Margin-of-Error, Confidence Interval, and Standard Deviation

WEEK 4 3 RD  DQ 

Margin-of-Error, Confidence Interval, and Standard Deviation

With the topics mentioned in the title, we start to get into “inferential statistics”, where we use the statistical information from the “sample” data to make “inferences” about the “population” parameters that the sample is supposed to represent.

The goal of most statistical studies is to learn something about an entire population because in most applications it is impractical, extremely time-consuming, extremely expensive, or impossible to gather data from the entire population. Thus, the heart of most statistical studies lies in “inferring” a conclusion about a population from the representative sample results.

Now, as you can imagine, due to sampling errors, you cannot expect the Mean calculated from a sample to equal the true population Mean. Thus, providing quantitative information about the accuracy of a sample (which would be an estimate) is vital, which leads to selecting a “confidence interval” and calculating the “margin-of-error”. 

Note the following: For example, for a given data set, a 95% confidence interval with a calculated 3.58% margin of error implies that the statistic will be within 3.58% points of the real population value, 95% of the time.

-The How to calculate the margin of error and standard deviation video is an excellent demonstration of how the margin-of-error increases with increased standard deviation. Notice that graphing the margin-of-error versus the standard deviation produces a straight line with a positive slope, indicating the linear relationship — therefore, as the standard deviation increases (meaning that the data distribution is more spread out), the margin-of-error increases. The video takes you through a clear numerical example of how the margin-of-error variables are determined.

-In the What factors affect the margin of error video, you will gain further insights on the margin-of-error formula, and how each variable in the formula affects the margin-of-error — I believe this is an excellent and well-presented video, full of insightful information.

I hope you will enjoy watching both videos and find them enlightening.

Correct and Incorrect ways of interpreting the “confidence interval”:

There is a correct, and also many different (and creative) incorrect interpretations of the confidence interval — the website Confidence intervals: 4 common mistakes explains a few examples of correct and incorrect interpretations.