Download - Dlsau Stat Presentation Sept 10
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Daisy Mae R. Bongtiwon
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Terminologies
Dependent Variables
IndependentVariables
Discrete Variables Continuous
Variables
Statistic
Parameter Class intervals
Class limits
Class boundaries
Class marks Class size Class
frequency Range Normal
Distribution
NullHypothesis
AlternativeHypothesis
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Types of Data
Qualitative Data
Quantitative Data
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Measurement of Scales
Nominal
Ordinal
Interval Ratio
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Sampling Techniques
Simple random sampling
Stratified random sampling
Systematic random sampling Cluster sampling
Multistage sampling
Sampling using a Formula
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Methods of Collecting Data
Direct or interview
Indirect or questionnaire
Observation Telephone Interview
Experiments
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Methods of Presenting Data Textular Method
Tabular Method
Semi-Tabular method Graphical presentation
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CONSTRUCTING THE FREQUENCY
DISTRIBUTION Determine the range of the distribution
Determine the class size.
The lower class limit must be multiples of class size. The lower class interval should include the lowest
score while the highest interval must contain thehighest score.
Find the class marks of the class intervals. Tally the frequencies for each interval and sum them.
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Graphical Presentation of Data
Histogram
Bar graph
Frequency Polygon Cumulative Frequency Polygon
Pie diagram
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MEAN
The mean is used for interval and ratio measurements.
The mean is used if higher statistical computations are
wanted. The mean is used if there are no extreme values in a
distribution since it is easily affected by extremely highor extremely low scores. Thus, the distribution is
approximately normal. The mean is used when the greatest reliability of the
measures of central tendency is wanted since itscomputations include all the given values.
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MEDIAN
The median is used for ordinal or rankedmeasurements.
If there are extreme cases, thus the distribution ismarkedly skewed.
If we desire to know whether the cases fall within theupper halves or lower halves of a distribution.
For an open-end distribution; that is, the lowest or thehighest class interval or both are not defined as 50 andbelow or 100 and above.
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MODE
The mode is used for nominal or categorical data;
If the most popular or most typical case or value in a
distribution is wanted, If a rough or quick estimate of a central value is
wanted..
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LIMITATIONS OF THE MEAN
It is the most widely used average, because it is themost familiar. It is often, however misused. It cannotbe used if the clustering of the values or items is notsubstantial. An example is when representing thescores or values, 10 and 100 since they are far apart.
When the given values do not tend to cluster aroundthe central value, the mean is a poor measure ofcentral location.
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LIMITATIONS OF THE MEAN
It is easily affected by extremely large or small values.One small value can easily pull down the mean.
The mean cannot be utilized to compare distributionssince the means of two or more distributions may bethe same but their other characteristics maybe entirelydifferent.
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LIMITATIONS OF THE MEAN
The means of distribution A whose values are 80, 85and 90 and distribution B whose values are 86, 85 and84 are both 85. However, we cannot imply that bothdistributions posses the same characteristics sincetheir patterns of dispersions or variations are markedlydifferent despite having the same mean.
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THE LIMITATIONS OF THE MEDIAN
It is easily affected by the number of items in adistribution.
It cannot be determined if the given values are notarrange according to magnitude.
If several values are contained in a distribution, itbecomes a laborious task to arrange them according to
magnitude. Its value is not as accurate as the mean because it is
just an ordinal statistics.
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THE LIMITATIONS OF THE MODE
It is rarely or seldom used since it does not alwaysexist.
It is very unstable because its value easily changesdepending on the approaches used in finding it.
Its value is just a rough estimate of the center ofconcentration of a distribution.
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QUANTILES
Quartiles
Deciles
Percentiles
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MEASURES OF VARIABILITY
Range
Mean Deviation
Standard DeviationVariance
Quartile Deviation
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TEST OF HYPOTHESIS
Examples: Title: The NSAT Scores and Academic achievement of the students in
Private and Public Schools Ho: There is no significant relationship between the NSAT
performance and the academic achievement among the four learning areas of
private schools, public schools and combination of private and public schools. H1: There is a significant relationship between the NSAT performance
and the academic achievement among the four learning areas of privateschools, public schools and combination of private and public schools.
Tile: A Comparative Study on the Consumers Acceptance of X and YToothpastes Ho: The consumers acceptance of X and Y toothpastes are the same. H1: The consumers acceptance of X and Y toothpastes are not the
same.
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Title: A study on the relationship of Smoking Habitsto Hypertension Among the Employees of ABC Corporation Ho: There is no relationship between smoking habits and
hypertension among the employees of ABC Corporation.
H1: There is a relationship between smoking habits andhypertension among the employees of ABC Corporation.
Title: Competencies of Nurses from the Government
Hospitals and Private Hospitals
Ho: The competencies of nurses from the governmenthospitals is equal to the competencies of nurses from privatehospitals.
H1: The competencies of nurses from the governmenthospitals is not equal to the competencies of nurses from privatehospitals.
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STEPS IN TESTING HYPOTHESIS
1. Formulate the null hypothesis.
2. Select an appropriate alternative hypothesis.
3. Determine the level of significance to be used.
4. Choose an appropriate test statistic and determinethe critical value of the test statistic.
5. Find the value of the test statistic using the sampledata.
6. Make the decision. Reject Ho if the absolutecomputed value of the test statistic is greater thanthe absolute critical value otherwise accept Ho.
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PAIRED OBSERVATION
Formula:
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Examples:A random sample of 10 female adults was taken to test the
effectiveness of a reducing pill. Their weight before taking the
pill and the weight 10 days after the pill had been taken wererecorded as follows:Weight in pounds before Weight in pounds after160 156144 142
137 134152 150159 154158 153149 146
164 159147 145156 152Test the hypothesis using the 0.1 level of significance.
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The teacher wants to test the effectiveness of a new learning strategy inincreasing the performance of the students . A sample of 8 children wereconsidered for the experiment. The pretest were given before the start of theexperiment, and then the learning strategy is implemented. After thecompletion of the learning strategy, the 8 children were given a posttest to
determine if there is a gain in performance. The result as follows:Student Pretest Posttest1 30 352 34 413 36 404 42 40
5 38 406 33 377 31 368 36 38
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CORRELATION ANALYSIS
Using Pearson Product Moment CorrelationCoefficient or simply Pearson r.
Formula:
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Examples:The following are the score on the NSAT examination and achievement grades of
15 students of a certain college.
Student No. NSAT Achievement Grade1 65 802 98 963 86 914 78 845 90 89
6 72 857 88 928 75 839 96 9410 87 9311 80 84
12 79 7613 84 8714 82 8515 93 93Determine the relationship existing between the two variables and the
significance of r using the 0.05 level.
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An exclusive school in Manila made a study on the relationship of age and teachingperformance of teachers as evaluated by the students using the 5-point scale where 5 isthe highest. With a random sample of 16 teachers, test if the relationship is significantusing the 0.05 level. The result of the sampling is shown:
Teacher No. Age Performance1 38 3.892 30 4.123 37 4.054 42 3.615 45 3.086 52 2.587 48 3.428 33 4.479 36 4.6810 32 4.3911 49 2.9612 48 3.01
13 56 2.8014 30 4.3415 44 3.6716 43 3.55
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REGRESSION ANALYSIS
Formula:
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A researcher wants to know if there is a relationship between hours spent in
studying a particular subject at home and the achievement of the student inthe subject. If a significant relationship can be established, what prediction
equation could be used to estimate achievement in the subject knowing thenumber of hours spent in studying the subject at home? Let = 0.05.
The following were the results of the observations:Student No. Hours Spent Achievement Grade1 2.5 89
2 2.75 883 1.5 824 1.0 775 3.0 906 2.5 917 1.25 80
8 3.5 939 1.5 8110 2.0 86What would be the predicted achievement grade of a student who spent 3.25 hrs
studying the subject?
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`A study was made to determine the relationship existing between thegrade in Calculus and the grade in Fortran Computer Language. Arandom sample of 10 computer students in a certain university weretaken and the following are the results of the sampling:
Student No Calculus Fortran1 75 782 83 873 80 78
4 77 765 89 926 78 817 92 898 86 89
9 93 9110 84 84
What would be the predicted grade of a student in Fortran who has agrade of 85 in Calculus and what regression equation could be used?
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CHI-SQUARE DISTRIBUTION
Formula:
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The following results were obtained in a survey
conducted with college students on the prohibiteddrug issue.
Do the responses of the two groups differ using the 0.05level of significance?
Gender / Opinion Agree Disagree
Male
Female
28
20
122
140
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Determine if gender is related to work performance asindicated by the data below:
Test the hypothesis using the 0.05 level.
Low Average High
Male
Female
35
30
46
57
53
48
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ANALYSIS OF VARIANCE
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A study was conducted to determine if there is asignificant difference existing in the meanachievement of students from three schools. The databelow show the result of the survey.
Use a 0.05 level of significance.
Student No School X School Y School Z
1
2
3
4
5
6
7
8
9
10
86
72
78
90
88
79
77
87
95
83
80
85
81
84
86
75
80
83
79
92
83
89
84
80
82
78
76
85
87
94
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Five teachers taught college statistics to five sections ofcollege students. The final grades of a random sample
of 8 per section are shown below.
Is there a significant difference in the final gradesgiven by the 5 teachers at the 0.05 level?
Student Section 1 2 3 4 5
1
2
3
4
5
6
7
8
86
80
85
91
87
92
86
90
75
84
83
86
79
83
81
88
89
79
86
92
78
82
81
90
90
88
86
93
94
85
84
88
78
82
84
81
84
87
83
79