Stratification Analysis. Summarizing an Output Variable by a Grouping Input Variable

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1 Stratification Analysis Summarizing an Output Variable by a Grouping Input Variable 1

2 Topics I. Stratification Analysis II. Stratification Analysis Tools Stratification Tables Bar Graphs / Pie Charts III. Stratification Case Study Loan Fees 2

3 I. What is Stratification Analysis? In analyzing a problem, it is often useful to separate an output variable into groups. Suppose you have three facilities, or two shifts, or two methods. In all of these cases, you may want to compare output performances by different groups. Compare On-time delivery of Facility A Vs. B Vs. C. Decomposing an output variable into groups is known as Stratification Analysis. 3

4 Example: Performance Output Suppose you conduct a study of on-time deliveries across multiple facilities. How may you improve % on-time? % On-Time Deliveries % On-Time Shipment 4

5 Stratification Example A common step in analyzing an output is to group your data by a stratification variable. Suppose you stratify these same data by facility. Now, it appears B is doing something better. Average Plant % On-Time A 74.9 B 83.5 C

6 Possible Stratification Variables Stratification Variable Examples Product/Service Type or Model Process/Method Used (e.g., Process #) Operator Manufacturing or Service Shift (Days, Nights) Time (Day, Month, Year) Department or Organizational Function Facility or Office or Manufacturing Plant Facility or Plant or Office Location 6

7 Stratification and Root Causes Although Facility B has the best performance, this input variable itself may not explain the root cause of the differences. Root cause is more likely related to: Differences in the methods being used. Differences in how personnel are trained. Differences in tracking systems used often manage what we measure. Although stratification variables may not identify the root cause, they often narrow the search. 7

8 II. Stratification Analysis Techniques Stratification Tables (Summary Statistics by Groups or Levels of an Output) Common Summary Statistics include: Mean, Standard Deviation, Sums, Counts Bar Graphs / Pie Charts Advanced: Stratify distributions using multiple histograms or multiple box plots (other lecture). 8

9 Stratification Table (Summary Statistics) Compute Descriptive Statistics/ Yield for Commission Fees (Y) by Loan Type (X) Loan Type: Conventional, FHA, Jumbo Using QETools >> Descriptive Statistics Tabulate the number of Fees < 700, and < 1500 Using QETools >> Binary Cross Tabulation 9

10 QE Tools: Descriptive Statistics with Grouping (Stratification) Variable QETools >> Descriptive Statistics Output (Y): CommFees; Grouping Variable: Loan Type CommFee CommFee CommFee Conventional FHA Jumbo Sample N Mean Median StDev Variance Min Max Range Data File: Loan-data.xls 10

11 Example: Bar Graph (Output Variable Y-axis) Suppose we wish to show only average fee results by three loan types: Conventional, FHA, Jumbo What is a possible concern with this type of graph? Loan Commission Fee by Loan Type Average Commission Fee Conventional FHA Jumbo Loan Category 11

12 Pie Chart Pie charts also provide an effective visual tool. Of the low commission fees (< $1500), most (201/215) are conventional loans. (Of course, most loans are conventional as well.) FHA, 10 Jumbo, 4 Conventional FHA Jumbo Conventional,

Cross Tabulation Binary Output: Fee<700 AND Fee < 1500 Grouping Variable: Loan Category Frequency Value Fee<700 Fee<1500 0 690 534 LoanCategory Conventional 583

13 Cross Tabulation Binary Output: Fee<700 AND Fee < 1500 Grouping Variable: Loan Category Frequency Value Fee<700 Fee< LoanCategory Conventional LoanCategory FHA LoanCategory Jumbo LoanCategory Conventional LoanCategory FHA 1 10 LoanCategory Jumbo 1 4 Data File: Loan-data.xls 13

14 III. Lecture Exercise Loan Fees Problem Definition Approx 30% of loans are being processed with fees less than $1500. While some of these are unavoidable, the company wishes to minimize the total number of low fee loans as they are a poor utilization of resources. Goal < 10% loans less than $1500 and < 1% less than $

15 Stratification Variables To identify the source of low fees, we have obtained a sample of 749. Data on fees (Y) and the following stratification variables (X s) Type of Loan (Conventional, FHA, Jumbo) Branch (A, B, C, D) Loan Officer Lending Institution 15

16 Fees by Loan Type Which type of loans should we focus? Should we shift our business to focus on these types of loans? Criteria Conventional FHA Jumbo All N (count) Average Median StDev Range # Fees < # Fees < % Loans < % 13% 12% 29% 16

17 Fees by Branch Is there a significant difference by branch for loans < $700? Branch Criteria A B C D N (count) Average Median StDev Min Range # Fees < % Loans < % 7% 5% 5% 17

18 Fees by Loan Officer Each Branch has 10 loan officers (40) Would you construct a stratification table by loan officer? What other tool might you utilize? 18

19 Low Fees by Loan Officer Is this chart appropriate? # Loan Fees < Loan Officers with Most Low Fees A-4 A-3 A-9 A-7 C-5 A-6 A-2 D-10 C-6 A-8 D-4 Loan Officer 19

20 Loan Fees by Officer Does this table provide more useful information? Loan Officer # Loans # Fees < 700 % < 700 A % A % A % A % C % A % A % D % 20

21 Fees by Lending Institution Which Lending Institution is yielding the lowest commission fees? What might you recommend for the loan officers of Branch A? # Loans Lender A B C D # Loans # Fees < 700 % < 700 E % C % J % Q % I % A % S % Totals

22 Conclusion Collecting output data only does not allow an efficient search for causes. Stratification variables and analysis can greatly narrow this search. Once you know where to look, it is much easier to identify solutions. 22

Description of Data I

Description of Data I (Summary and Variability measures) Objectives: Able to understand how to summarize the data Able to understand how to measure the variability of the data Able to use and interpret