Define if the distribution is normal or not

In summary, the conversation discusses methods for determining if a distribution is normal or not based on a table with numerical data. The individual is unsure of how to make this determination and asks for assistance. Suggestions are made for using hypothesis testing, chi-square distributions, and Q-Q plots to analyze the data.
  • #1
Vital
108
4
Hello.

I wonder how to see if the distribution is normal or not based on the numbers in the table. I attach the screenshot with the table, and it is written that "the distribution appears to be bimodal", so it appears to have two peaks. I understand the the question sounds silly, but I truly don't now how to determine this.

https://drive.google.com/file/d/1YwawScq_rWjd0CzY2FUsIG8dnaJBgfQC/view?usp=sharing

Thank you.
 
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  • #2
What is it we are looking at ?

Ever hear of hypothesis testing or chi square distributions ?

Template something for you ?
 
  • #4
You can also do Q-Q plots or a Chi-squared goodness of fit by finding sample mean and standard error
orand considering the percent of data within 1,2,3 s.e from the sample mean, altho maybe the Q-Q plot does this too.
 

1. What is a normal distribution?

A normal distribution is a probability distribution that is symmetrical and bell-shaped, with the highest frequency of values occurring in the middle and gradually decreasing towards the tails. It is characterized by its mean and standard deviation, with 68% of the data falling within one standard deviation of the mean, 95% falling within two standard deviations, and 99.7% falling within three standard deviations.

2. How do you determine if a distribution is normal?

There are several methods for determining if a distribution is normal. One way is to plot a histogram of the data and see if it resembles the typical bell-shaped curve. Another method is to calculate the skewness and kurtosis of the data and compare them to the expected values for a normal distribution (skewness=0, kurtosis=3). Additionally, statistical tests such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test can be used to formally test for normality.

3. Why is it important to know if a distribution is normal?

Knowing if a distribution is normal can provide valuable information about the data and can help with making accurate statistical inferences. Many statistical tests and models assume a normal distribution, so if the data is not normal, the results of these tests may not be reliable. Additionally, understanding the shape of the distribution can help with identifying outliers and making appropriate data transformations.

4. Can a distribution be partially normal?

No, a distribution cannot be partially normal. It is either normal or not. However, it is possible for a distribution to have some characteristics of a normal distribution (such as being symmetrical) but not be perfectly normal. In these cases, it is important to assess the level of deviation from normality and determine if it will impact the results of the analysis.

5. What should I do if my data is not normally distributed?

If your data is not normally distributed, there are a few options to consider. One option is to use non-parametric tests, which do not assume a normal distribution. Another option is to transform the data using mathematical functions such as logarithmic or square root transformations, which can sometimes make the data more normally distributed. Ultimately, the best approach will depend on the specific data and the goals of the analysis.

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