Statistical Topics

This topics list provides access to definitions, explanations, and examples for each of the major concepts covered in Statistics 101-103.

Describing and displaying data

Graphical displays: stemplots, histograms, boxplots,scatterplots.
Numerical Summaries: mean, median, quantiles, variance, standard deviation.
Normal Distributions: assessing normality, normal probability plots.
Categorical Data: two-way tables, bar graphs, segmented bar graphs.

Linear regression and correlation

Linear regression: least-squares, residuals, outliers and influential observations, extrapolation.
Correlation: correlation coefficient, r².
Inference in Linear Regression: confidence intervals for intercept and slope, significance tests, mean response and prediction intervals.
Multiple Linear Regression: confidence intervals, tests of significance, squared multiple correlation.
ANOVA for Regression: analysis of variance calculations for simple and multiple regression, F statistics.

Experiments and sampling

Experimental Design: experimentation, control, randomization, replication.
Sampling: simple, stratified, and multistage random sampling.
Sampling in Statistical Inference: sampling distributions, bias, variability.

Probability

Probability Models: components of probability models, basic rules of probability.
Conditional Probability: probabilities of intersections of events, Bayes's formula.
Random variables: discrete, continuous, density functions.
Mean and Variance of Random Variables: definitions, properties.
Binomial Distributions: counts, proportions, normal approximation.
Sample Means: mean, variance, distribution, Central Limit Theorem.

Hypothesis tests and confidence intervals

Confidence Intervals: inference about population mean, z and t critical values.
Tests of Significance: null and alternative hypotheses for population mean, one-sided and two-sided z and t tests, levels of significance, matched pairs analysis.
Comparison of Two Means: confidence intervals and significance tests, z and t statistics, pooled t procedures.
Inference for Categorical Data: confidence intervals and significance tests for a single proportion, comparison of two proportions.
Chi-square Goodness of Fit Test: chi-square test statistics, tests for discrete and continuous distributions.
Two-Way tables and the Chi-Square test: categorical data analysis for two variables, tests of association.

Wednesday, May 13, 2009

Wearable Sensors Watch Workers

Sensors that track social behavior highlight the benefits of face-to-face interaction.

By Kate Greene

Social sense: This sensor was worn by employees at a call center in Rhode Island to record activity and social interaction. MIT and New York University researchers correlated sensor data with productivity.
Credit: Sandy Pentland, MIT

Office workers who make time to chat face to face with colleagues may be far more productive than those who rely on e-mail, the phone, or Facebook, suggests a study carried out by researchers at MIT and New York University.

The researchers outfitted workers in a Rhode Island call center with a wearable sensor pack that records details of social interactions. They discovered that those employees who had in-person conversations with coworkers throughout the day also tended to be more productive.

The results aren't yet published, but they support research published last December by the same team. This study showed that employees at an IT company who completed tasks within a tight-knit group that communicated face to face were about 30 percent more productive than those who did not communicate in a face-to-face network.

"The big idea is that what you do on your coffee break and over lunch really matters for productivity," says Sandy Pentland, a professor at MIT's Media Lab, who led the study. "Face-to-face networks matter, and the implications are huge."

Many managers probably suspect a link between personal communication and productivity, says Pentland. Conventional wisdom suggests that face-to-face conversations are a useful way to create and maintain strong social networks, which could help workers solve complex customer problems or complete more calls at the center, he says.

However, some managers are slow to implement policies that foster this sort of communication because the connection has been difficult to prove with hard data, says Pentland. Usually, he says, workplace socializing is recorded using participant surveys, which tend to be filled with errors, since it can be difficult to remember the details of social interactions.

"There's all this knowledge that you see in anthropology and sociology [studies] that doesn't make it into management because it's sort of soft data," says Pentland. "But now we can tell which sort of folk wisdom is true . . . We can put some numbers on the table."

Pentland's study used a sociometer, a device about the size of a deck of cards, which participants wear around their necks as they would an identification badge. Each sociometer contains an accelerometer to measure their movement; a microphone that picks up their speech characteristics, such as intonation and cadence; a Bluetooth radio to detect other people wearing sociometers nearby; and an infrared sensor that can detect face-to-face interactions. Worn all day, the sociometers log workers' activity and conversations.

The data collected by each sociometer can, for instance, reveal how central a person is to a social network and how cohesive the network is overall. A more cohesive network is one in which all people talk to each other, thereby forming a closed loop. This may be an important measure of workplace social dynamics: workers in the most cohesive networks were about 30 percent more productive than those who weren't in such networks, according to the call-center study.

The researchers chose a call center for their research because productivity is constantly monitored and recorded--the number of calls and other tasks completed, and the time taken for each of them throughout the day.

"The thing that's really innovative is bringing social-network data together with productivity and performance data," says Eric Brynjolfsson, a professor at the Sloan Business School at MIT, who worked on the project.

The findings come at a time when telecommuting is booming, thanks to digital communication tools such as e-mail, instant messaging, and teleconferencing. Cameron Anderson, a professor at the Haas School of Business at the University of California, Berkeley, suggests that organizations could use such findings to weigh the costs and benefits of telecommuting, or to schedule break times for workers. "More interaction will likely bolster information transfer across individuals and departments," he says. "Studies have shown this is extremely important to organizational success."

In the case of the call center, Pentland notes that workers' break times were staggered, making it difficult for many of them to interact in person. "The people who managed to have more cohesive support groups were in atypical situations," he says. The next phase of the study is to see if productivity improves when workers are given opportunities for more direct social interaction.

"The underlying theme here is that humans are social beings," says Pentland, who will present details of the work at the Where 2.0 conference in San Jose, CA, next week. "Technology pushes us toward the abstract, and away from richer face-to-face communication." Without direct communication, he says, many physical signals, such as body language and facial expression, are lost.

Do's and Don'ts on Managing Risk in the Supply Chain

Do's and Don'ts on Managing Risk in the Supply Chain

Nine tips to help your supply chain operate at peak efficiency.

Wednesday, April 15, 2009
By David Blanchard

Do's

Establish closer collaborative relations with distribution channels. Get closer to the demand signal and sense variations continuously. Use sell-through demand (rather than sell-in demand) from sales channels to establish supply needs.

Implement multi-echelon inventory optimization. Segment your product portfolio by demand variability and strategically position inventory at different levels in the supply chain. This will enable companies to use inventory strategically to reduce out-of stocks at the shelf, and helps buffer against supply disruptions at the least total system-wide inventory cost.

Incorporate rapid scenario planning in the S&OP process. Use ranged forecasting to derive a range of possible demand outcomes. Companies can then better manage their assets to meet expected probability of demand given the expected reliability of supply.

Improve supply chain visibility. Synchronize information systems to provide demand and supply visibility, to track events and exceptions in supply chain performance and to monitor leading indicators to try to sense supply chain problems before they occur. Additionally, increase collaboration and communication among both sourcing and selling partners.

Streamline programs with strategic customers. Implement customer program management strategies (e.g., special programs, consignment programs, incentives, aggressive lead times, etc.) with customers that control a relatively large portion of demand. This will ensure that when your customers take measures to spread their risks, you are not significantly impacted.

Don'ts

Stay short-sighted. Avoid becoming overwhelmed by the prospect of balancing risk factors against the cost and benefits of implementing risk-mitigation strategies.

Sacrifice other strategic initiatives. Companies who ignore customer service levels, costs or working capital for the sake of a risk management initiative do so at their own peril.

"Once and done." Analyzing risk management is not a one-time project, but must be continuously evolving to accommodate changing market conditions.

Focus on "operational noise." There's a tendency to focus on sensational risks like product recalls while ignoring smaller risks such as yield busts that can still create friction in the supply chain.

Source: Ramesh Raghunathan, senior director, manufacturing industry, i2 Technologies

Understanding Risk: Avoiding Supply Chain Disruption

Understanding Risk: Avoiding Supply Chain Disruption

A supply chain disruption can cost a manufacturer up to $5 million, irreparably harm a brand and drive customers straight to the door of a competitor.

Monday, May 11, 2009
By

Discovering that a supplier is in danger of failing once a shipment has been missed is like getting caught in a rainstorm without an umbrella. Why? Because both situations can easily be avoided.

In 2008, 35% more companies filed for chapter 7 bankruptcy than in previous years, illustrating the increasing threat of failure in the supply chain. Given the economic meltdown, it's not a surprise. Manufacturers are searching for ways to reduce exposure to supplier failure. To do so, it is important for manufacturers to have insight into suppliers' operations to avoid surprises and disruptions in the supply chain. A supply chain disruption can cost a manufacturer up to $5 million, irreparably harm a brand and drive customers straight to the door of a competitor.

Risk management has historically been managed through a financial lens. Companies were under the impression that being financially stable trumped any other obstacles presented by the supplier. But as supply chains become increasingly global, and ownership moves further and further from the original equipment manufacturer, financial health is just the tip of the iceberg. Understanding supply risk requires much more than evaluating suppliers' financial conditions. Risk factors come in many shapes -- operational, managerial, geographic and more.

These pressures are driving intense effort and initiatives to reduce exposure to risk.

Market leaders are taking bold steps: increasing transparency when it comes to supplier information; monitoring suppliers on dozens of critical factors; working with suppliers to improve stability and operational performance and extending strategies beyond Tier 1 suppliers to protect the extended supply chain.

Supply Risk Strategy Starts with Supplier Data

The first challenge of supplier risk management is compiling all supplier information into one centralized location. Should be easy. But it's not. Supplier information lives in hundreds of places -- applications, divisions, systems and more. And supplier names may be entered in dozens of ways, e.g. IBM or Int'l. Business Machines, or maybe even Big Blue. Creating an accurate, consolidated and single source of truth about suppliers is the first step.

Once the suppliers are in a single location, the manufacturer can create master supplier lists broken into categories, such as single source and global, making it much easier to monitor suppliers' performance.

This system supports efforts to implement annual recertification of all registrants and allows access to external performance and financial data. The data can also be used to drive predictive indicators, giving insight into supplier viability as far out as 12 months into the future.

This central repository provides immediate visibility into what is being spent with each supplier and how critical that supplier is to the overall operation of the supply chain.

Manufacturers can determine the criticality of each supplier by asking the following questions:

• What need does this supplier fill?
• How essential is this supplier to the overall operations of the supply chain?
• How does this supplier fit into the company plan for supplier diversity and sustainability?
• What would happen if we were to lose this supplier? How would it be handled?

Understanding the criticality of a supplier allows the manufacturer to determine on a case-by-case basis how to address risk and put into place mitigation plans should a potentially damaging incident arise.

Beyond Financial Assessment

In today's economy, market leaders are looking far beyond financial health to evaluate and make informed assessments of a supplier's risk profile. Once there's a transparent, accessible and comprehensive set of supplier information, the next step is to monitor suppliers for behavioral changes. To be successful, manufacturers need to validate and enhance supplier-funded information -- which, as self-reported data, needs to be taken at face value only -- with a variety of other factors, which contribute to overall stability including:

• Changes in the supplier's management team
• EPA violations
• OSHA incidents
• Quality issues
• Noticeable lags in response time to inquiries
• OFAC violations

Changes in any of these conditions can be defined as parameters for raising an alert. For example, a financially stable supplier may in fact be about to lose it CEO to retirement -- which may cause a shake-up in management -- for better or for worse. Early visibility into that change, especially for a strategic supplier, gives the manufacturer time to act -- even if it's only to call the team in to discuss the transition and what they are planning to do to ensure it doesn't negatively affect customers.

Based on the criticality of the supplier and the nature of the alert received, the manufacturer can then chose to take action, such as calling or visiting the supplier, increase monitoring or take steps to terminate the relationship with the supplier and find a replacement.

Proactive Management Across the Enterprises Raises the Standard

The third step is to develop the supplier base through an analysis of risk associated with it. This includes evaluating supplier performance, establishing forward-looking supplier scorecards and implementing plans to further develop the individual suppliers' roles in the overall operation of the supply chain.

The final stage of establishing a strong supply base is extending the supplier enterprise by creating an integrated supplier network. This includes monitoring non-critical suppliers (tier two and three) in addition to the critical suppliers. It is important to have a firm understanding of how suppliers further down the line are operating and whether or not they are encountering potentially disruptive situations. Most manufacturers know the ins and outs of their most critical suppliers; it is problems with lower tiered suppliers that typically catch them by surprise.

To remain viable in this economy risk is something that manufacturers need to learn how to manage and ultimately use their advantage. By instituting better systems to evaluate suppliers and monitoring changes, manufacturers will never again be in the position where a missed shipment is the first indication of trouble.

Jim Lawton is senior vice president and general manager of D&B Supply Management Solutions (SMS). www.dnb.com.