dlsau stat presentation sept 10

8/14/2019 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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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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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

dlsau stat presentation sept 10

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