class lecture notes #4 (statistics for research)

Recording the Results of Observation

The following are the form used in recording the results of observation.

1. Checklist – a device which contains the items to be observed and a space for number or checkmark or short verbal entries.

Recording the Results of ObservationExamples:

a. Checklist with short verbal entries. Suppose a boy is to be observed in physical education. The items to be observed are listed down to be followed by short verbal description of each item.

Name_______________________ Date_________________

College Year Level_____________ Age________

Direction: Give a brief description of each item.

1. Type of activity _______________________________________

2. Interest ______________________________________________

3. Effort ________________________________________________

4. Coordination __________________________________________

5. Posture _______________________________________________

6. Skills in activity ________________________________________

7. Sportsmanship _________________________________________

8. Other factors ___________________________________________


b. Checklist that indicates the presence or absence of an item.

Name of Observed (Optional) __________________________________

Place of Observation ________________________ Date _____________

Direction for Observer: Fill the space before each item by a checkmark or “Yes” if the item is present and “No” or leave it blank if the item is absent.

1. Type of farming ______ dry ______ wet______ upland _____ lowland

2. Farming tools ______ plow ______ mudrake ______ hoe ______ bolo

3. Work animals ______ carabaos ______ oxen_______ horses

4. Water management ______ irrigated ______ rain fed ______ pump fed

5. Fertilizer ______ inorganic ______ organic ______ others (specify)


c. How to design a checklist.

The following are the steps in the construction of a checklist:

1. Enumerate (list down) the dimensions (factors) to be observed.

2. Define then very clearly. (What they are exactly)

3. Eliminate those that are vague or repetitive.

4. Arrange them in a sheet of paper in a manner most convenient for observing and recording.

5. Include space for identifying data.

6. Try out the form. (This is called a dry run)

7. Revise the form on the basis of the try out and your experience.

8. Write the checklist in its final form.


2. The Rating Scale – a device for evaluation.

- similar to a checklist but instead of marking the presence

or absence of an item, it is at once evaluated.

Example 1:

Name of observed ________________ Date__________

School ________________________________________

Direction for the observer: Rate the professor on trait by writing G on the space provide if the trait is good and write B if it is bad.

____________________________________________________________

_____ Grooming _____ Method of Teaching _____ Attitude


Choose the category that best describes the trait or activity and write its weight on the space provided at the right.

Always Very Often Usually Seldom

Category Weight/ 5 4 3 2 1

Activity or Trait Weight

Is punctual __________

Masters subject matter __________

Distributes Question __________

(More items may be added)


Remark: The number of categories to be evaluated or to be given weights is not definite. It may be two, three, four, five, etc. depending upon the degree of precision. The higher the degree of precision desired, the more the number of categories or gradations are required.

3. The Anecdotal Form – a checklist that provides for less breakdown of dimensions or factors and hence much space is provided for writing. It minimizes the use of highly subjective impressions in recording and obtains instead an objective description of behavior.


Example:

Name of Observed _________________________

Direction for Observer:

In the space provided, record observations that bear on the individual’s physical development and social development. Do not evaluate, but describe. Avoid vague words such as good, strong, shy, etc..

Physical Development

Social Development


Characteristics of Proper Anecdotal Recording

Proper anecdotal recording is characterized by the following:

1. What is written down is what is seen or heard. Inferences, guesses, assumptions are omitted unless they are labelled as inferences, guesses, or assumptions.

2. The observer has to determine what aspects of behavior are related to the dimension being appraised. He observes these only and records these only.

3. If the record is to be cumulative, a plan of periodic observation and recording established and adhered to.


4. Words and phrases are used whose meaning are clear, and, so far as possible, unequivocal.

5. Words and phrases are employed that are definable in terms of things rather than other words. Concrete statements are preferred to abstract ones.

6. Words and phrases that have strong emotional connotations are avoided, that is, love, hate, insolent, courteous, loyal, dishonest, etc..

7. Words and phrases are avoided which express the observer’s judgment or his opinion, and not just his perception. Among the frequently encountered “judgmental” terms that should be avoided are the following:

a. Well – behaved d. Didn’t ry g. happy

b. Delinquent e. Industrious

c. Aggressive f. Nervous


4. Mechanical Recording

The following are a partial summary of the mechanical aids available for recording: (Good and Scates)

a. Motion and still pictures;

b. Sound recording (tape or video – tape);

c. A one – vision screen or mirror;

d. An experimental or isolation cabinet for infants;

e. A photographic dome (with a one – way vision screen and tracks for movement of the camera;

f. An electric eye ”ticker” to count the number of autos passing a given spot;


4. Mechanical Recording

g. A counting apparatus at the gate or door to keep a current record of attendance;

h. An observer with a “ticker” device in his hand to count the number of persons passing a certain spot;

i. A mechanical recording device attached to the radio at home to indicate headquarters that the radio, or to register the extent to which the radio set is used);

j. A recorder of the number of telephone calls placed per month;

k. An applause meter;

l. Odometer on an auto.

Remark: The use of mechanical devices in observation is expensive but if the researcher can afford the expense, this assures a more accurate recording. The observer can replay the record again and again until he gets an accurate record of the observation.


5. Stenographic Recording – a fast way of recording observation.

- useful in anecdotal observation because all aspects of the variable being observed can be

recorded fast and immediately.

- however, transcription has to be as accurate as

possible.

Making Observation More Valid and Reliable

The following must be observed to make observation more valid and reliable:

1. Use observation where and when it is the only possible way of gathering more accurate data. In experimental research, especially in scientific ones, observation is very important. For instance, gathering data about atmospheric conditions can be done only through observation.

2. Use appropriate observation recording devices. Use the checklist for recording very objective data; the rating scale, if the phenomenon observed is to be judged immediately; anecdotal recording if the phenomenon observed is in action; and replayable mechanical devices for more accurate recording.

Making Observation More Valid and Reliable

3. Record at once. Forgetting sets in immediately after an observation and so things observed must be recorded immediately to avoid distortions of data.

4. Be as objective as possible. Record exactly what has been observed and evaluate the things observed as objectively as possible. If bias or stereotype conceptions are allowed to enter, inferences and conclusions become untenable.

5. Base evaluations on several observations. The average of several observations is surely a more accurate and reliable basis for making inferences and generalizations than the result of only one observation. This is especially true in science.

Test As Sources of Data

Definition: A test may be defined as a specific type of measuring instrument whose general characteristic is that it forces responses from a respondent and that the responses are considered to be indicative of the respondent’s skill, knowledge, attitudes, etc.. (Bradfiels and Moredock)

Examples:

1. True – False Test 5. Midterms

2. Essay Examinations 6. Finals

3. Attitude Scales 7. personality

4. Short Answer Tests inventory, etc.

Test As Sources of Data

Classification of Tests for Research Purposes

A. According to Standardization

1. Standard Test – one for which content has been selected and checked empirically, for which norms have been established, for which uniform methods of administration and scoring have been developed, and which may be scored with a high degree of objectivity (Good).

- generally prepared by specialists.

- especially useful in psychological studies.


2. Non – Standard Test – not standardized tests.

- usually made by non – specialists.

- usually prepared hurriedly to meet the deadlines for

administration.

Examples:

1. Quizzes

2. Essay Examinations

3. Objective Tests, and Etc.


B. According to Function

1. Psychological Test – a test that measures an individual’s

ability or personality as developed by general experience.

- a standardized tests. (Good)

Types of Psychological Tests

a. Intelligence Test – a composite test made up of parts that have been found to correlate well with some practical measure of intellectual ability, success in school.

- usually called an IQ test and it measures general mental

ability.


b. Aptitude Test – a test designed to indicate a person’s potential ability or performance of a certain type of activity.

- measures special talent ability. (Ibid)

Examples:

1. Musical Aptitude Test

2. Prognostic Test

3. Scholastic Aptitude Test

4. Mechanical Aptitude and the like


c. Personality Test – a test designed to measure some aspect

of an individuals’ personality.

- measures a person’s attitudes, emotional adjustment ,

tendencies toward introversion or extroversion, levels of

submissiveness or dominance, values, motives, and other

aspects of personality.

d. Vocational and Professional Interest Inventory – a test

used to determine the extent to which a person’s likes and

dislikes relate to a given vocation or profession. (Ibid)

- reveals in what type of work a person is interested in,

whether business, teaching, medicine, auto repair, etc..


2. Educational Test – an achievement test which aims to measure a person’s knowledge, skill, understanding, ability, and other outcomes in subjects taught in school

- may be standardized or professor made tests. (Ibid)

Examples: Achievement Tests in Statistics, Science, History, Mathematics, etc.

Characteristics of Tests

The characteristics of a good test are the following:

1. Validity – refers to the accuracy with which a test measures

what it aims to measure.

Example: If a test aims to measure knowledge and proficiency in statistics and it does measure to a high degree knowledge and proficiency in statistics, the test is valid. However, if the test measures knowledge and proficiency in arithmetic instead, the test is not valid.

Characteristics of Tests

2. Reliability – refers to consistency of measurement.

Example: A test is given twice to the same group and the average measures of the two test administrations are the same or almost the same, then the test is reliable.

3. Usability. When a test is easy to administer, easy to score, not expensive, and there are norms to compare the results with, and it can be used for the purpose it is intended to perform, the test is said to be usable.

Tests as Sources of Research - Data

Remark: Only standardized test are used to gather data for research purposes because of their validity, reliability and usability. They are also accompanied by manuals of instruction explaining how they are administered, scored, and how the results are interpreted in terms of the norms. They have also a comprehensive coverage of the knowledge, skills, abilities, personality traits, and other characteristics that are vital in research studies.

Registration in Research

Definition: Registration is the process of listing down data of the same kind in some systematic manner for record purposes.

Kinds and types of data that are being registered by and in different entities.

1. School Enrolment 7. court cases, etc..

2. Births

3. Deaths

4. Pathological Cases in Hospitals

5. Cattle

6. lands

Experiment in Research

Definition: Experimental research as a source of data is usually carried out in the laboratory under controlled conditions.

Remark: There are also experiments that are performed outside the laboratory.

Remark: Usually, the experimenter has two variables, one, the independent variable and the other, the dependent variable.


Example of an Experiment Perform in the laboratory:

A chemist wants to know the medicinal value of a drug to human beings. The drug is the independent variable. He gathers several rats and feed them with different graduated doses of the drug. Then he studies the effects of the different doses of the drug upon the rats. The dose that produces the best desired effect is then tried on human beings.

Remark: Usually, human beings are not the first to be used in drug experiments because sometimes drugs cause death or some other deleterious effects.


Example of an Experiment Perform outside the laboratory:

A science student wants to prove that beneficial effect of sunlight upon plants. He gets several plants, the dependent variable, of the same kind planted in vases with the same soil fertility and given the same amount of water. Then he exposes the plants to different shades of sunlight. After a period of six months, the experimenter finds out that the plant placed in the darkest place is the palest and the plant fully exposed to the sunlight is the most robust and most verdant.

Remark: There are thousands or more ways of performing experiments with different purposes. Such experiments are also very good sources of data and the results are often a boon to mankind.

Mechanical Devices in Gathering Data

The modern world owes its progress to the mechanical devices being used in research and in gathering data. In almost all areas of human endeavor are found mechanical gadgets used in research. In social and educational research, for instance, we have the camera, projector, tape recorder, video tape, etc. In the biological sciences as well as medical science research, the most common are the microscope, x-ray and ultra sound machines and other sophisticated devices. In physical science research, there are mechanical gadgets that measure force, gas pressure, electric energy, etc.. In studying the heavenly bodies and the atmosphere, we have the telescope, the barometer, and other more modern machines.

Remark: In using any mechanical device for gathering data for research purposes, use the latest model of the most reputable brand for a more valid and reliable infornation.

SAMPLING

Definition: Sampling is measuring a small portion of something and then making a general statement about the whole thing. (Bradfield and Moredock).

Example: One is buying a watermelon. He tastes a small chip of the fruit and if it tastes sweet, the buyer concludes that the whole fruit is sweet. In actual research, small portion of a large population is studied and the results of such study are alluded to the whole population.

Why We Need Sampling(Purposes and Advantages of Sampling)

There are advantages of sampling that impel us to utilize it in research. Some of these are the following:

1. Sampling enables the investigation of a large population. The universe or population to be studied may be too large, or even infinite, that it is almost impossible to reach all the members in the population.

Example: Suppose the age, height, weight, and scholastic aptitude distributions of all graduate students in the whole country are to be studied. It would be extremely difficult to reach every graduate students to get his or her age, height, weight and scholastic aptitude. But sampling makes the study possible, simpler, and easy.


2. Sampling reduces cost of research. Because sampling makes possible the use of a small portion of a study population, the cost of research may be reduced to a level that the researcher can afford. If a study involves 60,000 persons, the cost of interviewing all of them in terms of interviewers’ salaries will be tremendous. But sampling reduces this cost to the minimum.

3. Sampling enables the completion of a study within a reasonable period of time. When there is sampling, the researcher deals with fewer respondents and so the work is finished very much sooner than when he deals with the whole population.


4. Sampling makes data more relevant and accurate. Because of sampling, data gathered are more recent and hence more relevant and accurate. If there is no sampling, the collection of data may take a very long period of time, so much so that by the time the gathering of data has been completed, the first data gathered may already be obsolete and are no longer relevant and accurate.

5. Sampling avoids consuming all the sources of data. Suppose we want to know if all the kinds of food in an eatery are tasty. If there is no sampling, we have to eat all the kinds of food in the eatery before we can make any conclusion that all kinds of food in the eatery are tasty or not. But because of sampling this is avoided. We just taste every kind of food or a few and we can make our generalization.

General Types of Sampling

I. Non – Probability Sampling – the sample is not a proportion of the study population and there is no equal probability in the selection of the sample.

- there is no representative sampling from the study population.

Remark: Study population means the actual population from which the sample is taken and representative sampling means that all sections or groups of the study population are proportionally represented in the sample.

II. Probability Sampling – the sample is a proportion (a certain percent) of the study population and there is an equal probability in the selection of the sample. Sampling is also generally representative.

Types of Non-Probability Sampling

A. Accidental Sampling – as the name implies, the persons included in the sample are those who are met by chance or accidentally met by the researcher interviewer. For instance, the interviewer stands in a street corner and he interviews everyone who passes by. The problem with this type of sampling is that most likely the sample is biased and therefore lacks representativeness. If the interviewer happens to place himself in a business section, most of the people he meets are well-to-do and educated and if he places himself in a slum area most of the people he meets are poor and uneducated. There is no equal probability in sample selection.


B. Quota Sampling. In this type of sampling, many sectors of the population may be represented in the sample but there is no proportional representation. A specified number of each type is arbitrarily determined. For instance, ten doctors, eight lawyers, three business men, twenty farmers, and fifteen laborers may be included in the sample. There is no equal probability in the sample selection in each and anyone of each type may be approached to be a respondent. Besides, the opinion of the professionals who are in the minority may become more predominant than the opinion of the non-professionals who are in the majority


C. Convenience Sampling. This type of sampling is resorted to when there is a hot and controversial issue raging in the community. The respondents are selected and interviewed in the most convenient and fastest way. One example is to use people with telephones as a sample. They can be interviewed very easily by calling them on the phone. But in this case, the sample is surely biased because the people with telephones are a class by themselves. They are generally well-to-do and educated people. Unless the study is about themselves alone.


D. Purposive Sampling. In this sampling, the respondents are chosen on the basis of their knowledge of the information desired. If a certain method of teaching is to be studied, the sample should come from among professors. If rice production is to be investigated, the respondents should be rice farmers and agriculturists. If the history of a place or an institution is to be researched on, the old residents of the place and those early connected with the institution should be consulted.

Remark: Purposive Sampling is used in either the non-probability sampling or in probability sampling. When used in probability sampling, any of the probability sampling techniques may be used depending upon the situation.

Types and Techniques of Probability Sampling

A. Pure Random Sampling. This a type of sampling where there is an equiprobability in sample selection, that is, every element in the sample frame has an equal chance of being chosen. Elements are the members of the population an the sample frame is a list or roster of all the elements from which the sample is to be selected. Pure random sampling is also called lottery raffle type of sampling. This may be used when the population has no stratifications.

Example: Suppose there are 500 elements in the sampling frame and 20 percent are to be chosen to compose the sample. The names or numbers of the elements are written on small pieces of paper of equal size, folded in the same way and placed in a container convenient for the purpose. Then the pieces of paper are shuffled or mixed thoroughly and 20 percent of 500 or 100 pieces are drawn from the container by chance. The elements whose names or numbers are drawn shall compose the sample.


Remark: The main advantage of the technique is that it is easy to understand and easy to apply. Some researchers prefer to use the so – called table of random numbers. The use of table of random numbers is explained in good statistical books especially that of Peatman (pp. 181,204-207).

Remark: Pure random sampling is also called unrestricted random sampling which means that every sampling unit in the sampling frame is equiprobable. Sampling units are the elements from which selection is to be done. This sampling type is used in non-stratified populations.


B. Systematic Random Sampling. This is a sampling technique in which every nth sampling unit in the sampling frame is chosen to be included in the sample. This is used when the elements or subjects in the study are arrayed or arranged in some systematic or logical manner such as alphabetical arrangement, residential or house arrays, geographical placement as from north to south, etc..

Example: Suppose 20% of the population is the sample size. If 100% is divided by 20%, the answer is 5. So every fifth sampling unit or name in the sampling frame is selected. But there must be a random start. The researcher may close his eyes and runs his finger down the sampling frame or list and then stop. The number where his finger is on is the random start. Suppose this number is 10. This is the first selection. The succeeding numbers to be chosen are found by adding 5 to its predecessor. So the next number is 15 (10+5), the next is 20 (15+5), etc..


Remark: The main advantage of systematic sampling over the pure random sampling type is that it is faster, more convenient, and more economical. Its disadvantage is that it has the tendency to produced biased sample if the sampling units are a class by themselves, as in the case of a population composed of telephone owners.

Remark: The systematic random sampling is also used in non-stratified populations. It is a restricted random sampling.


C. Stratified Random Sampling. Stratified random sampling is used in selecting a sample when the population is segmented into differentiated groups or sections called stratifications or strata(singular, stratum). The differentiated groupings may be horizontal or vertical.

Example: In a graduate student population, the horizontal stratifications are sex (male or female) and courses being taken such as MBA, MSBA, MA Psych, MS Psych, MS Math, MS Physics, MS Chemistry, MS Biology, MAED, MS Statistics, MA English, MA Mass Com, MS Accountancy, MS Engineering, etc.. An example of vertical stratification of the graduate students such as first and second years.


Remark: In a stratified population, selection is done in every stratum or section using either the pure random sampling or the systematic random sampling. The selection is proportional, that is, the same percent is used in every stratum or section in determining the sample size in every stratum or section. This contributes much to the representativeness of the sample which is the main advantage of this technique of sampling.


Example: Suppose the respondents in an investigation are graduate students. To ensure representativeness, the graduate students are stratified according to courses being taken, sex, and curricular years they are in. The sample of 20% is taken from every stratum based on course, sex, and curricular year. Selection in each stratum or section is done either by pure random sampling or systematic sampling.

D. Cluster Sampling. Cluster sampling is used when the total population of a big geographical area is studied. Generally, the following procedure is used. Suppose all the households of a city are to be studied. Suppose also that the sample to be used is 20%. The city is divided into clusters or blocks, the number and the sizes of which are decided upon by the researcher. Suppose there are 40 clusters or blocks, 20 percent of which are 8 clusters.

These 8 clusters are to be selected either by pure random sampling or by systematic random sampling. Then 20% of the households within each of the 8 clusters are to be picked out by systematic random sampling which, in this situation, is probably better and more convenient to use than the pure random sampling technique.


E. Multistage Sampling. Multistage sampling is used especially when the subjects of an investigation are scattered all over a big geographical area. Generally, the following procedure is used. Suppose all aspects of the educative process in all universities in a region of 8 provinces are to be investigated. Suppose also that 20% is decided upon to be the sample. The 20 percent of 8 equals 1.6 or two regions. These two provinces may be chosen by pure random sampling. The two provinces chosen are called the primary sampling units. The second sampling units are the towns. Suppose a province has 28 towns and the other has 31 towns. Twenty percent of 28 equals 5.6 or 6 towns in that province and 20% of 31 towns equals 6.2 or 6 towns also in the other province. These towns may be chosen by either pure random or systematic sampling. The third and final sampling units are the universities. Take 20 percent of the universities from each of the six towns in one province and 20% of the universities in each town of the six towns in the other province. The universities may be selected by pure random or systematic random sampling. In addition, stratified random sampling should now be applied in choosing 20 percent of the instructors or professors, 20% of the students and 20 percent of the parents.

Principles of Sampling(Bradfield and Moredock)

1. Appraisals that involve sampling are estimates and

predictions only.

2. Estimates based on sampling are least accurate when the

sample is a small proportion of the whole and when the

sample is not representative. Conversely, estimations based

on proportionately large samples and on representative

samples are most accurate.

3. Sampling may be categorical or temporal. Sampling is categorical if the

sample is taken proportionally from categories or groups. Sampling is

temporal when the sample is in terms of time, as for example the pulse of

a patient is taken every ten minutes.

Defective Sampling

1. Sampling is defective if it is biased and not representative. A

sample is biased and not representative if the differentiated

groups or sections in the study population are not

proportionally represented in it.

2. Sampling is defective if the sample size is too small to

warrant a valid, reliable, and tenable generalization. For

instance, a sample of 10 is probably too small as a sample for

a study population of 1,000. This is true in descriptive studies

especially in normative surveys.

Defective Sampling

3. Sampling is defective if not all the sampling units in the

study population possess the common characteristic which is

the basis of the study. For example, a study is to be

conducted to determine the profile of the instructors or

professors in a certain university. If the administrators and

non-teaching personnel are included in the sample, sampling

becomes defective.

4. Sampling is defective if the researcher does not possess the

necessary skill and technical know how in sampling

procedures.

Guidelines for Determining Adequate Sampling

The size of a sample is usually determined before the start of a study. But there are no fixed rules for determining the size of a sample. However, there are broad guidelines in determining the size of a sample. Some of these are the following: (Calderon)

1. When the universe or population is more or less homogeneous and only

the typical normal or average is desired to be known a smaller sample is

enough. However, if differences are desired to be known, a larger sample

is needed.

2. When the universe or population is more or less heterogeneous and the

typical normal or average is desired to be known, a larger sample is

needed. However, if only the differences are desired to be known, a

smaller sample is sufficient.

Guidelines for Determining Adequate Sampling3. The proportional size of a sample is inversely proportional to the size of

the population. A larger proportion (percent) is required of a smaller

population and a smaller proportion may do for a bigger population. For

a population of 5,000, a sample of 10 percent may do but for a

population of 500, a proportion of 30% may be more desirable.

4. For a greater accuracy and reliability of results, a greater sample

proportion is desired. This is especially true in descriptive research.

5. In biological and chemical research experiments such as testing the

effects of drugs and other substances, the use of a few persons is

sufficient to determine the reactions of humans to such drugs and other

substances. This is feasible since the biological and physiological systems

of humans are almost if not exactly the same.


6. When the subjects (sample) are likely to be destroyed during the research

experiment, it is more feasible to use non-humans such as animals

especially rats.

7. In addition, in most theses and dissertations surveyed from 20 to 25

percent had been used as sample proportions. This is in theses and

dissertations dealing with descriptive research. Some even used higher

proportions. It seems that the sample proportions of 20 to 25 percent used

in descriptive research are acceptable as ideal enough by most people

concerned in research. But as mentioned before, when the population is

too big, say into thousands, the proportion may be lessened.


8. For a more definite way of determining the sample size, the

following formula used by Pagoso, et. al may be utilized:

in which n = the size of the sample

N = the size of the population

e = the margin of error

21 Ne

Nn


Remark: The maximum margin of error that may be used is 5 percent. That would give a confidence level of 95 %. But with the use of above formula, it is strongly suggested that the margin of error to be used must be 3%. This will give a fairly good size of a sample from which adequate data can be gathered from which more valid, reliable and tenable generalizations may be formulated.

Steps in Computing the Sample Size of a Sample

The steps in computing the size of a sample are as follows:

1. Determine the size of the study population. This is determined from the scope and delimitation of the study.

2. Decide on the margin of error. The margin of error should not be higher than 5 percent. Preferably, use 3 percent.

3. Apply the formula (Unless 20% is chosen at once)

4. If the study population is stratified or if the sampling is cluster or multistage, compute the sample proportion by dividing the result in Step #3 by the study population.

21 Ne

Nn

Steps in Computing the Sample Size of a Sample

5. Multiply the number of sampling units in each sampling stratum in each

sampling stage by the sample proportion (percent) to find the sample from

each stratum.

6. Add the samples from all the final sampling strata to find the total

sample.

Example: Suppose a study of values of the university personnel of a certain university is to be conducted. The total of the university personnel is 4,551broken down as follows: teaching personnel 3,376 of whom 1,311 are male and 2,065 are female; non-teaching personnel are 1,175 of whom 478 are male and 697 are female.

Example of a Sample Size Computations (Continuation)

The sampling procedure are as follows:

Step 1: The population is 4,551.Step 2: The margin of error to be used is 3%.Step 3: Using the formula and solving for n:

Step 4: The personnel are stratified into teaching and non-teaching, male and female and so the sampling proportion must be computed.

Sampling Proportion (%) or 19.62%

893

03.0551,41

551,42

n

1962.04551

893

N

n

Example of a Sample Size Computations (Continuation)

The sampling proportion of 19.62% may be rounded to 20% for convenience of computations.

Step 5 and 6.

Personnel Male 20% Female 20% Total 20%

Teaching 1311 262 2065 413 3376 675

Non-teaching 478 96 697 139 1175 235

Total 1789 358 2762 552 4551 910Total Sample

Problem Set # 3:

Enrolment of the School of Graduate Studies of a Certain University

Programs Male Female Total

MS BA

MS Psych

MS Statistics

MS Math

MAED

MA English

MA Psych

MS Physics

MS Accountancy

MBA

MS Engineering

MS Biology

55

67

20

10

150

100

200

15

110

220

50

45

30

33

10

8

85

55

150

18

80

100

15

25

85

100

30

18

235

155

350

33

190

320

65

70

Problem Set # 3:

Question:Using the most appropriate technique of sampling,

compute the size of the sample, using 3% as the margin of error.

class lecture notes #4 (statistics for research)

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