily with standardized
  testing to determine if the test scores of a
  particular sample of test takers are within or
  outside of the standard performance of test
  takers.

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Pearson Correlation

• The PEARSON Correlation is a calculation between
  the correlation coefficient between two
  measurement variables when measurements on each
  variable are observed for each of N subjects.
• (Any missing observation for any subject causes
  that subject to be ignored in the analysis.) The
  Correlation analysis tool is particularly useful
  when there are more than two measurement
  variables for each subject. It provides an output
  table, a correlation matrix, showing the value
  applied to each possible pair of measurement
  variables.

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Two-Sample t-Test

• The Two-Sample t-Test analysis tools test for
  equality of the population means underlying each
  sample. The three tools employ different
  assumptions that the population variances are
  equal, that the population variances are not
  equal, and that the two samples represent before
  treatment and after treatment observations on the
  same subjects.

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Research Techniques

• Types of hypothesis testing
• T-test comparing the mean of two groups
• ANOVA Analysis of Variance used to compare the
  means of several variables
• Correlation compares the relationship of two
  groups
• Chi Square of independence explains if is a
  relationship between the attributes of two
  variables.
• Linear regression the prediction of one variable
  based on another variable, when the relationship
  between the variables is assumed to assumed to be
  linear.

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Normal Curve
In practice, one often assumes that data are from
an approximately normally distributed population.
If that assumption is justified, then about 68
of the values are at within 1 standard deviation
away from the mean, about 95 of the values are
within two standard deviations and about 99.7
lie within 3 standard deviations. This is known
as the "68-95-99.7 rule" or the "Empirical Rule".
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Key points
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Comparing groups for Sig Diff
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Key Terms

• Use for new terms in profession (cognitive
  processing skills)
• Give preciseness to ambiguous term (learner)
• General term used in special way (learning style)
• Writing definition
• State term
• Give broad class to which term belongs
• Specify how term is used that differs
• Conclusion not always used
• Summarizes if necessary
• Tells reader what to expect

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Survey Construction

• Parts
• Title
• Directions introduction to survey
• Scales
• Items (a list of statements or questions)
• Usually with a scale of some type
• Rating
• Ranking
• Semantic differential
• Likert type scale
• Demographical info

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Likert type scale

• Ice cream is good for breakfast
• Strongly disagree
• Disagree
• Neither agree nor disagree
• Agree
• Strongly agree

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Rating

• Scale of 1 to 5 or 1 to 7 , etc.
• ? 1 Best or highest
• ? 5 Best or highest
• Even number of items or odd?
• Forced choice no fence sitting
• Middle allows a middle ground response
• Might allow for not opinion, (NA or NO)

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Semantic differential
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• In order to succeed you must know what you are
  doing, like what you are doing, and believe in
  what you are doing
• Will
  Rogers

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Setting Alpha Level

• Set alpha at something like 0.05
• Conduct a statistical test
• Obtain a p-value

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• Parametric tests
• Pearson Product Correlation Coefficient
• Student t-Test
• The z-Test
• ANOVA
• Nonparametric tests
• Chi-Squared
• Spearman Rank Coefficient
• Mann-Whitney U Test
• Kruskal-Wallis Test