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Although a commonly used phrase, there is no such thing as a “statistically significant sample” – it’s the result that can be statistically significant, not the sample. Word-mincing aside, for any study that requires sampling – e.g. surveys and A/B tests – making sure we have enough data to ensure confidence in results is absolutely critical.

Generally considered to be “stats 101” material, sample size determination is actually a non-trivial task. There is no “optimal” answer that can be derived by fitting a model to a dataset; the answer depends solely on the assumptions and requirements we specify in advance.

The most common way to determine the necessary sample size is through a prospective power analysis – a classic technique that can be used to derive the sample size needed to detect an effect of a given size at a given level of confidence. The purpose of this post is to demystify power analysis for those who are new to data science, as well as to provide some tips that make life easier when determining the necessary sample size. Specifically, we will cover the following areas:

Overview of hypothesis testing and power analysis for basic A/B testing. How to deal with the detectable difference. Examples of how to generate power analyses in R using the Back Up Tiz sandals Black Stuart Weitzman HaHC82QDgP
.

In order to understand classic power analysis, you have to understand the basics of frequentist hypothesis testing. Hence we will cover this topic first.

In order to explain hypothesis testing, we’ll use a classic “intervention” example found in most industries. Let’s say we want to conduct an experiment to test if a certain action helps prevent the occurrence of an adverse event. Depending on the business, this event could be fraud, attrition, downgrades, account closure, etc. The goal is to contact just enough people to decide if the action should be launched at full scale.

Defining the null and alternative hypotheses is the first step:

Note that the event rate refers to the proportion of clients for whom the event is observed (e.g., fraud, attrition, downgrades, etc.).

The null hypothesis is the hypothesis of no impact, while the alternative hypothesis is that the action will have an impact. This is a two-sided hypothesis, since we are testing if the event rate improved or worsened. An example of a one-sided hypothesis would be to only test if the event rate improved.

Let’s say we draw a sample of N N clients where 50% are exposed to the action and 50% are not. Note that the split is random, but does not have to be 50/50. We’ll learn how to choose N N later.

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Article

nickigilmour

Interviewing for a new job – especially one you really want – is always nerve-wracking. These days, it seems the entire process is more grueling than ever. In an annual review of the “ FOOTWEAR Pumps on YOOXCOM Daniele Ancarani pxXRXriloc
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For executive and C-level positions, your preparation must go above and beyond the standard checklist of interview do’s and don’ts. We all know the basics – dress well, have good posture, research the company thoroughly, and ask good questions – but when you’re called back multiple times, how can you ensure that you continue to present the best version of yourself?

Know and Represent Your Personal Brand

During a lengthy interview process, you will stand apart from other candidates if you know who you are as a leader, and can convey that message succinctly, with confidence and humility. Recognizing your passions –and exhibiting proven success in those professional endeavors related to your passions –can differentiate you from others.

According to Nicki Gilmour, who coaches many executives via Evolved Employer, the consulting arm of theglasshammer.com, “It is a really useful exercise to ask yourself what parts of your current or last job excited you most? You will find that it is easy to talk about many actual examples of the work when you feel good about the work that you did.”

Additionally, the more senior the role for which you are interviewing, the more you may need to internalize a leadership identity, which research has shown to happen less frequently for women and is known as the Imposter syndrome . Gracia Martore, CEO of Gannett was once towel logo cotton slides Miu Miu 58kpOG
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Talking the Talk

Executive search pioneer, Russell S. Reynolds, Jr., offered “10 Job Interview Tips from a CEO Headhunter” in a 2012 Fast Company crocoembossed sandals Grey Stella McCartney ibaFjbUjg
. Here, he explained reasons for particular types of interview questions and the often counter-intuitive responses that may actually be the best answers.

For example, he shared that, “If you can’t discuss a failure or mistake, the recruiter might conclude that you don’t possess the depth of experience necessary to do the job.” The best leaders take risks, and most leaders will tell you that their failures make them better leaders. When it comes to answering negative questions or discussing failures or weaknesses, Reynolds’ advice boils down to being honest yet brief – tell the truth, but don’t dwell on the negative.

In this version, I take the same approach and also fill the statistically significant cells. Because the cells are pretty wide (driven by the 0.567 value in the first column), I’m not sure I love the way this looks.

Dot Plots

Moving away from the tables, I played around with different dot plots. Of course, I could have used a standard column chart or some kind of box-and-whisker chart, but I think the dot plot might be the best choice (plus, the column chart approach has some issues ). Plus, I really like the approach Madame Butterfly Embellished Suede And Perspex Slides Silver Sophia Webster aJR3SPB
in his response to Ann’s post (also see Dolce amp; Gabbana Woman Crystalembellished Fringetrimmed Printed Patentleather Sandals Red Size 355 Dolce amp; Gabbana K3XVJ
).

I tried four different dot plots, just playing around with different kinds of labeling:

Version 1 plots just the estimates with the error bars (that I made up based on the level of statistical significance).

Version 2 adds labels to that basic dot plot.

-In Version 3 , I tried playing around with the labels. I didn’t really like how the labels looked in Version 2, so here I put them in the middle of the point. This required me to shrink the text size just a bit and blow up the size of the bubble. It’s not necessarily great because it hides some of the error bars, so you can’t quite tell which are statistically significant and which are not.

-Finally, in Version 4 , I added color to the dot plot by filling in those markers that are statistically significant and leaving empty those estimates that are not statistically significant. This has the same issue with hiding the error bars as in Version 3 , but the addition of the marker color helps denote which estimates are statistically significance and which are not. I also think this helps satisfy Ann’s “Squint Test.”

Wrap-Up

I’m basically left where I began: While I like Ann’s approach because it makes the table easier to read and adds visual elements, it ignores the different magnitudes of the point estimates, which are likely to be important for any sort of policy recommendation or action. I get the idea of making something very visual in the body of a report and leaving the details to the back or someplace else, but I think there are alternative visual approaches rather than getting rid of the numbers altogether.

March 8, 2018
2 Comments
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Great article. I’m so glad that you’re keeping the conversation going.

Geez, it’s hard to write blog posts that anonymize the client’s data and still provide enough context for the reader.

I’ll add that: – This was the first page of the Results chapter of the report. The real table was much longer (closer to 20 variables instead of my nine simplified ones for the blog post). Chapter 1 was a short intro (about the program, the countries they worked in, etc.). Chapter 2 was the results. So consider this Chapter 2, page 1. – The rest of Chapter 2 (pages 2 through 21ish) were deeper dives into each of the 20ish variables. On those pages, we included both the significant and non-significant variables. – We considered leaving out the non-significant variables, but felt it was important to show where the program wasn’t effective… especially for areas that we assumed would’ve been. Like if you provide meals to children in an orphanage then you would assume that their nutritional outcomes would be better off, but this wasn’t necessarily the case–lots of good discussions came from the report! – The dot plots are really promising. I hope that you/we/others continue exploring them. – Yep, we defined statistical significance (a paragraph in the Results chapter and a page in the Appendix). The Appendix had lots of methodological nerdy goodies. We didn’t actually expect the report’s audience to look at the appendix, but I’m a huge fan of including tons of details in appendices for the sake of transparency and accountability.

To be continued. Have to run and give a webinar now. Good job!

Reply

Thanks to both of you for this discussion. I’m currently dealing with three levels of statistical significance for a client. In one case, I used a heat map approach, with the lightest for p-value<0.1 and darkest for p-value<0.01. In another case, it's a connected scatterplot and I used the empty/filled markers approach of Ann's initial design and Jon's circles above. I might write a blog post when I'm done.

One suggestion I might make for your designs above is to also differentiate the variable name format when the result is significant across the board (bold, italic, background…) – it would spare the reader the work of figuring it out for each row.

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