Title: Session 7 Introduction to Research and Evaluation
1Session 7 Introduction to Research and
Evaluation
- Topic 1 Research Questions and Hypothesis
Testing - And
- Topic 2 Introduction to Statistics
2For Tonight
3Today
- Review the contents of the proposal
- Topics tonight
- Finish the research questions
- Types of data review
- Hypothesis Testing
- Intro to Stats
4The phases of a research project
- Problem statement
- Purpose
- Hypothesis development / research question(s)
- Population / Sample type
- Results reporting (data)
- Statistical testing
- Conclusions Recommendations
5Parts of the Research Report
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- References
- Appendix
6Components 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)
7Characteristics 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
8Characteristics 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
9Ways 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
10Characteristics of Components
- Delimitations as needed
- Not flaws
- Establishes the boundaries can study be
generalized? - Consider
- sample
- Setting
- time period
- methods
11Stating 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
12TYPES OF DATA
13Variables
- 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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15Variables
- 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.
16Types 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.
17- 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
18Nominal 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
19Ordinal 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.
20Interval 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
21Ratio level of measurement
- Absolute zero
- Interval scale
- Examples -- distance, weight
- Statistics -- all statistical determinations
22Which are these?
- Never married
- Lower middle Class
- Divorced
- Age
- Separated
- Middle class
- Widowed
- Weight
- Religious Affiliations
- Height
- Political Affiliations
- Distance
- freshmen
23Which 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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30Key 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)
31Example 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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36Statistics for Teachers
37StatisticsIf 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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40What is the mean medium and the mode in this
example?
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45Descriptive 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.
46Inferential statistics
47For 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
48Tools 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
49Data 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
50Inferential 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
51Parameters 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
52What 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.
53Parameters 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
54Stats 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
55Results
56Results
- 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
57Conclusion
- 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
58ANOVA
- A factorial ANOVA has two or more categorical
independent variables (either with or without the
interactions) and a single normally distributed
interval dependent variable.
59ANOVA
- 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.
60Z 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.
61Pearson 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.
62Two-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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64Research 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.
65Normal 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".
66Key points
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97Comparing groups for Sig Diff
98Key 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
99Survey 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
100Likert type scale
- Ice cream is good for breakfast
- Strongly disagree
- Disagree
- Neither agree nor disagree
- Agree
- Strongly agree
101Rating
- 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)
102Semantic differential
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105- 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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114Setting Alpha Level
- Set alpha at something like 0.05
- Conduct a statistical test
- Obtain a p-value
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120- 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