Refer an earlier article on the difference between continuous and discrete data points. Normal distribution is strictly only applicable for data that is continuous though in some cases we can use the normal distribution to approximate data that is discrete. What is distribution? A distribution graph shows the frequency of occurrence of certain values in the data set.
An example distribution which by the way is not normal is shown below. The distribution shows which data values are more likely to occur. For example, for the figure below, the data values are all positive with the most likely values close to 1 highest frequency. As the data values get close to 0 and very large, the frequency of occurrence also drops. The area under this curve indicates the probability of occurrence of these values.
For example, if we are interested in finding out what is the probability of getting data points greater than 2, then we would need to calculate the area of the distribution below the blue curve that is greater than 2. What is a normal distribution? A normal distribution is a special type of distribution that arises when we are working with certain types of data. It is also referred to as the Gaussian distribution. A normal distribution is a symmetric distribution which is centered at the mean value and the width of the distribution depends on the standard deviation.
For the normal distribution, the most frequently occurring values are close to the mean of the data set. An example normal distribution with a mean of 0 and a standard deviation of 1 is shown in the figure below.
For the figure shown below, we can see that the 0 value has the highest frequency of occurrence and as the values are farther away from 0, the frequency of occurrence goes down. The total area under the distribution indicates the probability of occurrence of those values. For this example, the area between these two limits is equal to 0.
Due to the complex nature of the curves, we cannot do these calculations by hand. Introduction to statistics: The normal distribution. Introduction Interpreting statistics Data and variable types Descriptive statistics The normal distribution Inferential statistics Glossary Feedback. Introduction to statistics.
Numeracy Skills Fundamentals Algebra Statistics. EndNote Essentials Extras Online. Enter Search Words. Close UniSkills. Assignment Skills. Study Skills. Digital Skills. Numeracy Skills. Site map. Interpreting statistics Interpreting descriptive statistics Interpreting inferential statistics References. Data and variable types What is data? What is a variable? Categorical and continuous data Independent and dependent variables.
Descriptive statistics What are descriptive statistics? Displaying data for one categorical variable Descriptive statistics for one categorical variable Displaying data for one continuous variable Descriptive statistics for one continuous variable Comparing means Displaying data for two categorical variables Descriptive statistics for two categorical variables Displaying data for two continuous variables Descriptive statistics for two continuous variables.
The normal distribution What is the normal distribution? Testing for normality Transforming variables. This is useful in cases when you have only a few observations in any given factorial combination.
There are both visual and formal statistical tests that can help you check if your model residuals meet the assumption of normality. The most common graphical tool for assessing normality is the Q-Q plot.
In these plots, the observed data is plotted against the expected quantiles of a normal distribution. It takes practice to read these plots. In theory, sampled data from a normal distribution would fall along the dotted line. In reality, even data sampled from a normal distribution, such as the example QQ plot below, can exhibit some deviation from the line.
You may also visually check normality by plotting a frequency distribution , also called a histogram, of the data and visually comparing it to a normal distribution overlaid in red.
In a frequency distribution, each data point is put into a discrete bin, for example ,-5], -5, 0], 0, 5], etc. The plot shows the proportion of data points in each bin. While this is a useful tool to visually summarize your data, a major drawback is that the bin size can greatly affect how the data look. The following histogram is the same data as above but using smaller bin sizes.
Each of the tests produces a p-value that tests the null hypothesis that the values the sample were sampled from a Normal Gaussian distribution or population. There is evidence that the data may not be normally distributed after all. If that does not fit with your intuition, remember that the null hypothesis for these tests is that your sample came from a normally distributed population of data. So as with any significant test result, you are rejecting the idea that the data was normally distributed.
See our guide for more specific information and background on interpreting normality test p-values. We recommend both. This is especially true with medium to large sample sizes over 70 observations , because in these cases, the normality tests can detect very slight deviations from normality.
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