Collection of Data

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EXERCISES

1. Frame at least four appropriate multiple-choice options for following questions:

(i)

Which of the following is the most important when you buy a new dress?

(ii)

How often do you use computers?

(iii)

Which of the newspapers do you read regularly?

(iv)

Rise in the price of petrol is justified.

(v)

What is the monthly income of your family?

Which of the following is the most important when you buy a new dress?

Style and design

Fabric quality

Price

Brand name

How often do you use computers?

Daily

A few times a week

Occasionally

Rarely or never

Which of the newspapers do you read regularly?

The Times of India

Hindustan Times

The Hindu

I do not read newspapers regularly

Rise in the price of petrol is justified.

Strongly agree

Agree

Disagree

Strongly disagree

What is the monthly income of your family?

Less than ₹ 20,000

₹ 20,000 to ₹ 50,000

₹ 50,000 to ₹ 1,00,000

More than ₹ 1,00,000

2. Frame five two-way questions (with ‘Yes’ or ‘No’).

Do you think the use of primary data is essential for accurate economic research?

– Yes

– No

Is it feasible to conduct a census in large countries like India every year?

– Yes

– No

Can non-sampling errors significantly impact the results of an economic survey?

– Yes

– No

Do you believe that telephonic interviews are an effective method for collecting economic data?

– Yes

– No

Have you ever participated in a statistical survey related to economic research?

– Yes

– No

3. State whether the following statements are True or False.

(i)

There are many sources of data.

(ii)

Telephone survey is the most suitable method of collecting data, when the population is literate and spread over a large area.

(iii)

Data collected by investigator is called the secondary data.

(iv)

There is a certain bias involved in the non-random selection of samples.

(v)

Non-sampling errors can be minimised by taking large samples.

There are many sources of data.

❌ False:

There are mainly two sources of data: Primary and Secondary (only two and not many).

Telephone survey is the most suitable method of collecting data, when the population is literate and spread over a large area.

❌ False:

While telephone surveys are useful, they are not necessarily the most suitable method for all situations, especially when the population is literate and spread over a large area. Different methods like mailed interviews or personal interviews may also be suitable depending on the circumstances.

Data collected by the investigator is called secondary data.

❌ False:

The data collected by an investigator for the first time is referred to as primary data. Secondary data refers to data that has been collected by someone else and is being reused.

There is a certain bias involved in the non-random selection of samples.

✔ True:

The passage mentions sampling bias, which occurs when some members of the target population could not possibly be included in the sample, indicating a bias in non-random selection.

Non-sampling errors can be minimised by taking large samples.

❌ False:

Non-sampling errors are not necessarily reduced by increasing the sample size. These errors are more related to the method of data collection, data processing, and respondent behavior, rather than the size of the sample.

4. What do you think about the following questions? Do you find any problem with these questions? Describe.

(i)

How far do you live from the closest market?

(ii)

If plastic bags are only 5 per cent of our garbage, should it be banned?

(iii)

Wouldn’t you be opposed to increase in price of petrol?

(iv)

Do you agree with the use of chemical fertilisers?

(v)

Do you use fertilisers in your fields?

(vi)

What is the yield per hectare in your field?

Assuming that all these questions are asked independently, and are not related to each other (though the last three seem to be related), the following are the recommendations:

How far do you live from the closest market?

–

Problem: This question lacks specificity in terms of measurement units (kilometers, meters, etc.). It could lead to inconsistent responses.

–

Response: It should specify a unit of measurement for distance.

If plastic bags are only 5 per cent of our garbage, should it be banned?

–

Problem: The question is leading and suggests a premise that may not be agreed upon by all (the significance of 5% in terms of impact).

–

Response: It should be more neutral and not imply a conclusion.

Wouldn’t you be opposed to increase in price of petrol?

–

Problem: This is a leading question and assumes that the respondent is against the increase.

–

Response: It should be rephrased to a more neutral form, like “What is your opinion on the increase in the price of petrol?”

Do you agree with the use of chemical fertilisers?

–

Problem: The question is straightforward but might lack context about the environmental or economic aspects being considered.

–

Response: Providing context or specifying the aspect (environmental, economic) could make it clearer.

Do you use fertilisers in your fields?

–

Problem: Assumes the respondent has fields, which may not be applicable to all.

–

Response: It could be preceded by a question asking if the respondent is involved in agriculture.

What is the yield per hectare in your field?

–

Problem: Assumes the respondent is involved in agriculture and knows the specific yield per hectare, which might not be common knowledge.

–

Response: Could be restructured to cater to a broader audience or be part of a more detailed agricultural survey.

5. You want to do a research on the popularity of Vegetable Atta Noodles among children. Design a suitable questionnaire for collecting this information.

To conduct research on the popularity of Vegetable Atta Noodles among children, a suitable questionnaire can be designed considering various aspects like taste preferences, health consciousness, and eating habits. This questionnaire will aim to gather comprehensive data on children’s opinions and preferences regarding Vegetable Atta Noodles. The design will be based on the principles of survey design.

The questionnaire is structured to elicit both quantitative and qualitative data about the popularity and perception of Vegetable Atta Noodles among children. It is designed to be clear, concise, and age-appropriate, ensuring that the responses are as informative and accurate as possible.

6. In a village of 200 farms, a study was conducted to find the cropping pattern. Out of the 50 farms surveyed, 50% grew only wheat. What is the population and the sample size?

In the context of the given scenario about a study in a village of 200 farms to find the cropping pattern:

–

Population: The population refers to the entire group that is the subject of the study. In this case, the population is all the farms in the village, which totals to 200 farms.

–

Sample Size: The sample size is the part of the population that is actually observed or analyzed to make inferences about the entire population. In this scenario, the sample size is the number of farms surveyed, which is 50 farms.

So, for the study conducted in the village:

–

The population is 200 farms.

–

The sample size is 50 farms.

7. Give two examples each of sample, population and variable.

The following are two examples each of sample, population, and variable:

Sample

In a study of student reading habits in a school of 1,000 students, a group of 100 students is selected at random to participate in a survey.

–

Here, the 100 students surveyed are the sample.

In a research study to understand the average yield of wheat farms in a region with 500 farms, 60 farms are chosen for detailed analysis.

–

In this case, the 60 wheat farms chosen represent the sample.

Population

All the residents of a small town being studied for their water usage patterns.

–

The population here comprises every resident of the town.

Every employee working in a large corporation being surveyed for job satisfaction.

–

The population in this example includes all the employees in the corporation.

Variable

The age of individuals in a demographic study.

–

Age is a variable as it varies from person to person.

The annual income of households in a socio-economic survey.

–

Annual income is a variable since it differs among different households.

These examples demonstrate the differences between samples, populations, and variables in the context of statistical research.

8. Which of the following methods give better results and why?

(a)

Census

(b)

Sample

In considering whether a census or a sample survey method gives better results, it’s important to understand that the effectiveness of each method depends on the context and objectives of the study. The following is teh analysis based on the general statistical principles:

Census

–

Definition: A census is a study that collects data from every member of the population.

–

Advantages:

–

Comprehensive: Covers every individual/unit in the population, ensuring no segment is overlooked.

–

Accuracy: Tends to be more accurate as it doesn’t rely on estimations or predictions.

–

Disadvantages:

–

Costly and Time-Consuming: Requires more resources and time to conduct.

–

Data Overload: Managing and analyzing the vast amount of data can be challenging.

–

Not Feasible for Large Populations: In large populations, conducting a census can be impractical.

Sample Survey

–

Definition: A sample survey collects data from a subset of the population, representing the whole.

–

Advantages:

–

Cost-Effective: Less expensive and faster to conduct than a census.

–

Flexibility and Efficiency: Easier to manage and analyze data from a smaller group.

–

Practical for Large Populations: More feasible for large or widespread populations.

–

Disadvantages:

–

Sampling Error: Can lead to errors if the sample isn’t representative of the entire population.

–

Bias: Risk of bias in selecting the sample.

Which is Better?

–

Depends on the Situation:

–

Census: Best for small, manageable populations where accuracy and comprehensive data are crucial.

–

Sample Survey: Ideal for large populations or when time and resources are limited, provided the sample is representative.

–

Objective of the Study: The choice also depends on the specific needs and goals of the research.

In summary, both methods have their merits, and the choice between a census and a sample survey depends on factors like the size of the population, resource availability, time constraints, and the level of detail and accuracy required.

9. Which of the following errors is more serious and why?

(a)

Sampling error

(b)

Non-Sampling error

Understanding the seriousness of sampling and non-sampling errors involves analyzing their impacts on the research results. Based on the general statistical principles:

Sampling Error

–

Definition: Sampling error occurs due to the difference between the results from a sample and the actual values in the population.

–

Characteristics:

–

Quantifiable: It can be measured and calculated.

–

Reducible: Can be minimized by increasing the sample size or using better sampling techniques.

–

Impact: Affects the precision of the results but is generally considered a part of the sampling process.

Non-Sampling Error

–

Definition: Non-sampling errors arise from factors other than the sampling process, such as data collection errors, data processing mistakes, respondent errors, and survey design flaws.

–

Characteristics:

–

Hard to Quantify: Often difficult to measure and identify.

–

Not Always Reducible: Can occur even with a perfect sample and are not always reduced by increasing the sample size.

–

Impact: Can lead to systematic bias in the results, affecting the accuracy and reliability of the study.

Which is More Serious and Why?

–

Non-Sampling Error: Generally considered more serious because:

–

Bias Introduction: They can introduce systematic biases that are not just related to the sample size but to the overall methodology and execution of the study.

–

Less Controllable: More challenging to control and rectify, especially if unnoticed during the initial stages of research.

–

Affects Entire Study: Can compromise the entire research, regardless of how well the sampling is done.

In conclusion, while sampling errors are part and parcel of using a sample, non-sampling errors are more serious as they can fundamentally undermine the validity and reliability of the research findings.

10. Suppose there are 10 students in your class. You want to select three out of them. How many samples are possible?

In the scenario where there are 10 students in your class and you want to select three out of them, the number of possible samples that can be formed is calculated based on the combination formula, which is used for selecting items where the order does not matter.

The formula for a combination is

{^nC_r = \dfrac{n!}{r!(n-r)!}}

, where:

–

{n}

is the total number of items (students in this case),

–

{r}

is the number of items to choose (students to be selected),

–

{!}

denotes factorial, which is the product of all positive integers up to that number.

Using this formula, the number of possible samples when choosing 3 students out of 10 is calculated as,

{^{10}C_3}

{= \dfrac{10!}{(10 - 3)!}}

{= \dfrac{10!}{3!~7!}}

{= \dfrac{10 × 9 × 8 × 7!}{3 × 2 × 1 × 7!}}

= 120

11. Discuss how you would use the lottery method to select 3 students out of 10 in your class.

To use the lottery method for selecting 3 students out of 10 in a class, the following steps can be followed. This approach is based on the principles of random sampling, a key concept in “Statistics for Economics”:

Assign Numbers to Each Student: Assign a unique number to each of the 10 students in the class. For instance, numbers 1 through 10.

Prepare Lottery Tickets: Create 10 slips of paper (lottery tickets), each bearing one of the assigned numbers. Ensure that the slips are identical in size, shape, and color to avoid any bias.

Mix the Tickets: Place all the slips into a container and mix them thoroughly. This ensures that every slip has an equal chance of being selected.

Draw the Tickets: Without looking, draw three slips from the container one at a time. Drawing without looking is crucial to maintain the randomness of the selection.

Identify the Selected Students: Match the numbers on the drawn slips with the assigned numbers of the students. The students whose numbers correspond to the drawn slips are the ones selected.

Ensure Fairness: To maintain fairness and randomness, ensure that the drawing process is transparent and that the person drawing the tickets has no way to differentiate between the slips.

This method is a simple and effective way to randomly select a sample from a larger group, which is a fundamental technique in statistical studies.

12. Does the lottery method always give you a random sample? Explain.

Yes. The lottery method, when used correctly, is designed to give a random sample. However, whether it always achieves this goal depends on several factors:

Equal Probability: Each member of the population must have an equal chance of being selected. This is fundamental to the lottery method. If all members are equally represented in the lottery (each with a single ticket of the same size, shape, and texture), then each has an equal probability of being chosen.

Proper Mixing and Drawing: The tickets must be thoroughly mixed to ensure randomness. Additionally, the drawing of the tickets should be done blindly (without looking) to prevent any bias.

No External Influence: The process must be free from external influences that could affect the selection. This includes ensuring that the person drawing the tickets cannot feel the difference between them.

Large Enough Population: In a very small population, the lottery method might not be as effective because the randomness can be more easily skewed by slight variations in the process.

Implementation: Any deviation from a fair and unbiased process can compromise the randomness. For example, if some tickets are larger, have a different texture, or are folded differently, they might have a higher or lower chance of being selected.

In summary, while the lottery method is designed to provide a random sample, its effectiveness in doing so depends on strict adherence to a fair and unbiased process. If these conditions are met, it typically does provide a random sample.

13. Explain the procedure for selecting a random sample of 3 students out of 10 in your class by using random number tables.

To select a random sample of 3 students out of 10 in a class using random number tables, the following procedure can be used. This method aligns with the principles of random sampling, a key concept in statistics:

Assign Numbers to Each Student: Number the students from 01 to 10. This is necessary as the random number table will refer to these numbers.

Use a Random Number Table: Obtain a random number table. These tables consist of a sequence of numbers arranged randomly.

Choose a Starting Point: Randomly choose a starting point in the random number table. This can be done by closing your eyes and pointing to a spot on the table, or by using some other random method.

Select Numbers Matching Student Numbers: From your starting point, read across or down the table and identify the first three distinct numbers between 01 and 10. Each number corresponds to a student in your class.

Ensure Distinct Selections: If the same number appears more than once in your first three selections, skip it and move to the next number until you have three distinct numbers.

Identify the Selected Students: The students corresponding to these three numbers are the members of your random sample.

It’s important to note that the random number table must be used correctly to ensure each student has an equal chance of being selected. The process should be free from any personal biases or patterns in selection.

14. Do samples provide better results than surveys? Give reasons for your answer.

Definition of Samples and Surveys:

–

Samples: A sample is a subset of a larger population used in statistical analysis. The purpose of a sample is to make inferences about the larger population from which it is drawn.

–

Surveys: A survey is a method for collecting information or data as reported by individuals. Surveys can be conducted on a sample or an entire population.

Comparison of Effectiveness:

–

Dependence on Purpose: Whether samples provide better results than surveys depends on the research objectives. For some studies, a sample survey is more practical and cost-effective, especially in large populations. In other cases, a survey of the entire population (a census) may be necessary for complete and accurate information.

–

Sample Surveys: Often used because they are more feasible and less costly than surveying an entire population. If the sample is representative, the results can be very reliable and extrapolated to the larger population.

–

Full Population Surveys: Provide comprehensive data but are often impractical for large populations due to high costs and time requirements.

Quality of Results:

–

Accuracy and Reliability: The accuracy of results from samples depends on how representative the sample is. A well-chosen sample can yield results almost as accurate as a full population survey.

–

Biases and Errors: Both methods have potential biases and errors. Sample surveys might have sampling errors, while full population surveys might suffer from non-sampling errors like data collection and processing errors.

In conclusion, whether samples provide better results than surveys isn’t a straightforward matter. It depends on the research objectives, resources available, and the need for accuracy and comprehensiveness. In many practical scenarios, especially in economics, a well-designed sample survey is often found to be the most efficient method.