A QUANTITATIVE RESEARCH PROJECT - GS/PPAL 6200 3.00   Sections M&N Research Methods and Information Systems A QUANTITATIVE RESEARCH PROJECT - DATA COLLECTION DATA DESCRIPTION DATA ANALYSIS

Variables Vocabulary Nominal (or Categorical) Variables: units composed of discrete categories (Male/Female/Neither e.g.) Ordinal Variables: variables that can be ordered but are not equal across the range (Frequencies measured as Always/Usually/Rarely/Never, e.g.) Interval Variables: variables that can be measured with equidistant units (Age in years; Amount studied in hours per month)

DATA DESCRIPTION Describing Nominal, Ordinal, and Interval Data with Graphs, Charts, Tables Describing the Interval Data (CGPA) with Descriptive Statistics Mean, range, minimum value, maximum value, standard deviation, standard error Deciles, Quintiles, Percentiles Z-scores

Graphs, Charts and Tables Create a Table of Cases #1-10 for CGPA, Hours Studied, and Main Reasons for Attending University Graph a scatterplot of CGPA and Hours Studied for these 10 cases Draw a Pie Chart showing the Main Reasons for Attending University for these 10 cases

Describing the CGPA Data Refer to Cases #1-10 in our survey results What is the sample mean of CGPA for these 10 observations? Consider the student graduating with CGPA = 6.33 How many grade points above the mean is this student? How does this student’s CGPA compare with that of other students?

Ranking Concepts: Quintiles and Deciles Order the 10 observations from lowest CGPA to highest Divide the number of observations by 5 to obtain the quintile units (10/5 = 2); in which quintile is the student with CGPA = 6.33? Divide the number of observations by 10 to obtain the decile units (10/10 = 1); in which decile is the student with CGPA = 6.33?

Statistical Description of the Data Distribution: Frequency – what is the frequency of each value? Central Tendency: Mean, Median, and Mode – what are the measures of the “centre” of the data? Dispersion: Range and Standard Deviation – what is the spread around the centre (Mean)?

Frequency and Central Tendency How many times does the value CGPA = 7.67 occur? … CGPA = 6.33? What is this occurrence as a % of the total # observations? What is the Mean of the CGPA in the sample? What is the Median of the CGPA?

Dispersion around the Mean Standard Deviation (True) dispersion of values around the true population mean = σ Standard Deviation (Sample) dispersion of values around the sample mean = s Standard Error of the Mean (SEM) = Standard Deviation (Sample, s) of the sample mean’s estimate (avgX) of the population mean (μ)

Dispersion about the Sample Mean What is the range of CGPA in the sample? What is the standard deviation (average distance from the mean) of the sample? Calculate the difference between each sample value and the sample mean. Square each result and add the squared values together (“Sum of Squares”) Divide by n-1 (“Degrees of Freedom”) * Take square root of the answer (*)

Standard Error of the Mean If a standard error of the mean (SEM) is calculated by the sample standard deviation divided by the square root of the sample size, what is the SEM of this 10-case sample? @ 95% CI what is the Confidence Level? @ 95% CI then CL = +/- 1.96*SEM = 0.86 If the hypothesized mean is 6.5, is the mean of this sample significantly different @ 95% CI? Upper Limit = Sample Mean + 0.86 = 6.96 Lower Limit – Sample Mean – 0.86 = 5.24

Dispersion about the True Mean For a comparison of the academic performance of this student with the rest of her graduating class, it is good to look at where they are ranked in the class but better to look at this in relation to the dispersion around the mean How many standard deviations is a CGPA of 6.33 away from the population mean (assume μ = 6.47)? If the standard deviation of CGPA for all graduating classes is known (σ = 1.48), then the CGPA is -0.095 standard deviations below the population mean: (6.33 – 6.47)/ 1.48 = -0.095 = z-score

Ranking Concept: Percentile For a student who graduates with a 6.33 CGPA, what percentile is he in? If he is in the 46th percentile, 46% of the other CGPA values of other graduating students fall below his grade. Unlike Quintiles and Deciles, scales in Percentile ranks are not of equal intervals; they are adjusted for the dispersion (frequency) of the numbers The pth percentile is calculated by pi = 100 (i-0.5)/n ; for n = total number of observations and i = the rank What percentile is the CGPA = 6.33 for this student relative to the sample of 10 graduating students? CGPA 4.17 5.00 6.33 i 1 2 3 4  Percentile = pi = 100 (i-0.5)/n (for n = 10) = 100*(1 - 0.5)/10 = 5 = 100*(2 - 0.5)/10 = 15 = 100*(3 - 0.5)/10 = 35  

Percentile Calculations in Excel The 40th percentile of the sample and 46th percentile of the population, assuming the population is normally distributed. RESULT EXCEL COMMAND 0.4 PERCENTRANK.EXC(data array, 6.33, TRUE) 0.4623 NORM.DIST (6.33, 6.47, 1.48, TRUE), for mean 6.47, and std dev 1.48 If the z-score is -0.095 (for same mean and standard deviation), Excel generates: 0.4621 NORM.S.DIST(-0.095, TRUE)