Table of Contents
What test to use if data is skewed?
A t-test will often work quite well in this situation, but watch out. The data are skewed and the most useful comparison may be to use a Wilcoxon-Mann-Whitney test. The data are skewed and are better analysed on a transformed (e.g. logarithmic) scale.
What can I use instead of a t-test?
The Wilcoxon rank-sum test (Mann-Whitney U test) is a general test to compare two distributions in independent samples. It is a commonly used alternative to the two-sample t-test when the assumptions are not met.
Can you do t-test with skewed data?
Unless the skewness is severe, or the sample size very small, the t test may perform adequately. Whether or not the population is skewed can be assessed either informally (including graphically), or by examining the sample skewness statistic or conducting a test for skewness.
How do you analyze skewed data?
We can quantify how skewed our data is by using a measure aptly named skewness, which represents the magnitude and direction of the asymmetry of data: large negative values indicate a long left-tail distribution, and large positive values indicate a long right-tail distribution.
Is t-test affected by outliers?
For the t-test on independent samples, the data in each sample must be normal or at least reasonably symmetric and that the presence of outliers does not distort either of these results.
How do you test for skewness?
As a general rule of thumb:
- If skewness is less than -1 or greater than 1, the distribution is highly skewed.
- If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately skewed.
- If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.
What is the nonparametric alternative to a 1 sample t-test for means?
one-sample Wilcoxon signed rank test
The one-sample Wilcoxon signed rank test is a non-parametric alternative to one-sample t-test when the data cannot be assumed to be normally distributed. It’s used to determine whether the median of the sample is equal to a known standard value (i.e. theoretical value).
Which of the following is a non-parametric alternative to t-test for independent samples?
Mann-Whitney U test
The Mann-Whitney U test is often considered the nonparametric alternative to the independent t-test although this is not always the case.
Can we use t-test for large samples?
A t-test, however, can still be applied to larger samples and as the sample size n grows larger and larger, the results of a t-test and z-test become closer and closer. This is because only one population parameter (the population mean)is being estimated by a sample statistic (the sample mean).
Is t-test robust to skewness?
Overall, the two sample t-test is reasonably power-robust to symmetric non-normality (the true type-I-error-rate is affected somewhat by kurtosis, the power is impacted mostly by that). When the two samples are mildly skew in the same direction, the one-tailed t-test is no longer unbiased.
What does highly skewed data mean?
Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve, or normal distribution, in a set of data. If the curve is shifted to the left or to the right, it is said to be skewed.
What do you do if data is highly skewed?
Dealing with skew data:
- log transformation: transform skewed distribution to a normal distribution.
- Remove outliers.
- Normalize (min-max)
- Cube root: when values are too large.
- Square root: applied only to positive values.
- Reciprocal.
- Square: apply on left skew.
What is the p-value of t-test for two sample data?
Welch Two Sample t-test data: x and y t = -0.4777, df = 3366.488, p-value = 0.6329 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -2185.896 1329.358 sample estimates: mean of x mean of y 4536.186 4964.455 I know its not correct to use a t-test on this data since its so badly non-normal.
How to check the skewness of the data?
You can check it empirically via simulation, of course, but if you’re wrong about the exponentiality you may need larger samples. This is what the distribution of sample sums (and hence, sample means) of exponential data look like when n=40: Very slightly skew. This skewness decreases as the square root of the sample size.
What is the skewness of the sample means of exponential data?
This is what the distribution of sample sums (and hence, sample means) of exponential data look like when n=40: Very slightly skew. This skewness decreases as the square root of the sample size. So at n=160, it’s half as skew. At n=640 it’s one quarter as skew:
Is an equal-variance t-test enough for a histogram?
So a equal-variance t-test should still be okay (in which case the above good approximation you see in the histogram may even be slightly better). If the null is true, and you have exponential distributions, you’re testing equality of the scale parameters.