How is Sample Size Related to Standard Error, Power, Confidence Level, and Effect Size?

When conducting statistical analysis, especially during experimental design, one practical issue that one cannot avoid is to determine the sample size for the experiment. For example, when designing the layout of a web page, we want to know whether increasing the size of the click button will increase the click-through probability. In this case, AB testing is an experimental method that is commonly used to solve this problem.

Moving to the details of this experiment, you will first decide how many users I will need to assign to the experiment group, and how many we need for the control group. The sample size is closely related to four variables, standard error of the sample, statistical power, confidence level, and the effect size of this experiment.

In this article, we will demonstrate their relationships with the sample size by graphs. Specifically, we will discuss different scenarios with one-tail hypothesis testing.

Standard Error and Sample Size

The standard error of a statistic corresponds with the standard deviation of a parameter. Since it is nearly impossible to know the population distribution in most cases, we can estimate the standard deviation of a parameter by calculating the standard error of a sampling distribution. The standard error measures the dispersion of the distribution. As the sample size gets larger, the dispersion gets smaller, and the mean of the distribution is closer to the population mean (Central Limit Theory). Thus, the sample size is negatively correlated with the standard error of a sample. The graph below shows how distributions shape differently with different sample sizes

#statistics #statistical-power #statistical-analysis #data-science #sample-size

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How is Sample Size Related to Standard Error, Power, Confidence Level, and Effect Size?

How is Sample Size Related to Standard Error, Power, Confidence Level, and Effect Size?

When conducting statistical analysis, especially during experimental design, one practical issue that one cannot avoid is to determine the sample size for the experiment. For example, when designing the layout of a web page, we want to know whether increasing the size of the click button will increase the click-through probability. In this case, AB testing is an experimental method that is commonly used to solve this problem.

Moving to the details of this experiment, you will first decide how many users I will need to assign to the experiment group, and how many we need for the control group. The sample size is closely related to four variables, standard error of the sample, statistical power, confidence level, and the effect size of this experiment.

In this article, we will demonstrate their relationships with the sample size by graphs. Specifically, we will discuss different scenarios with one-tail hypothesis testing.

Standard Error and Sample Size

The standard error of a statistic corresponds with the standard deviation of a parameter. Since it is nearly impossible to know the population distribution in most cases, we can estimate the standard deviation of a parameter by calculating the standard error of a sampling distribution. The standard error measures the dispersion of the distribution. As the sample size gets larger, the dispersion gets smaller, and the mean of the distribution is closer to the population mean (Central Limit Theory). Thus, the sample size is negatively correlated with the standard error of a sample. The graph below shows how distributions shape differently with different sample sizes

#statistics #statistical-power #statistical-analysis #data-science #sample-size

The Relationship between Significance, Power, Sample Size

Congratulations, your experiment has yielded significant results! You can be sure (well, 95% sure) that the independent variable influenced your dependent variable. I guess all you have left to do is write up your discussion and submit your results to a scholarly journal. Right…………?

Obtaining significant results is a tremendous accomplishment in itself self but it does not tell the entire story behind your results. I want to take this time and discuss statistical significance, sample size, statistical power, and effect size, all of which have an enormous impact on how we interpret our results.

Significance (p = 0.05)

First and foremost, let’s discuss statistical significance as it forms the cornerstone of inferential statistics. We’ll discuss significance in the context of true experiments as it is the most relevant and easily understood. A true experiment is used to test a specific hypothesis(s) we have regarding the causal relationship between one or many variables. Specifically, we hypothesize that one or more variables (ie. independent variables) produce a change in another variable (ie. dependent variable). The change is our inferred causality. If you would like to learn more about the various research design types visit my article (LINK).

For example, we want to test a hypothesis that an authoritative teaching style will produce higher test scores in students. In order to accurately test this hypothesis, we randomly select 2 groups of students that get randomly placed into one of two classrooms. One classroom is taught by an authoritarian teacher and one taught by an authoritative teacher. Throughout the semester, we collect all the test scores among all the classrooms. At the end of the year, we average all the scores to produce a grand average for each classroom. Let’s assume the average test score for the authoritarian classroom was 80%, and the authoritative classroom was 88%. It would seem your hypothesis was correct, the students taught by the authoritative teacher scored on average 8% higher on their tests compared to the students taught by the authoritarian teacher. However, what if we ran this experiment 100 times, each time with different groups of students do you think we would obtain similar results? What is the likelihood that this effect of teaching style on student test scores occurred by chance or another latent (ie. unmeasured) variable? Last but not least, is 8% considered “high enough” to be that different from 80%?

#type-i-error #power-analysis #statistical-significance #sample-size #effect-size #data analysis

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Is Power BI Actually Useful?

The short answer, for most of you, is no. However, the complexity and capability of the products could be beneficial depending on what type of position or organization you work in.
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In my effort to answer this common question about Power BI I researched the following:
– Power BI Desktop Gateway
– Syncing on-prem SQL server data
– Syncing SharePoint Online list data
– Syncing data from an Excel workbook
– Building, and sharing a dashboard
– Inserting a Power BI visualization into PowerPoint

To get in-Depth knowledge on Power BI you can enroll for a live demo on Power BI online training

The feature spread above gave me the opportunity to explore the main features of Power BI which break down as:
– Ingesting data, building a data set
– Creating dashboard or reports with visualizations based on that data

In a nutshell Power BI is a simple concept. You take a data set, and build visualizations that answer questions about that data. For example, how many products have we sold in Category A in the last month? Quarter? Year? Power BI is especially powerful when drilling up or down in time scale.
And there are some interesting ways to visualize that data:
However, there are a number of drawbacks to the current product that prevented me from being able to fold these visualizations into our existing business processes.

  1. Integration with PowerPoint is not free. This shocked me.

The most inspiring Power BI demo I saw at a Microsoft event showed a beautiful globe visualization within a PowerPoint presentation. It rendered flawlessly within PowerPoint and was a beautiful, interactive way to explore a geographically disparate data set. I was able to derive conclusions about the sales data displayed without having to look at an old, boring chart.

During the demo, nothing was mentioned about the technology required to make this embedded chart a reality. After looking into the PowerPoint integration I learned that not only was the add-in built by a third party, it was not free, and when I signed up for a free trial the add-in could barely render my Power BI visualization. The data drill up/down functionality was non-existent and not all of the visualizations were supported. Learn more from Power bi online course

  1. Only Dashboards can be shared with other users, and cannot be embedded in our organization’s community on SharePoint.

Folks in our organization spent 50% of their time in Outlook, and the rest in SharePoint, OneNote, Excel, Word, and the other applications needed for producing documents, and other work. Adding yet another destination to that list to check on how something is doing was impossible for us. Habits are extremely hard to change, and I see that consistently in our client’s organizations as well.

Because I was not able to fold in the visualizations with the PowerPoint decks we use during meetings, I had to stop presentations in the middle, navigate to Internet Explorer (because the visualizations only render well in that browser), and then go back to PowerPoint once we were done looking at the dashboard.

This broke up the flow of our meetings, and led to more distractions. I also followed up with coworkers after meetings to see if they ever visited the dashboard themselves at their desk. None of them had ever navigated to a dashboard outside of a meeting.

  1. The visualizations aren’t actually that great.

Creating visualizations that cover such a wide variety of data sets is difficult. But, the Excel team has been working on this problem for over 15 years. When I import my SharePoint or SQL data to Excel I’m able to create extremely customized Pivot Tables and Charts that show precisely the data I need to see.

I was never able to replicate visualizations from Excel in Power BI, to produce the types of visualizations I actually needed. Excel has the ability to do conditional formatting, and other customizations in charts and tables that is simply not possible with Power BI. Because of how generic the charts are, and the limited customization it looks “cool” without being functional.

In conclusion, if you have spare time and want to explore Power BI for your organization you should. However, if you are seriously thinking about how you can fold this product into your work processes, challenge yourself to build a dashboard and look at it once a week. See if you can keep that up for a month, and then think about how that change affected your work habits and whether the data analysis actually contributed value each time. At least half of you will realize that this gimmicky product is fancy, but not actually useful.

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