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T-distributions tend to be flatter and more spread out than normal distributions due to their heavier tails. Unlike the normal distribution, which has thin tails, t-distributions account for uncertainty in sample variance estimation, making them more robust for smaller sample sizes. The additional variability inherent in t-distributions arises from the incorporation of the sample size through the degrees of freedom parameter. As the degrees of freedom decrease, the t-distribution becomes more spread out and flatter, reflecting increased uncertainty and variability in the estimates. This property makes t-distributions well-suited for inferential statistics, particularly when dealing with small sample sizes.

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ouma alphonce

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1y ago

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Why in a normal distribution the distribution will be less spread out when the standard diviation of the raw scores is small?

The standard deviation (SD) is a measure of spread so small sd = small spread. So the above is true for any distribution, not just the Normal.


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Yes, the normal distribution is uniquely defined by its mean and standard deviation. The mean determines the center of the distribution, while the standard deviation indicates the spread or dispersion of the data. Together, these two parameters specify the shape and location of the normal distribution curve.


Is the middle spread that is the middle 50 percent of the normal distribution is equal to one standard deviation?

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What does the normal allow you to measure?

The normal distribution allows you to measure the distribution of a set of data points. It helps to determine the average (mean) of the data and how spread out the data is (standard deviation). By using the normal distribution, you can make predictions about the likelihood of certain values occurring within the data set.


What happens in a normal distribution when the means are equal but the standard deviation changes?

The two distributions are symmetrical about the same point (the mean). The distribution where the sd is larger will be more flattened - with a lower peak and more spread out.


What standard deviation tells us about a distribution?

It is a measure of the spread of the distribution: whether all the observations are clustered around a central measure or if they are spread out.


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Is normal distribution symmetrical?

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In a statistical sense, spread, otherwise known as statistical dispersion, is one of various measures of distribution.


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Population distribution refers to the patterns that a population creates as they spread within an area. A sampling distribution is a representative, random sample of that population.


What is the definition of spread math?

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How do outliers influence the shape and spread of the data?

Outliers will make give the graph a long tail (or tails). Overall, the graph will be flatter and wider.