learning task 3 draft.docx

7/27/2019 learning task 3 draft.docx

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De La Salle University2401 Taft Avenue, Manila 1004

Science Education Department

College of Education

Statistics for Science Education SCE500M

Learning Task 3: Sampling, Presenting Data & Measuring VariabilityRoxanne Diane R. Uy Master of Science in Teaching Biology

The facts of variability, of the struggle for existence, of adaptation to conditions, were notorious

enough; but none of us had suspected that the road to the heart of the species problem lay

through them, until Darwin and Wallace dispelled the darkness. Thomas Henry Huxley

QUESTIONS

1. Give illustrative examples/situations for the various methods/ways on random sampling andnon-random sampling

Three primary methods of non-probability sampling are used in quantitative studies:

convenience/incidental, quota, and purposive.

Example of a convenience sample

Shaker, Scott, and Reid (2004) studied the infant feeding attitudes (breastfeeding versus

formula feeding) of expectant mother. Their sample was convenience sample of 108

expectant mothers and their partners attending three maternity clinics in Scotland.

Example of a quota sample

Reyes, Meininger, Liehr, Chan, and Mueller (2003) examined the differences in adolescents

anger by gender, age, and ethnicity. They used quota sampling to ensure adequate

representation of diverse subgroups of adolescents.

Example of a purposive sample

Staggers, Gassert, and Curran (2002) conducted a study to identify informatics competencies

needed for nurses at various levels of practice. They conducted 3-round survey with a

purposive sample of expert nurses who had at least 5 years of experience in nursing

informatics and had high visibility within the specialty.

The four most commonly used probability sampling design are simple random, stratified

random, cluster, and systematic sampling.

Example of a random sampling

Criste (2003) examined whether nurse anesthetists demonstrate gender bias in treating pain.

Questionnaires were mailed to a national random sample of 450 currently practicing Certified


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Registered Nurse Anesthetists in the United States.

Example of a stratified random samplingUlrich, Soeken, and Miller (2003) studies views of nurse practitioners (NPs) regarding

ethical conflicts associated with managed care. The researchers mailed questionnaires to a

stratified random sample of 700 NPs licensed to practice in the state of Maryland. The

stratifying variable was primary care specialty (Family Health, Pediatrics,

Obstetrics/Gynecology, and Adult Health) as listed with the Maryland State Board of

Nursing.

Example of a systematic sampling

Ruchala, Metheny, Essenpreis, and Borcherding (2003) surveyed a national sample of

obstetric units in the United States to determine the types of intravenous fluids used to dilute

oxytocin for labor induction. They mailed questionnaires to a systematic random sample of

nurse managers in 700 obstetric units with 50 or more births per year as listed by the

American Hospital Association.

2. What are the possible ways in which data can be presented? Give illustrative example foreach possible way.

Textual method

Ungrouped data can be presented in textual form, as in paragraph form. This involves

enumerating the important characteristics, giving emphasis in significant figures ad

identifying important features of the data.

3 13 17 20 27 30 32 35 40 43

9 13 18 21 28 30 33 36 40 4610 14 18 25 28 31 34 37 40 48

10 15 19 26 28 31 35 38 41 50

12 16 20 26 29 32 35 39 42 50


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Textual Presentation for the given data:

The highest score obtained is 50 and the lowest is 3. Ten students got a score of 40 and

above while only 4 got ten and below. Generally, the students performed well in the test with33 students or 66% getting a score of 25% and above.

Tabular method

Sometimes, we could hardly grasp information from a textual presentation of data. Thus, we

may present data using tables. By organizing the data in tables, important features about the

data can be readily understood and comparison can easily be made. Thus, a table shows

complete information regarding the data. A frequency distribution table is a table which

shows the data arranged unto different classes and the number of cases which fall into each

class.

Favorite Colors of the Class

Tally Marks Frequency

2

1

5

8

4

Graphical Method

Some readers find graphical presentation of data easier to comprehend than when data are

presented in tabular form. A graph adds life and beauty to ones work, but more than this, it

helps facilitate comparison and interpretation without going through the numerical data.


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GRAPH DESCRIPTION

A bar chart is a graph represented by either

vertical or horizontal rectangles whose basesrepresent the class intervals and whose

heights represent the frequencies. Bar charts

are useful for showing trends over time andplotting many data series.

A histogram is a graph represented by

vertical or horizontal rectangles whose bases

are the class mark and whose heights are thefrequencies.

A pie chart is a circle graph showing the

proportion of each class through either therelative or percentage frequency. Pie charts

are useful for highlighting proportions.

Line graphs are useful for emphasizing the

movement or trend of numerical data over

time, since they allow a viewer to trace theevolution of a particular point by workingbackwards or interpolating. Highs and lows,

rapid or slow movement, or a tendency

towards stability are all types of trends thatare well suited to a line graph.

Area charts are useful for emphasizing the

magnitude of change over time. Stacked area

charts are also used to show the relationship

of parts to the whole.


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Bubble charts, like scatter charts, use data

points and bubbles to plot measuresanywhere along a scale. The size of the

bubble represents a third measure.

Scatter charts use data points to plot two

measures anywhere along a scale, not only at

regular tick marks.

Radar graphs are used to compare two ormore data sets. You can use axes or polygonsto represent values in a star or spider

configuration. They are essentially analogous

to a line chart, except that the scale wraps

around. Radar graphs work well with anydata that are cyclical, such as the months of a

year.

A Waterfall chart is a cumulative stacked

chart. The waterfall chart will automatically

perform the cumulative sum when usingSubtotal or Total. Waterfall charts essentially

require one data value for each series or

group marker to be drawn in a chart.

3. What are the most commonly used measures of variability? Describe each.

There are several measures of variability or dispersion. Among them are the range, mean

absolute deviation, variance and standard deviation, to name a few.

Range is the difference between the highest and the lowest values. This is the simplest but

the most unreliable measure of variability since it uses only two values in the distribution.


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A more reliable measure of variability takes into account all the data in the given distribution.

One of them is the mean absolute deviation (MAD). Mean absolute deviation is the average

of the summation of the absolute deviation of each observation from the mean.

Variance is the average of the squared deviation from the mean.

Standard deviation is the square root of the average deviation from the mean, or simply the

square root of the variance.

Coefficient of variation is the ratio of the standard deviation to the mean. It is used to

compare the variability of two or more sets of data even when they are expressed in different

unit of measurement.

4. What is the effect on the standard deviation when:

a. a constant is added to each score in the distribution?b.a constant is multiplied to each score in the distribution?A linear transformation of a data set is one where each element is increased by or multiplied

by a constant.

In addition, if a constant c is added to each member of a set, the standard deviation will not

be affected; this can be proved by letting be the standard deviation, before adding c, and t

be the mean after the transformation. Finally, let the original set be {a1, a2, . . . , an}, so that

the transformed set is {a1 + c, a2 + c, . . . , an + c}.

Another type of transformation is multiplication. If each member of a set is multiplied by a

constant c, then the standard deviation will be |c| times its value before the constant was

multiplied. Using the same notation as before, the equation would be:


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5. A class in Educational Statistics consisting of 40 students were given a diagnostic test. Theresults if this test will be used to decide whether the students will be advised to attend a

remedial class or not before acceptance to the Stat class. A score lower than 70 means thatthe student has to attend remedial class. The following set of data are the students scores in

the diagnostic test:

a. What is the range of the values?

42

45

47

49

55

55

56

57

59

59

61

63

65

65

65

66

68

68

69

72

72

74

78

78

79

79

80

80

81

81

82

83

84

85

87

88

88

90

91

95

Formula

R= HvLv

Where

R = rangeHv = highest value

Lv = lowest value

Computation

95-42= 53

53 is the range


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b.Organize the data into a frequency distribution having the following class intervals: 40-49, 50-59, 60-69, . and 90-99

Class Interval Frequency

40-49 4

50-59 6

60-69 9

70-79 7

80-89 11

90-99 3

c. Organize the data into a stem-and-leaf plotStem Leaf

4 2 5 7 9

5 5 5 6 7 9 9

6 1 3 5 5 5 6 8 8 9

7 2 2 4 8 8 9 9

8 0 0 1 1 2 3 4 5 7 8 8

9 0 1 5

d.Construct a histogram, and a frequency polygon for the frequency distribution derived in

(b)

Figure 1.Histogram for the frequency distribution

0

2

4

6

8

10

12

40-49 50-59 60-69 70-79 80-89 90-99

Frequency

Class Interval

Diagnostic Test Result Score of

Educational Statistic Students


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Figure 2.Frequency Polygon for the frequency distribution

e. Give a short description about the results. Based on the frequency distribution and stem-and-leaf plot, how many students need to attend the remedial class?

By looking at the stem-and-leaf plot, the ten lowest scores are: 42, 45, 47, 49, 55, 55, 56,57, 59, and 59, while the ten highest scores are: 82, 83, 84, 85, 87, 88, 88, 90, 91 and 95.

Most of the students scores are between 80-89 because 11 out of the 40 students scored

in this class interval, followed by the class interval 60-69 (9 students), then 70-79 (7students), then 50-59 (6 students), 4 students scored within the lowest class interval of40-49, while 3 students scored in the highest class interval of 90-99.

Given that a score lower than 70 means that the student has to attend remedial class, 19out of the 40 Educational Statistics students need to attend the remedial class.

6. The performance rating of twelve Grade 7 students in Science, Mathematics and Englishduring the first quarter of the school year are given in the following table:

Student No. Sex Science Mathematics English

1 M 82 83 782 M 80 79 79

3 M 87 86 85

4 F 79 83 82

5 F 85 86 85

6 F 95 93 82

7 M 80 85 80

0

2

4

6

8

10

12

40-49 50-59 60-69 70-79 80-89 90-99

Diagnostic Test Result Score of

Educational Statistic Students


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8 M 85 82 80

9 F 82 88 95

10 M 82 86 8511 F 80 84 82

12 F 73 82 87

a. Calculate the mean and standard deviation of students ratings in each if the threesubjects. (Note use standard deviation of samples scores)

__

mean= X

sample standard deviation= s

Student No. Science Mathematics English1 82 83 78

2 80 79 79

3 87 86 85

4 79 83 82

5 85 86 85

6 95 93 82

7 80 85 80

8 85 82 80

9 82 88 9510 82 86 85

11 80 84 82

12 73 82 87

__

X 82.50 84.75 83.33

s 5.32 3.55 4.599 or 4.60

b. How do the performance ratings of the two groups (Male and Female) compare in each ofthe three subjects?


1 M 82 83 78

2 M 80 79 79

3 M 87 86 85

7 M 80 85 80

8 M 85 82 80


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10 M 82 86 85

__

X 82.67 83.50 81.17

s 2.80 2.74 3.06


4 F 79 83 82

5 F 85 86 85

6 F 95 93 82

9 F 82 88 95

11F 80 84 82

12 F 73 82 87

__

X 82.33 86 85.50

s 7.37 4.049 or 4.05 5.089 or 5.09

c. How do the variations in scores of the two groups of samples in the three subjectscompare?

Male Female

Science

__

X 82.67 82.33s 2.80 7.37

Mathematics

__

X 83.50 86

S 2.74 4.05

English

__

X 81.17 85.50

s 3.06 5.09

Females have a higher average in Mathematics and English. However, their scores are more

spread out since their standard deviation is greater than the males scores. The males

average is higher in Science, and all have a smaller standard deviation compared to females,

meaning that their scores are more close to each other.


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Learning Task 3: Sampling, Presenting Data & Measuring VariabilityR Di R U

References

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Philippines: Diwa Scholastic Press.

IBM (n.d.). IBM cognos express version 10.1 information center. Retrieved from

http://pic.dhe.ibm.com/infocenter/cx/v10r1m0/index.jsp?topic=%2Fcom.ibm.swg.ba.cog

nos.ug_cr_rptstd.10.1.0.doc%2Fc_cr_rptstd_chrts_appndx_chart_types_appendix.html

Polit, D. F., & Beck, C. T. (2006). Essentials of nursing research: Methods, appraisal, and

utilization (6th ed.). Philadelphia, USA: Lippincott Williams & Wilkins.

WebFOCUS (2007). Selecting a graph type and style. Retrieved from

http://www.csueastbay.edu/FOCUS/wf761doc/ibi_html/javaassist/intl/EN/help/topic247.

htm

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learning task 3 draft.docx