1. Quantitative Data analysis
EDU 702
RESEARCH METHODOLOGY
Quantitative
Data analysis
Presented by :
NORAZLIYATI YAHYA
NURHARANI SELAMAT
NUR HAFIZA NGADENIN

2. QUANTITATIVE DATA ANALYSIS
STATISTICS IN PERSPECTIVE
DESCRITIVE STATISTICS
INFERENTIAL STATISTICS
11/28/2018

3. Techniques for summarizing quantitative data
Frequency
polygons
Histogram &
Stem-leaf
Plots
Skewed
polygons
Techniques for summarizing quantitative data
Normal
Curve
Correlation
Standard scores
& Normal Curve
Average
Spreads

4. FREQUENCY POLYGONS Constructing a frequency polygon
List all scores in order of size,
group scores into interval
Label the horizontal axis by placing all the possible scores at equal intervals
Label the vertical axis by indicating frequencies at equal interval
Find the point where for each score intersect with frequency, place a dot at the point
Connect all the dots with a straight line. l

5. SKEWED POLYGONS Positively Skewed Polygon Negatively Skewed Polygon
The tail of the distribution trails off to the right,
in the direction of the higher score value
The longer tail of the distribution goes off to the left

6. HISTOGRAM Histogram facts
Bars arranged from left to right on horizontal axis
Width of the bar indicate the range of value in each bar
Frequencies are shown in vertical axis, point of intersection is always zero
Bars in the histogram touch, indicate they illustrate quantitative rather than categorical data

7. STEM-LEAF PLOTS Constructing a Stem-Leaf Plot Mathematics Quiz Score2 9 3 72 4
655 5
41555 6
Separate number into a stem and a leaf
Group number with the same stem in numerical order
Mathematics
Quiz Score
STEM
LEAF 2 9 3 27 4
556 5
14555 6
Reorder the leaf values in sequence

8. NORMAL CURVE Normal Distribution
The smooth curve (distribution curve) shows a generalized distribution of scores that is not limited to one specific set of data
Majority of the scores are concentrated in the middle of the distribution, scores decrease in frequency the farther away from
the middle
The normal curve is symmetrical and bell-curved, commonly used to estimate height and weight, spatial ability and creativity.

9. AVERAGES Measure of Central Tendency Mode Mean Median
The most frequent score in a distribution
Average of all the score in a distribution
The midpoint - middlemost score or halfway between the two middlemost score

10. SPREADS Variability Standard Deviation Facts
34%
34%
Represents the spreads of a distribution, describe the variability based on how greater or smaller the standard deviation
68%
13.5%
13.5%
95%
2.15%
99.7%
50% of all observation fall on each side of the mean
-2 SD
-1 SD
Mean
1 SD
2 SD
27% of the observation fall between one or two standard deviation away from the mean
68% of the score fall within one standard deviation of the mean
99.7% fall within three standard deviations of the mean

11. STANDARD SCORE & NORMAL CURVE
z-score
How far a raw score is from the mean in standard deviation units
.3413
.3413
Probability
Percentage associated with areas under a normal curve, stated in decimal form
.0215
.1359
.1359
.0215

12. CORRELATION Correlation Coefficient and Scatterplots
Express the degree of relationship between two sets of scores
Used to illustrate different degrees of correlation
Positive relationship is indicated when high score on one variable accompanied by high score on the other and when low score on one accompanied by low score on the other

13. CATEGORICAL DATA Techniques for summarizing categorical data
Bar Graphs and Pie Charts
Frequency Table
Techniques for summarizing categorical data
Crossbreak Table

14. CROSSBREAK TABLE
Reported a relationship between two categorical variables of interest
Grade Level and Gender of Teachers (Hypothetical Data)
Male
Female
Total
Junior High School Teacher 40 60
100
High School Teacher
200
Junior high school teacher is more likely to be female. A high school teacher is more likely to be male. Exactly one-half of the total group of teachers are female. If gender is unrelated to grade level, the same proportion of junior high school and high school teachers are would be expected female.
Male
Female
Total
Junior High School Teacher 40 60
100
High School Teacher
200

15. A researcher administered a study on the average IQ of primary school students at Shah Alam district and finds their average IQ score is 85.
I don’t want to obtain data for entire population but how am I going to estimate how closely the average sample IQ scores with population IQ scores?
If different, how are they different? Are their IQ scores higher or lower?
Does the average IQ score of students in entire population is also equal to 85 or this sample of students differ from other students in Shah Alam district?

16. INFERENTIAL STATISTIC
What is inferential statistic?
It is the Statistical Technique/Method using obtained sample data to infer the corresponding population.
Type of inferential statistics
POPULATION μ =?
SAMPLE = 10.14
1. Estimation
Using a sample mean to estimate
a population mean
Example:
Interval Estimation: Confidence Intervals
2. Hypothesis testing
Comparing 2 means
Comparing 2 proportions
Association between one
variable and another variable

17. 1. INTERVAL ESTIMATION RESEARCH OBJECTIVE :
To identify the average IQ of primary school students at Shah Alam district.
Population: 1,000 students of Shah Alam primary schools
Sample : 65 primary school students
Sample Mean : 85
Standard Error of Mean : 2.0
Interval Estimation :
95% Confidence Interval = (2)
= = or 88.92
Interpretation: Researcher has 95% confidence that the average IQ of primary students at Shah Alam district is between or 88.92

18. SAMPLING ERROR What is sampling error? Why does sampling error occurs?
The difference between the population mean and the sample mean
Why does sampling error occurs?
Different samples drawn from the same population can have different
properties
How can we quantify sampling error?
Using standard error of mean.
It is useful because it allows us to represent the amount of sampling error associated with our sampling process—how much error we can expect on average. S S P S

19. 1. HYPOTHESIS TESTING What is hypothesis testing?
A hypothesis is an assumption about the population
parameter.
A parameter is a characteristic of the population; mean or relationship.
The parameter must be identified before analysis.
Steps in conducting hypothesis testing
State the null hypothesis and research hypothesis.
Identify the appropriate test.
State the decision rule for rejecting null hypothesis.

20. NULL HYPOTHESIS RESEARCH HYPOTHESIS
There is NO difference between the population mean of students using method A and the population mean of students using method B
Treatment X has NO EFFECT on outcome Y
The grade point average of juniors is LESS than 3.0
The average IQ score of primary school students at Shah Alam district EQUAL to 85
The population mean of students using method A is GREATER than the population mean of students using method B
Treatment X has AN EFFECT on outcome Y
The grade point average of juniors is AT LEAST 3.0
The average IQ score of primary school students at Shah Alam district is GREATER 85

21. NULL HYPOTHESIS The average IQ score of primary school students at Shah Alam district EQUAL to 85
This test is called one sample t test.
At the end of the hypothesis testing, we will get a P value.
If the P value is less than 0.05, we reject the Null Hypothesis and conclude as Research Hypothesis.
If the P value is more than or equal to 0.05, we cannot reject the Null Hypothesis.
In above example, if we get P =0.01, we reject the null
hypothesis, then we conclude Research Hypothesis “the average IQ score of primary school students at Shah Alam district is GREATER 85 ”.

22. ONE AND TWO-TAILED TEST

23. A HYPOTHETICAL EXAMPLE OF TYPE 1 AND TYPE II ERRORS
Susie has pneumonia
Susie does not have pneumonia
Doctors says that symptoms like Susie’s occur only 5 percent of the time in healthy people. To be safe, however, he decides to treat Susie for pneumonia
Doctor is correct. Susie does have pneumonia and the treatment cures her.
Doctor is wrong. Susie’s treatment was unnecessary and possibly unpleasant and expensive.
Type 1 error.
Doctor says that symptoms like Susie’s occur 95 percent of the time in healthy people. In his judgement, therefore, her symptoms are a false alarm and do not warrant treatment, and he decides not to treat Susie for pneumonia
Doctor is wrong. Susie is not treated and may suffer serious consequences.
Type II error.
Doctor is correct. Unnecessary treatment is avoided.

24. TYPE OF TESTS PARAMETRIC TEST NON PARAMETRIC TEST Quantitative data
t-test for means
ANOVA
ANCOVA
MANOVA
MANCOVA
t-test for r
Categorical data
t-test for difference in proportion
NON PARAMETRIC TEST
Quantitative data
Mann-Whitney U test
Kruskall-Wallis one way analysis of variance
Sign test
Friedman two ways analysis of variance
Categorical data
Chi-square test

25. Comparing Groups Quantitative Data
Frequency polygons → central tendency
Most research in education is done in 2 ways:
Comparing 2/more groups
Relating variables within 1 group
Frequency polygons:
Prepare frequency polygons 4 each group’s score
Use these 2 decide d appropriate measure 2 calculate.

26. Interpretation Information of known groups Effect size, ES:
Inferential statistics
Mean experimental gain –
mean comparison gain
Std dev. of gain of comparison group

27. Comparing Groups Categorical Data
Crossbreak tables
Table 1 Felony Sentences for Fraud by Gender
Type of Sentence
Gender
Probation
Prison
Totals
Male 24 11 35
Female 13 22 37 33 70
1. Reporting either %ages / frequencies in crossbreak tables

28. Table 1 Felony Sentences for Fraud by Gender
Probation
Prison
Totals
Male 24
(3.178) 11
(2.398) 35
Female 13
(2.565) 22
(3.091) 37 33 70
Table 1 Felony Sentences for Fraud by Gender
(frequencies added)

29. Interpretation c = √ Place data in tables
Calculate contingency coefficient
c = √ X2
X2 + n

30. THANK YOU...