Transcript Statistics for teachers

Session 8
Today
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Handouts—
Review of last week topics
Content validity and reliability
Survey construction
– Two research questions
 Leadership development activity – Pre post
 Perception about Teaching -- pre -post
 Next SPSS Activity --To the Lab
Components of Chapter 1
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Introduction to chapter
Background of the study
Problem statement
Significance of study
Overview of methodology
Delimitations of study
Definitions of key terms
Conclusion (optional)
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
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
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
Characteristics of
Components
 Delimitations – as needed
– Not flaws
– Establishes the boundaries – can study be
generalized?
– Consider:
 sample
 Setting
 time period
 methods
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
Survey Construction
 Parts:
– Title
– Directions introduction to survey
 Scales
– Items (a list of statements or questions)
 Usually with a scale of some type
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Rating
Ranking
Semantic differential
Likert type scale
 Demographical info
Likert type scale
 Ice cream is good for breakfast
– Strongly disagree
– Disagree
– Neither agree nor disagree
– Agree
– Strongly agree
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)
Semantic differential
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
 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 zero
 Ratio Data -- 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.
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
Ordinal level of
measurement
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Things are rank-ordered -- >, <
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, chisquare, rank correlation.
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
Ratio level of measurement
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Absolute zero
Interval scale
Examples -- distance, weight
Statistics -- all statistical
determinations
Which are these?
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Never married
Lower middle Class
Divorced
Age
Separated
Middle class
Widowed
Weight
Religious Affiliations
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Height
Political Affiliations
Distance
freshmen
Which are these?
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Never married N
Lower middle Class O
Divorced N
Age I/R
Separated N
Middle class O
Widowed N
Weight I/R
Religious Affiliations N
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Height I\R
Political Affiliations N
Distance I\R
freshmen O
Minutes 1\R
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".
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
Review
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Name 5 types of research.
What are the 2 types of Research, by Philosophy?
What are the 4 purposes of research?
What are the Criteria for Research Project?
What is a Population in terms of research?
What is the purpose of a review of literature?
Where can you go to do a review of literature?
Why is sampling important?
Now Your Assignment
 The two articles to review…..
 Open ended…..not much direction--for a reason…
 Ask for a short summary, ½ to 1 page, of what you
can learn or tell me about the research.
 Last week we had discussed different kinds of
research, etc…..based just on that discussion
alone you might come up with some things to look
for associated with each article….
What can be learned from a
research article?
 Purpose of any research article is to share
results
– Conclusions & Recommendations
 Before you accept the conclusions and
recommendations of any research article
what do you need to know?
What Did You Learn From Your
Review of the Two Articles?
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What kind of study was this?
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What was the purpose of the study?
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What were the research questions? Were they questions or hypotheses?
What was the population?
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Survey
Experimental
Historical
Experimental
Correlational
Evaluation
Naturalistic
Was there a sample? Did the paper describe how the sample was taken?
How big was the sample? Did it describe how they determine sample size
Was it qualitative or quantitative? How can you tell?
Did the author give a good intro to the problem?
Describe the methods used?
What statistics were used?
How was the paper divided? What were the sections?
Article 1:
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What kind of study was this?
What was the purpose of the study?
What was the population?
Was it qualitative or quantitative? How can you
tell?
 Did the author give a good intro to the problem?
 Describe the methods used?
 What statistics were used?
Article 2: Evaluation of a Livestock
Ethics Curriculum for High School Youth
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What kind of study was this? This used a quasi-experimental design
What was the population? Agricultural Education students from Indiana high schools.
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Was there a sample? yes
Did the paper describe how the sample was taken? yes
How big was the sample? 305 students
Did it describe how they determine sample size? no
Was it qualitative or quantitative? Qualitative How can you tell? Answered questions like a survey
What was the purpose of the study? Evaluate effectiveness of a livestock ethics curriculum developed for high
school students in Agricultural Education classes.
– Are participants aware of the principles involved in making ethical choices when faced with decisions in youth
livestock programs?
– Are participants able to determine whether certain practices at a youth livestock show are ethical or unethical?
– Will participants make ethical choices when faced with decisions in youth livestock programs as demonstrated by
real life case study analysis?
– Will demographics such as current grade in school, gender, years enrolled in 4-H, years enrolled in FFA, years
enrolled in beef, swine, sheep. Horse, dairy, and other livestock projects, or previous participation in a livestock
ethics curriculum; help explain the difference in pre and post-test scores amongst participants?
Pre-test and post-test; given before and after the curriculum is taught.
Describe the methods used?
Stats used? Descriptive.
What were the parts of the article?
Article 3: Teacher Attrition Among Women
in Secondary Agricultural Education
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What kind of study was this? Mixed-method case study
What was the population? Female students who took at least one
pre service course at Oklahoma State University between 1999 to 2004.
n=36; N=78
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Was it qualitative or quantitative? Qualitative, it says so.
Purpose of the Study? To investigate female under-
representation in AGED through the lens of Grissmer & Kirby’s
theory of teacher attrition to better understand this phenomenon.
Res Questions
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Profile the women demographically.
Analyze attrition trends of the students in the pre service program.
Qualitatively explore women’s experiences in the AGED context.
Methods? Interviews; semi-structured interview protocol.
Stats? Descriptive
Article 4: A Study of Supervisor and Employee
Perceptions of Work Attitudes in Information
Age Manufacturing Industries.
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What kind of study was this? Experimental design
What was the population? Employees of manufacturing industries in central Illinois area.
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Sample group? Cluster sampling (without replacement where each industry was treated as a cluster)
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-1209 for six industries
-yes; n=N/(N(d)^2+1) where n = sample size, N= total population, d= level of significance (0.05)
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Was it qualitative or quantitative? Qualitative, used questionnaires
What was the purpose of the study? To investigate (a) whether the type of job (i.e. information job
versus non-information job) was related to employee work attitudes. (b) if there existed any difference between
work attitudes as perceived by employees and as perceived by their supervisors, and (c) if there existed any
relationship between employee work attitudes and demographic variables such as age, gender, level of education,
and length of service.
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Hypotheses:
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H01: At the p 0.05 level of confidence, there is no significant difference between the self-perceptions of work attitudes of industrial
employees with information jobs and their work attitudes as rated by their supervisors.
H02: At the p 0.05 level of confidence, there is no significant difference between the self-perceptions of work attitudes of industrial
employees with non-information jobs and their work attitudes of industrial jobs and their work attitudes as rated by their supervisors.
H03: At the p 0.05 level of confidence, there is no significant difference between the perceptions of work attitudes of industrial
employees with non-informational jobs and industrial employees with information jobs.
H04: At the p 0.05 level of confidence, there is no significant relationship between the work attitudes of information employees and the
variables of gender, age, level of education, and length of service.
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H05: At the p 0.05 level of confidence, there is no significant relationship between the work attitudes of noninformation
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Describe the methods used?
Stats?
For Tonight
Statistics for Teachers
Based on:
Hyperstat Online and Learning Statistics Through
Playing Cards by Thomas R. Knapp (1996)
Adapted by: Tammie Pannells and David Agnew
Statistics
“If 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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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
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
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.
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.
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.
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
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
σ
s
Proportion
π
p
Correlation
ρ
r
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
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.
References
 David M. Lance HyperStat Online Statistics Textbook
http://davidmlane.com/hyperstat/
 Knap, T. R. (1996). Learning Statistics Through Playing
Cards. SAGE publications London
 Sanocki, T. (2001). Student Friendly Statistics. PrenticeHall
Upper Saddle River NJ
 Fox, J. A. & Levin, J. ( 2005). Elementary Statistics in the
Criminal Justice Reseach The Essentials Pearson Boston
Review from last week, Answers
Criteria for Research
Project
 Universality -- can be completed by
anyone
 Replication -- can be repeated under
same conditions with same results
 Control -- use parameters to control as
many variables as possible
 Measurement -- important to quantify as
much as possible
Types of Research
-- by Method
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Experimental
Correlational
Evaluation
Historical
Naturalistic
Survey
Types of Research
-- by Philosophy
 Quantitative -- (Positivistic)
– Things are meaningful only if we can verify
them with our five senses.
 Qualitative -- (Post-positivistic)
– All research is value-laden. Can’t remove
self from research.
What is the Purpose of
Research?
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Describe -- Ex: settings
Predict -- Ex: success based on ACT
Improve--Ex: teaching methods
Explain -- answers “why?”