Sampling Design

Question 1

Describe the different between Probability and Non-probability Sampling Designs

Answer

Each of the probability and non-probability sampling designs has been discussed with examples in the book. Overheads provided can be used while discussing the sampling designs. An aspect that needs to be stressed is that the term "random" used in sampling, such as simple random sampling, does not mean haphazardness, but is used to denote a systematic pattern. When we talk of simple random sampling, we mean that every single element in the population has a known and equal chance of being selected. Students seem to confuse the term used in a statistical sense with the layperson's usage of the term to mean ill-arranged, or haphazard. Each of the sampling designs can be discussed with reference to the student population in a university setting. The simple random sampling, and the systematic sampling designs can be used with the university register of students as the sampling frame. Stratified random sampling can be used stratifying the student population along the lines of professional/nonprofessional schools, traditional/nontraditional students, or academic status (undergraduate/graduate), etc. Cluster sampling could use several classes in session, or several narrow specializations, etc. Area-sampling could be explained in terms of location of the campus -- north wing, south wing, etc. Double sampling would be resorted to when a subset of the students sampled are again approached for more information.

In the non-probability sampling designs, Convenience Sampling can be illustrated as the instructor talking to students who are readily available to ascertain how they are experiencing the course. Purposive  Judgment Sampling would constitute sampling the students who can supply the information needed. For instance, if research is conducted on the types of sexual harassment that students experience, it is only those who have undergone sexual harassment in some form or the other, who would be able to provide the needed information. Thus this group would constitute the purposive judgment sample. Such members can perhaps be reached at a workshop conducted on sexual harassment. Snowball sampling can be used to determine a sample of international students who may be experiencing difficulties understanding the language used in lectures.  An initial group may be identified from their assignments, and these students can be asked to indicate students who may be experiencing language difficulties.  Quota sampling can be used to obtain information regarding experiences of say, NZ Europeans, NZ Maoris, and international students, specifying a quota to be sampled from each group, so that minority groups are adequately represented. Another example would be to stipulate quotas from the various disciplines and then sampling the students from each discipline on a convenience basis.

Question2

What kinds of sampling designs would be used for the following:

a. A study to get a quick idea of the medical acceptability of a new aspirin substitute which cannot be dispensed over the counter without prescription.

b. A study involving a sample of 325 students in a university where 2,000 students are enrolled.

c. An investigation of the career salience of professionals in the fields of medicine, engineering, business, and law.

d. The generalisability of the attitudes of blue collar workers from a sample of 184, to the total population of 350 blue collar workers in the entire factory of a particular company.

Answers

a. Purposive Judgment Sampling.

b. A Systematic sampling design (using university listing of students).

c. A Stratified Random sampling with stratification along profession, gender, age, etc.

d. Simple random sampling because of the importance attached to high generalisability.

Type of scale and Types of measurement scales

1. Construct a semantic differential scale to assess the properties of a particular brand of coffee or tea.

Semantic Differential Scale for Good Brew Tea Bags

------------------------------------------------------------------------------------------------------------

                                                                       

Fine  Flavour        8        7        6        5        4         3         2         1    No Flavour

Smooth Brew     8        7        6        5        4         3         2         1      Thick Brew

Good Taste        8        7        6        5        4         3         2         1      Distasteful

Lifts the spirit      8        7        6        5        4         3         2         1     Depresses

Gives Energy      8        7        6        5        4         3         2         1     Debilitates

  
2. Describe the four types of measurement scales.

The four scales are nominal, ordinal, interval, and ratio.

1. The nominal scale separates individuals or items into categories -- e.g. seniors and juniors. 
2. The ordinal scale helps to rank order the separated items. 
3. The interval scale helps to determine the extent to which the items are different from each other. In other words, is the difference between item 1 and 2 the same as the difference between 4 and 5?   
4. The ratio scale helps to determine the proportion of differences among items since it has an absolute zero origin, and is the most powerful of the four scales.

Research Design

9. Below are two scenarios. For each, indicate how the researcher should proceed with the following, giving reasons:

a. The purpose of the study

b. The type of investigation

c. The extent of researcher interference

d. The study setting

e. The time horizon for the study

f. The unit of analysis.

Scenario A

Ms. Aminah, the owner of a small business (a woman's dress boutique), has invited a consultant to tell her how she is different from similar small business within a 60-mile radius, in regard to her usage of the most modern computer technology, sales volume, profit margin, and staff training.

ANSWER

This will be a descriptive study (describing how she compares with the others). Data will be collected on the use of computers, sales volume, profit margin, and training programs and comparisons made. Some of these descriptions might be qualitative, as for example, in describing training methods. This will be a field study (using many similar small businesses), and researcher interference will be minimal. It will be a one-shot study, and the unit of analysis will be small business systems.

Scenario B

Mr. Ali, the owner of several restaurants is concerned about the wide differences in the profit margins of the various restaurants. He would like to try some incentive plans for increasing the efficiency levels of those restaurants that are lagging behind. But, before he introduces this, he would like to be sure that the idea will work. He asks a researcher to help him with this issue.

ANSWER

This would be a causal, hypothesis-testing study. It will be a field experiment, using one or two restaurants to manipulate incentive plans and see if this causes an increase in profit margins in those restaurants. Because of the manipulation, there will be some researcher interference with the natural flow of events. The time horizon for the study would be longitudinal since data will be obtained on sales, profits, etc., both before and after the manipulation. The unit of analysis would be the restaurant.

How to Intrepret SPSS output

Below are Tables 14A to 14D, summarising    the results of data analyses of research conducted in a sales organisation that operates in 50 different cities of the country, with a total sales force of about 500.  The number of salesmen sampled for the study was 150.

Question

You are to: 

1. Interpret the information contained in each of the tables, in as much detail as  possible.
2. Summarise the results for the CEO of the company.
3. Make recommendations based on your interpretation of the results.

                                Table 14A

Means, Standard Deviations, Minimum, and Maximum

----------------------------------------------------------------------------------------------------------

                                                                    Std.

Variable                                Mean      Deviation      Minimum        Maximum

------------------------------------------------------------------------------------------------------------

Sales (in $000s)                      75.1             8.6               45.2                    97.3

No. of salespeople                   25                6                   5                       50

Population (in 000s)                  5.1             0.8                 2.78                    7.12

Per capita income (in 000s      20.3           20.1               10.1                   75.9

Advertising (in $000s)            10.3            5.2                   6.1                   15.7

                     ------------------------------------------------------------------------------------------------------------

 Answer

The average population of the three cities is 5100 and the mean per capita income of the people is $ 20,300. There is a wide variation in the income (std. dev. = 20.1), indicating that some are quite rich while others are poor. For an average advertisement expenditure of $10,300, the mean sales of $ 75,100 gets about $7.5 for each dollar expended on advertisement.

Correlations Among the Variables

------------------------------------------------------------------------------------------------------------

                                     Sales       Salesmen    Population    Income   Advertisement

------------------------------------------------------------------------------------------------------------

Sales                           1.0

No. of salesmen          .76                  1.0

Population                   .62                    .06                   1.0

Income                         .56                   .21                   .11              1.0

Ad. Expenditure          .68                    .16                   .36              .23                 1.0

------------------------------------------------------------------------------------------------------------

All figures above .15 are significant at  p - .05.

                        All figures above .35 are significant at  p < .001.

  Answer

Sales, obviously the dependent variable, is highly significantly positively correlated to the number of salespersons, the population, the income of the people, and the advertisement dollars expended. This makes good sense. High income areas have more salespersons who cover the territory to sell the product, More advertising is aimed at the high income groups, and the more populated areas, which seem to be good strategies for increasing sales and income for the company.

In other words, sales are significantly correlated at p<.001 level with all four of the variables in the study. The number of salesmen and the advertisement expenditure are understandably related to sales (r=.76 and .68, respectively) . 

There are four other significant correlations, but they may not be of much relevance to  our interpretation of sales data.

Table 14C

Results of Oneway ANOVA: Sales by Level of Education

-------------------------------------------------------------------------------------------------------

Source of              Sums of                           Mean                        Significance

Variation               Squares         Df              Square           F               of  F

------------------------------------------------------------------------------------------------------------

Between Groups        50.7             2                 12.7            3.6                  .05

Within Groups          501.8         147                   3.5

Total                        552.5         149

------------------------------------------------------------------------------------------------------------

Answer

The level of education of the salespersons does have an influence on the sales they make, since the F value is significant at the .05 level. If we are to detect where the differences lie, the Duncan Multiple Range test can be performed. 

To put it differently, the one-way ANOVA table indicates that there is a significant difference in the sales made by the three groups of salesmen with different educational levels (F=3.6, p=.05). Further tests such as the Duncan Multiple Range or the Bonferroni test will have to be conducted to know which of the groups are significantly different.

Table 14D

Results of Regression Analysis

-----------------------------------------------------------

Multiple R                           .65924       

R square                             .43459       

Adjusted R square              .35225       

Standard error                    .41173

DF                                       (5,144)

F                                           5.278

Sig                                          .000     

-----------------------------------------------------------------------------------

          Variable                        BETA                t                Sig  t

-----------------------------------------------------------------------------------

Training of salesmen                 .28                 2.768          .000

No. of salesmen                       .34                  3.55            .000

Population                                 .09                  0.97            .467

Per capita income                    .12                  1.20            .089

Advertisement                          .47                  4.54            .000

                       -----------------------------------------------------------------------------------

Answer

 

The five independent variables, together, explain 43 percent of the variance in Sales. Advertisement seems to have the greatest influence on sales, judged by the Beta weight of .47 (which is the highest), followed by the number of salespersons (Beta of .34). The training of the salespersons also has a significant influence on sales (Beta of .28). The population and per capita income do not individually explain the variance in sales volume significantly. So, if sales are to be increased, spending more advertising dollars, increasing the number of salespersons, and offering good training to them, would help.

Summary of Results for CEO

The sales made by different salespersons vary considerably, depending on many factors. There is also considerable variation in the number of salespersons, the population, and the per capita income of the people in the various areas.

The level of education of the salespersons makes a difference to the sales volume generated by the individuals. Further analysis can be done to see the best level of education for generating more sales.

Advertisements seem to boost sales considerably. The greater the number of salespersons deployed, the more the sales. Better trained salespersons generate more sales than those who are not as well trained. Neither the per capita income nor the population size, seems to make a difference to the sales volume when all the variables are considered simultaneously.

Recommendation 

If the goal of the company is to increase the volume of sales, spend more money on advertising, increase the number of salespersons, and train them better. Recruiting salespersons who have the optimum level of education will also help.