New Video,
Skew, Skewness, uploaded to the book's channel.For a list of available and planned videos, see the Videos page on this website.
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"Statistics is the part of mathematics that even mathematicians don't particularly like." Alan Smith, Data Visual Editor, the Financial Times in London.
http://bit.ly/2DmPueDRandomness is likely to be representative, and Simple Random Sampling (SRS) can often be the most effective way to achieve it. But in certain situations, other methods such as Systematic, Stratified, and Clustered Sampling may have an advantage. In our Tip of the Week for November 27, 2017, Stratified Sampling was described. This Tip is about Clustered Sampling. To perform Clustered Sampling,- Divide the Population or Process into small clusters (e.g. city blocks)
- Select a Simple Random Sample of these clusters
- Collect data from each unit within each cluster
Advantage: It can be less time-consuming and less expensive. For example, the Population is the inhabitants of a city, and a cluster is a city block. We randomly select an SRS of city blocks. There is less time and travel involved in traveling to a limited number of city blocks and then walking door to door, compared with traveling to more-widely-separated individuals all over the city. Also, one does not need a Sampling Frame listing all individuals, just all clusters. Disadvantage: The increased Variability due to between-cluster differences may reduce accuracy. Chi-Square is a Test Statistic; as such, it has a family of Distributions. There is a different Chi-Square Distribution for each value of Degrees of Freedom, df.
Commonly, Degrees of Freedom is the Sample Size minus 1. But this isn't always the case with Chi-Square. That will be covered in a future Tip of the Week. Here are some examples of how the Chi-Square Distribution varies as df increases. You might observe that the shape of the Chi-Square Distribution is similar to that of the F-Distribution. For more on the Chi-Square, its Distributions and Tests, see the book or this video. I just uploaded a new video.: https://youtu.be/3GCJU_RCgoM It's an addition to the playlist on Probability Distributions.Check out the "
Videos" page of this website for a list of completed videos and plans for upcoming videos.David Leonhardt is an Op-Ed columnist for the New York Times. In
his Christmas Eve column, he writes about probabilities. He is in favor of using them to communicate, but says, "They are inherently hard to grasp."And, as we know, statistics is based on probabilities -- which is why so many find it confusing. Continuing to add videos on Distributions to the YouTube channel for the book. The latest is on the Exponential Distribution. This is the 9th in the playlist on Distributions. The Videos page of this website has the latest status on videos.
Many of the most common statistical analyses have fairly stringent "Assumptions". These are requirements that must be met if the analysis is to be valid. The most common Assumption is that the Population or Process data must have Parameters which approximate those of Normal Distributions like these: Parameters are statistical properties of a Population or Process, like the Mean or Standard Deviation. (Corresponding properties of Samples are called Statistics.) The key Parameters which define a Parametric (approximately Normal) Distribution are: - Mean = Mode = Median
- Skewness = 0 (the shape is Symmetrical)
Parametric Assumption: Equal Variance Parametric methods which use 2 or more Samples from 2 different Populations or Processes usually assume roughly equal Variance. Nonparametric methods don't. Nonparametric methods can work with these: Nonparametric methods are often called "distribution-free", because they are free of any assumptions about the source Distribution(s).
Here are some commonly-used Nonparametric tests and their Parametric Counterparts: "Reject the Null Hypothesis" is one of two possible outcomes of a Hypothesis Test. The other is "Fail to Reject the Null Hypothesis". Both of these statements can be confusing to many people. Let's try to clarify the concept of "Reject the Null Hypothesis". The Null Hypothesis states that there is no (Statistically Significant) - difference,
- or change,
- or effect
For example, - There is no difference between the Means of these two Populations.
- There has been no change in the Mean of this Population from its historical Mean.
- This treatment has no effect.
If the results of a statistical test indicate " Reject the Null Hypothesis", that means that we conclude that there is a (Statistically Significant)- difference,
- or change,
- or effect
What is the Null Hypothesis to which she is referring? As we said earlier, the Null Hypothesis says there is no difference, change, or effect. Before his proposal, they were not engaged to be married. So, if there is to be no difference, change, or effect in their relationship as a result of his proposal and her response, the Null Hypothesis would say that they are not to be engaged. But she
rejects the Null Hypothesis. This indicates that she does want there to be a difference, change, or effect. She does want to change their status to engaged to be married.If you still find this a little confusing, you might want to go to my YouTube channel and see the video on this subject: Reject the Null Hypothesis. There are also videos on these related concepts: __Null Hypothesis____Alternative Hypothesis____Fail to Reject the Null Hypothesis____Alpha, p, Critical Value and Test Statistic -- How They Work Together__
For more on available and planned videos based on content from my book, see the Videos page on this website. |
## AuthorAndrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley. ## Archives
January 2018
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