presented by : norazliyati yahya2009905123 nurharani selamat2009324059
DESCRIPTION
EDU 702 RESEARCH METHODOLOGY. Quantitative Data analysis. Presented by : NORAZLIYATI YAHYA2009905123 NURHARANI SELAMAT2009324059 NUR HAFIZA NGADENIN2009720649. QUANTITATIVE DATA ANALYSIS. DATA ANALYSIS. STATISTICS IN PERSPECTIVE. DESCRITIVE STATISTICS. INFERENTIAL STATISTICS. - PowerPoint PPT PresentationTRANSCRIPT
Presented by :
NORAZLIYATI YAHYA 2009905123
NURHARANI SELAMAT 2009324059
NUR HAFIZA NGADENIN 2009720649
QUANTITATIVE DATA ANALYSIS
04/20/23 2
DATA ANALYSIS
DESCRITIVE STATISTICS INFERENTIAL
STATISTICS
STATISTICS IN PERSPECTIVE
QUANTITATIVE DATA Frequency polygons
Techniques for summarizing
quantitative data
Skewed polygons
Histogram &
Stem-leaf Plots
Normal Curve
Average
Spreads
Standard scores & Normal Curve
Correlation
4
FREQUENCY POLYGONSConstructing 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
SKEWED POLYGONS
5
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
HISTOGRAM
6
Bars arranged from left to right on horizontal axis
Width of the bar indicate the range of value in each bar
Histogram facts
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
STEM-LEAF PLOTS
STEM LEAF
2 9
3 72
4 655
5 41555
6 0
7
STEM LEAF
2 9
3 27
4 556
5 14555
6 0
Constructing a Stem-Leaf Plot
Mathematics Quiz Score
Separate number into a stem and a leaf
Group number with the same stem in numerical order
Reorder the leaf values in sequence
NORMAL CURVE
8
Normal Distribution
Majority of the scores are concentrated in the middle of the distribution, scores decrease in
frequency the farther away from the middle
The smooth curve (distribution curve) shows a generalized
distribution of scores that is not limited to one specific set of data
The normal curve is symmetrical and bell-curved, commonly used
to estimate height and weight, spatial ability and creativity.
AVERAGES
9
Measure of Central Tendency
Mode
The most frequent score in
a distribution
Median
The midpoint - middlemost score or halfway between the
two middlemost score
Mean
Average of all the score in a distribution
SPREADS
10
Variability
Standard Deviation Facts
Represents the spreads of a distribution, describe the
variability based on how greater or smaller the standard deviation
34%34%
68%
95%
13.5%13.5%
99.7%2.15%
Mean 1 SD 2 SD-1 SD-2 SD50% of all observation fall on each
side of the mean
68% of the score fall within one standard deviation of the mean
27% of the observation fall between one or two standard deviation away from the mean
99.7% fall within three standard deviations of the mean
STANDARD SCORE & NORMAL CURVE
11
Standard score & Normal Curve z-score
How far a raw score is from the mean in standard
deviation units
Probability
Percentage associated with areas under a normal curve,
stated in decimal form
.3413.3413
.1359.1359 .0215.0215
CORRELATION
12
Correlation Coefficient and Scatterplots
Express the degree of relationship between two
sets of scores
Correlation Coefficient
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
Scatterplots
Used to illustrate different degrees of correlation
CATEGORICAL DATA
13
Techniques for summarizing
categorical data
Frequency TableBar Graphs and
Pie Charts
Crossbreak Table
CROSSBREAK TABLE
14
Grade Level and Gender of Teachers (Hypothetical Data)
Male Female Total
Junior High School Teacher 40 60 100
High School Teacher 60 40 100
Total 100 100 200
Male Female Total
Junior High School Teacher 40 60 100
High School Teacher 60 40 100
Total 100 100 200
Reported a relationship between two categorical variables of interest
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.
A researcher administered a study on the average A researcher administered a study on the average IQ of primary school students at Shah Alam district IQ of primary school students at Shah Alam district and findsand finds their average IQ score is 85.their average IQ score is 85.
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?
If different, how are they different? Are their IQ scores higher or lower?
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?
INFERENTIAL STATISTICINFERENTIAL STATISTICo What is inferential statistic?What is inferential statistic?
It is the Statistical Technique/Method using obtained sample It is the Statistical Technique/Method using obtained sample data to infer the corresponding population.data to infer the corresponding population.
o Type of inferential statisticsType of inferential statistics
SAMPLE SAMPLE = 10.14
POPULATION μ =?
1. EstimationUsing a sample mean to estimate a population mean
Example: Interval Estimation: Confidence Intervals
2. Hypothesis testingComparing 2 meansComparing 2 proportionsAssociation between onevariable and another variable
1. INTERVAL ESTIMATION1. INTERVAL ESTIMATION
RESEARCH OBJECTIVE : RESEARCH OBJECTIVE :
To identify the average IQ of primary school To identify the average IQ of primary school students at Shah Alam district.students at Shah Alam district.
o PopulationPopulation: 1,000 students of Shah Alam primary schools
o SampleSample : 65 primary school students o Sample MeanSample Mean : 85o Standard Error of MeanStandard Error of Mean : 2.0o Interval Estimation Interval Estimation : 95% Confidence Interval = 85 1.96(2) = 85 3.92 = 81.08 or 88.92o InterpretationInterpretation: Researcher has 95% confidence that the
average IQ of primary students at Shah Alam district is between 81.08 or 88.92
SAMPLING ERRORSAMPLING ERROR
What is sampling error?What is sampling error? The difference between the population mean and the sample mean
Why does sampling error occurs?Why does sampling error occurs? Different samples drawn from the same population can have
different properties
How can we quantify sampling error?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
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1. HYPOTHESIS TESTING1. HYPOTHESIS TESTING
What is hypothesis testing?What is hypothesis testing?o A hypothesis is an assumption about the
population parameter.o A parameter is a characteristic of the population;
mean or relationship.o The parameter must be identified before analysis.
Steps in conducting hypothesis testingSteps in conducting hypothesis testing1. State the null hypothesis and research hypothesis.2. Identify the appropriate test.3. State the decision rule for rejecting null hypothesis.
NULL HYPOTHESISNULL HYPOTHESIS RESEARCH HYPOTHESISRESEARCH HYPOTHESIS
There is NONO difference between the population mean of students using method A and the population mean of students using method B
Treatment X has NO EFFECTNO EFFECT on outcome Y
The grade point average of juniors is LESSLESS than 3.0
The average IQ score of primary school students at Shah Alam district EQUALEQUAL to 85
The population mean of students using method A is GREATERGREATER than the population mean of students using method B
Treatment X has AN EFFECTAN EFFECT on outcome Y
The grade point average of juniors is AT LEASTAT LEAST 3.0
The average IQ score of primary school students at Shah Alam district is GREATERGREATER 85
NULL HYPOTHESISNULL HYPOTHESIS The average IQ score of primary school students at Shah Alam
district EQUALEQUAL 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 nullhypothesis, then we conclude Research Hypothesis “the average IQ
score of primary school students at Shah Alam district is GREATERGREATER 85 ”.
ONE AND TWO-TAILED TESTONE AND TWO-TAILED TEST
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.
A HYPOTHETICAL EXAMPLE OF TYPE 1 AND TYPE II A HYPOTHETICAL EXAMPLE OF TYPE 1 AND TYPE II ERRORSERRORS
TYPE OF TESTSTYPE OF TESTS
Quantitative dataQuantitative datat-test for meansANOVAANCOVAMANOVAMANCOVAt-test for r
Categorical dataCategorical data
t-test for difference in proportion
PARAMETRIC TEST
NON PARAMETRIC TEST
Quantitative dataQuantitative dataMann-Whitney U testKruskall-Wallis one way analysis of varianceSign testFriedman two ways analysis of variance
Categorical dataCategorical data
Chi-square test
Comparing Groups
Quantitative DataQuantitative Data• Frequency polygons → central tendency
Interpretation
1. Information of known groups
2. Effect size, ES:
3. Inferential statistics
Mean experimental gain – mean comparison gain
Std dev. of gain of comparison group
Comparing Groups
Categorical DataCategorical Data• Crossbreak tables
Table 1 Felony Sentences for Fraud by Gender
Type of SentenceGender Probation Prison Totals
Male 24 11 35
Female 13 22 35
Totals 37 33 70
Table 1 Felony Sentences for Fraud by Gender (frequencies added)
Gender Probation Prison Totals
Male24
(3.178)11
(2.398) 35
Female13
(2.565)22
(3.091) 35
Totals 37 33 70
Interpretation
• Place data in tables
• Calculate contingency coefficient
c = √ X2
X2 + n
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