Chapter I
Introduction to Inferential Statistics for Education
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Objetive
Chapter
Introduction of the course
Education in statistics deals with evidence-based reasoning, particularly with data analysis. Therefore, education in statistics has strong similarities with education in empirical disciplines such as psychology, in which education is closely linked to "practical" experimentation. It specifically helps in the assessment which leads to the improvement of teaching and learning statistics at all levels of education. The applications of basic statistical concepts in real life which aims to solve problems found in educational research and related policies. The focus is on understanding how to use and interpret the statistical procedures commonly used in quantitative research with the help of statistical software to aid in data analysis
Research design and statistics
In a quantitative research, Statistics is directly related to the design and analysis of the data, transforming it into information. Therefore, part of the course focuses on developing skills to locate, understand, interpret and criticize educational research. The course provides an overview of the design and process of research, introduces the concepts and skills involved in the understanding and analysis of research in education, and provides an overview of basic and general knowledge of various research methodologies. The objectives of the course are:
Understand the relationship between research questions, designs and methodologies Understand different research designs and methods as correlational, experimental, .... Understand and interpret statistical data and findings
Understand and apply concepts of validity and evidence of reliability of an instrument such as a test or survey.
Research questions in Education and Psychology
Family Engagement: Strengthening Family Involvement to Improve Outcomes for Children
Family engagement seeks better outcomes for children and families by actively involving them in the different systems that serve them. Lacy Wood and Rebecca Ornelas discuss how family engagement may improve both academic outcomes and mental health for children.
School Improvement Explained: The Geography of School Improvement in Texas
School improvement efforts are often influenced by where schools are located. In this video, Trent Sharp talks about his work with the Texas Comprehensive Center to examine the geographic and social factors that affect low performing schools and high performing Title one schools, which serve a large percentage of low-income students, throughout the state.
Is Reading Contagious? Examining Parents’ and Children’s Reading Attitudes and Behaviors
When children have positive attitudes and behavior towards reading, they generally also demonstrate strong reading skills. Strong reading skills enable children to access and learn content in a variety of subjects and reap a host of other academic and nonacademic benefits. On July 13, 2016, AIR hosted a presentation and discussion that examined whether parents’ reading attitudes and behaviors are shared by their children—that is, if reading attitudes and behaviors are “contagious.”
Sources of data:
You begin every statistical analysis by identifying the source of the data. Among the important sources of data are published sources, experiments, and surveys.
Survey. A process that uses questionnaire or similar means to gather values for the responses from a set of participants.
Address to find data in Rwanda:
www.statistics.gov.rw/
https://www.unicef.org/rwanda/education.html
http://www.tradingeconomics.com/rwanda/school-enrollment-primary-percent-net-wb-data.html School enrollment - primary (% net) in Rwanda
http://rwanda.opendataforafrica.org/mlhmqxf/rwanda-census?lang=en http://hdirwanda.org/?gclid=CMSpgo2Dw9ECFRMW0wode3cAOg
http://www.memoireonline.com/11/11/4963/The-role-of-SMEs-in-rwanda-from-1995-to-2010.html
1.1 Why study Statistics?
The study of statistics will serve to enhance and further develop critical and analytic thinking skills. To do well in statistics one must develop and use formal logical thinking abilities that are both high level and creative.
Statistics and probability are important for making decisions in life.
Test score trends are one of the most commonly used statistics in the field of education. They are used to evaluate the effectiveness of classroom teachers and the validity of the tests themselves as well as the effects of various risk factors on educational outcomes.
One of the most important reasons is to be able to effectively conduct research. Without the use of statistics it would be very difficult to make decisions based on the data collected from a research project. Educational research employs scientific methods to find out how teaching and learning can be improved. This can take place within or outside the school setting or it can take place at various levels of education, such as early childhood, primary, secondary or tertiary levels.
Other important reason is to be able to read journals. Most technical journals you will read contain some form of statistics.
No matter what your career, you will make professional decisions that involve data. An understanding of statistical methods will help you make these decisions efectively.
Standard Scores and Normal Curve
In practice, we report on our students after examinations by adding together their scores in the various subjects and thereafter calculate the average or percentage as the case may be. This does not give a fair and reliable assessment. Instead of using raw scores, it is better to use derived scores or standard score. A derived score usually expresses every raw score in terms of other raw score on the test. The commonly used ones in the class room are the Z-Scores, T-Score, Stanines, Percentiles, and others. The computation of each of these will be demonstrated.
Commonly Reported Test Scores Based on the Normal Curve
mean = median = mode
The Normal Curve
• Derived scores are used to specify where the individual score falls on the curve and how far above or below the mean the score falls
• Raw scores are transformed into percentiles, stanine or other standard scores
All scoring scales are drawn parallel to the baseline of the normal curve; and use the deviation from the mean as the reference to compare an individual score with the mean score of a group
Z Scores
The most fundamental standard score, which is a simple conversion of an individual’s raw score to a new score that has a mean of 0 and standard deviation of 1.
To compute a Z score, subtract the mean from a raw score and divide by the SD
To convert a Z score back to a raw score, multiply the Z score by the SD and then add the mean
Raw scores above the mean usually have positive scores while those below the mean have negative Z-scores. Z-scores can be used to compare a child’s performance with his peers in a test or his performance in one subject with another.
Example to converting a raw score to a z-score
Interpreting
Interpreting
Student Raw Score
(x) Z-score
Probabilistic Normal value
Percentile
1 15 0.66 0.7454 74.54%
2 10 -0.71 (1-0.7611)=
0.2389
23.89%
3 17 1.21 0.8869 88.69%
4 13 0.11 0.5438 54.38%
5 8 -1.26 (1-0.8962)=
0.1038 10.38%
From this example we can see the first student “1” that individual who scored a 15 on the exam has a z-score of 0.66. By examining probabilistic Normal table you can see that this student has a value is 0.7454, that mean has a percentile score of approximately 74.54% (The meaning is that approximately 75% of the students obtained less than 15 of raw score).
Procedure to obtain ‘Probabilistic Normal Value’ with Excel
Exercise: determine what the z-score would be for an individual who had a raw score of 12 on this same test, and determine the approximate percentile that this student obtained?
Assignment 1
1. (a) Determine what the z-score would be for an individual student and compare the performance in both course (For the average of the courses and also the analysis per course)
Student
Score in Inferential
Score in
Research Z-Score
A 68 20
B 58 45
C 47 39
D 45 40
E 54 42
F 50 48
G 62 30
I 48 46
J 52 41
(b) Draw a box diagram with the variables score for Inferential and Research
2. An ordinal scale of measurement (Answer the multiple choice questions be writing the correct response (letter).) a. Provides a constant unit of measurement
b. Assumes that values of the variable can be rank-ordered from highest to the lowest, has to do with the naming of categories of people, events, etc, or
c. Compares numbers by saying it is twice or three times another number. 3. Make use of the following scores to answer question
40 31 63 40 48 63 42 67 36 63 39 36 70
a. The median of those score is:_________49.1 0.28 42 13.9 39 b. The mean of those scores is: _________49.1 0.28 42 13.9 39 c. The range of those scores is: _________49.1 0.28 42 13.9 39
d. The standard deviation of those scores is: _________49.1 0.28 42 13.9 39
e. The coefficient of variation of those scores is: _________49.1 0.28 42 13.9 39 Interpret each statistic
4. Under what condition might you prefer to use the median rather than the mean as the best measure of central tendency?
5. Explain why a census is often not the best way to obtain information about population 6. Explain the purpose of a measure of variation
7. What are the two major types of statistics? Describe them in detail, using illustrative examples from your life-world.
Solution Assignment 1 with SPSS
Q1.
First: Fill the data for Q1
Third: Go to the data view and you find there Zscore for each variable
.
Mean Standard Deviation
Minimum Maximum
Score in Inferential 54.30 7.35 45.00 68.00 Score in Research 38.70 8.37 20.00 48.00
Interpret each statistics
Student Score in Inferential Score in Research Z-Inferential Z-Research Probability Inferential Probability Research % Inferential % Research
A 68 20 1.86 -2.23 0.97 0.01 96.88 1.27
B 58 45 0.50 0.75 0.69 0.77 69.27 77.43
C 47 39 -0.99 0.04 0.16 0.51 16.03 51.43
D 45 40 -1.27 0.16 0.10 0.56 10.29 56.17
E 54 42 -0.04 0.39 0.48 0.65 48.37 65.34
F 50 48 -0.59 1.11 0.28 0.87 27.92 86.68
G 62 30 1.05 -1.04 0.85 0.15 85.26 14.92
H 59 36 0.64 -0.32 0.74 0.37 73.88 37.35
I 48 46 -0.86 0.87 0.20 0.81 19.57 80.85
J 52 41 -0.31 0.27 0.38 0.61 37.72 60.83
