# Quantitative Data Analysis

Quantitative Data Analysis

Workshop Objectives

Students will have:

• Highlighted the advantages and the disadvantages of different types of probability sampling designs.

• Identified the choice points in sampling design shown in Figure 11.3 in the textbook and provided in PowerPoint example in Chapter 10

• Understood BASIC statistical concepts.

• Analyzed data using any of the available PC software programs.

• Explained how the frequency distribution becomes a tool for explaining sample characteristics.

• Connected the application of descriptive statistics such as the means, standard deviations, and variance to the dependent and independent variables of interest to any study in order to get an idea of the central tendencies and to obtain a feel for the data.

• Interpreted the results they obtain from data analysis

Student Preparation

Students will construct the following from a data set from the instructor Due Oct 14

1. Frequency Distribution Assignment

2. Central tendency Assignment

Reading: Sekaran and Bougie text: Chapters 10 and 11

Selected end of the chapter questions from Sekaran and Bougie

Class 5 on-line Oct 5

Workshop Objectives

Students will have:

• Highlighted the advantages and the disadvantages of different types of probability sampling designs.

• Identified the choice points in sampling design shown in Figure 11.3 in the textbook and provided in PowerPoint example in Chapter 10

• Understood BASIC statistical concepts.

• Analyzed data using any of the available PC software programs.

• Explained how the frequency distribution becomes a tool for explaining sample characteristics.

• Connected the application of descriptive statistics such as the means, standard deviations, and variance to the dependent and independent variables of interest to any study in order to get an idea of the central tendencies and to obtain a feel for the data.

• Interpreted the results they obtain from data analysis

Student Preparation

Students will construct the following from a data set from the instructor Due Oct 14

1. Frequency Distribution Assignment

2. Central tendency Assignment

Reading: Sekaran and Bougie text: Chapters 10 and 11

Selected end of the chapter questions from Sekaran and Bougie

On-Line Activities

Activity 5-1:

Students will collect data and have a conversation with the instructor on sampling and statistics. They will post what they have learned on Blackboard

Activity 5-2:

Students will construct a frequency distribution given a data set from the instructor

Example On Frequency Distributions

Below is a tabulation of the demographic data from the Frequency distribution of a survey done .The sample consisted of 148 of a total of 3,700 clerical employees in three service organizations. Based on the tabulation provided below, describe the sample characteristics.

Table 1: Frequency Distributions of Sample (n = 148)

RACE EDUCATION GENDER

Non-whites = 48 (32%) High School = 38 (26%) Males = 11(75%)

Whites = 100 (68%) College Degree = 74 (50%) Females = 37 (25%)

Masters Degree = 36 (24%)

AGE # OF YEARS IN ORG. MARITAL STATUS

< 20 = 10(7%) < 1 year = 5 (3%) Single 20 (14%)

20-30 = 20(14%) 1-3 = 25(17%) Married 108 (73%)

31-40 = 30(20%) 4-10 = 98(66%) Divorced 13 (9%)

>40 = 88(59%) >10 = 20(14%) Alternative7 (4%)

Lifestyle

Activity 5-3:

Students will use the same data set to compile central tendency statistics. What does it all mean?

Example of Central Tendencies: Means, Standard Deviations, and Other Statistics

Here is another tabulation of the Means, Standard Deviations, etc., for Ms. Jones’ data. How would you interpret these data?

Table 2: Means, Standard Deviations and Other Statistics

VARIABLE MEAN STD. DEV MODE MIN MAX

Age 37.5 18 38 20 64

# of Years Married 12.1 24 15 0 32

Stress 3.7 1.79 3 1 5

Job Involvement 3.9 1.63 4 2 5

Performance 3.6 0.86 3 3 5

Measures of Central Tendency

The Mean. The mean or the average is a measure of central tendency that offers a general picture of the data without unnecessarily inundating one with each of the observations in a data set. The mean or average of a set of say, 10 observations is the sum of the 10 individual observations divided by 10 (the total number of observations).

The Median. The median is the central item in a group of observations when they are arrayed in either an ascending or a descending order.

The Mode. In some cases, a set of observations would not lend itself to a meaningful representation through either the mean or the median, but can be signified by the most frequently occurring phenomenon.

Measures of Dispersion

Range. Range refers to the extreme values in a set of observations.

Variance. The variance is calculated by subtracting the mean from each of the observations in the data set, taking the square of this difference, and dividing the total of these by the number of observations.

Standard Deviation. The standard deviation, which is another measure of dispersion for interval and ratio scaled data, offers an index of the spread of a distribution or the variability in the data.

Other Measures of Dispersion. When the median is the measure of central tendency, percentiles, deciles, and quartiles become meaningful. Just as the median divides the total realm of observations into two equal halves, the quar¬tile divides it into four equal parts, the decile into 10, and the percentile to 100 equal parts. The percentile is useful when huge masses of data, such as the GRE or GMAT scores, are handled. When the area of observations is divided into 100 equal parts, there are 99 percentile points. Any given score has a probability of .01 that it will fall in any one of those points. If John’s score is in the 16th percentile, it indicates that 84% of those who took the exam scored better than he did, while 15% did worse.

Oftentimes we are interested in knowing where we stand in comparison to others — are we in the middle, in the upper 10 or 25%, or in the lower 20 or 25%, or where? For instance, if in a company-administered test, Mr. Chou scores 78 out of a total of 100 points, he would be unhappy if he were in the bottom 10% among his colleagues (the test-takers), but would be reasonably pleased if he were in the top 10%, despite the fact that his score remains the same. The central tendency median and the percentile he falls in can determine his standing in relation to the others.

The measure of dispersion for the median, the interquartile range, consists of the middle 50% of the observations (i.e., observations excluding the bottom and top 25% quartiles). The interquartile range could be very useful when comparisons are to be made among several groups. For instance, telephone companies can compare long-distance charges of customers in several areas by taking samples of customer bills from each of the cities to be compared.

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