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### Statistics for Teachers

Review

- 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?

- What kind of study was this?
- Survey
- Experimental
- Historical
- Experimental
- Correlational
- Evaluation
- Naturalistic
- What was the purpose of the study?
- What were the research questions? Were they questions or hypotheses?
- What was the population?
- 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:

- 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

- What kind of study was this? This used a quasi-experimental design
- What was the population? Agricultural Education students from Indiana high schools.
- 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

- 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
- 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

- 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.

- What kind of study was this?Experimental design
- What was the population?Employees of manufacturing industries in central Illinois area.
- Sample group? Cluster sampling (without replacement where each industry was treated as a cluster)
- -1209 for six industries
- -yes; n=N/(N(d)^2+1) where n = sample size, N= total population, d= level of significance (0.05)
- 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.
- Hypotheses:
- 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.
- H05: At the p 0.05 level of confidence, there is no significant relationship between the work attitudes of non-information
- Describe the methods used?
- Stats?

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.

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

Greek letters are used to designate parameters

- 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.

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 Textbookhttp://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

- 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

- 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?

- Describe -- Ex: settings
- Predict -- Ex: success based on ACT
- Improve--Ex: teaching methods
- Explain -- answers “why?”

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