To most researchers and practitioners using statistical inference, the popular hypothesis testing universe consists of two hypotheses: H0 is the null hypothesis of “zero effect” H1 is the alternative hypothesis of “a non-zero effect” The alternative hypothesis (H1) is typically what the researcher is trying to find: a different outcome for a treatment and control group in an experiment, a regression coefficient that is non-zero, etc. Recently, several independent colleagues have asked me if there’s a statistical way to show that an effect is zero, or, that there’s no difference between groups. Can we simply use the above setup? The answer … Continue reading Statistical test for “no difference”
Regression models are the most popular tool for modeling the relationship between an outcome and a set of inputs. Models can be used for descriptive, causal-explanatory, and predictive goals (but in very different ways! see Shmueli 2010 for more). The family of regression models includes two especially popular members: linear regression and logistic regression (with probit regression more popular than logistic in some research areas). Common knowledge, as taught in statistics courses, is: use linear regression for a continuous outcome and logistic regression for a binary or categorical outcome. But why not use linear regression for a binary outcome? the … Continue reading Linear regression for a binary outcome: is it Kosher?
“Big Data” is a big buzzword. I bet that sentiment analysis of news coverage, blog posts and other social media sources would show a strong positive sentiment associated with Big Data. What exactly is big data depends on who you ask. Some people talk about lots of measurements (what I call “fat data”), others of huge numbers of records (“long data”), and some talk of both. How much is big? Again, depends who you ask. As a statistician who’s (luckily) strayed into data mining, I initially had the traditional knee-jerk reaction of “just get a good sample and get it … Continue reading Big Data: The Big Bad Wolf?
Multiple testing (or multiple comparisons) arises when multiple hypotheses are tested using the same dataset via statistical inference. If each test has false alert level α, then the combined false alert rate of testing k hypotheses (also called the “overall type I error rate”) can be as large as 1-(1-α)^k (exponential in the number of hypotheses k). This is a serious problem and ignoring it can lead to false discoveries. See an earlier post with links to examples. There are various proposed corrections for multiple testing, the most basic principle being reducing the individual α’s. However, the various corrections suffer in this way … Continue reading Multiple testing with large samples
While huge datasets have become ubiquitos in fields such as genomics, large datasets are now also becoming to infiltrate research in the social sciences. Data from eCommerce sites, online dating sites, etc. are now collected as part of research in information systems, marketing and related fields. We can now find social science research papers with hundreds of thousands of observations and more. A common type of research question in such studies is about the relationship between two variables. For example, how does the final price of an online auction relate to the seller’s feedback rating? A classic exploratory tool for examining such … Continue reading Scatter plots for large samples
I am currently visiting the Indian School of Business (ISB) and enjoying their excellent library. As in my student days, I roam the bookshelves and discover books on topics that I know little, some, or a lot. Reading and leafing through a variety of books, especially across different disciplines, gives some serious points for thought. As a statistician I have the urge to see how statistics is taught and used in other disciplines. I discovered an interesting book coming from the psychology literature by Herman Aguinas called Regression Analysis for Categorical Moderators. “Moderators” in statistician language is “interactions”. However, when … Continue reading Discovering moderated relationship in the era of large samples