Can you compare standard deviations with different means?
Can you compare standard deviations with different means?
In many experimental contexts, the finding of different standard deviations is as important as the finding of different means. If the standard deviations are different, then the populations are different regardless of what the t test concludes about differences between the means.
How do you compare two standard deviations?
We can use the F-test to compare any two variances. Then, if we reject that the variances are equal, we reject that the standard deviations are equal. (Do not make the mistake of thinking that the F-test compares that variances of multiple groups, however.)
Can you compare standard deviation with different sample sizes?
Thus as the sample size increases, the standard deviation of the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.
What does comparing standard deviation mean?
It tells us how far, on average the results are from the mean. Therefore if the standard deviation is small, then this tells us that the results are close to the mean, whereas if the standard deviation is large, then the results are more spread out.
Can two sets of data have the same mean but a different standard deviation?
Though the two data sets have the same mean, the second data set has a higher standard deviation. This means that scores in that data set will be more spread out around the mean value of 50 compared to the first data set. If you think of a normal distribution, it will help make the point clear.
Why is it better to compare standard deviations?
Comparing the two standard deviations shows that the data in the first dataset is much more spread out than the data in the second dataset.
Can two data sets have different means but the same standard deviation?
The data set 13, 14, 15, 16, 17 also has a mean of 15, but the standard deviation is smaller. 2. For example, the following two data sets will have the same standard deviations but are centered in different places….Solution.
Standard deviation | Data Set |
---|---|
2.3 | 1 |
How do you compare two standard distributions?
The simplest way to compare two distributions is via the Z-test. The error in the mean is calculated by dividing the dispersion by the square root of the number of data points….So far this example:
- X1 = 51.5.
- X2 = 39.5.
- X1 – X2 = 12.
- σx1 = 1.6.
- σx2 = 1.4.
- sqrt of σx12 + σx22 =sqrt(1.62 + 1.42) = sqrt(2.56 +1.96) = 2.1.
How do you compare two data sets of different sizes?
One way to compare the two different size data sets is to divide the large set into an N number of equal size sets. The comparison can be based on absolute sum of of difference. THis will measure how many sets from the Nset are in close match with the single 4 sample set.
Can I do a t-test with unequal sample sizes?
Even though you can perform a t-test when the sample size is unequal between two groups, it is more efficient to have an equal sample size in two groups to increase the power of the t-test.
How do you know which standard deviation is better?
A high standard deviation shows that the data is widely spread (less reliable) and a low standard deviation shows that the data are clustered closely around the mean (more reliable).
Can two normal curves have the same standard deviation and different means?
The larger the standard deviation, the more dispersed, or spread out, the distribution is. Figure (b) shows two normal distributions with the same standard deviation but with different means. These curves have the same shapes but are located at different positions on the x axis.