I need an urgent suggestion my sample size is more than 400 and the normality test is showing z score, 2.3 (.273, std E , .114, skewness and kurtosis -7, Shapiro-Wilk p value is 0.00. It clearly shows that this is unequal distribution. I was interested in applying parametric test , but now applying non-parametric test.
All the test is telling you is that you have enough data to have good evidence that this sample doesn't perfectly follow a normal distribution. Since no real data is perfectly normal, this is unlikely to be a useful result.
In general, using a hypothesis test for normality as a pre-condition to using a certain statistical analysis isn't usually helpful.
It's more useful to use a plot to visually assess your data. A q-q plot or perhaps a histogram.
Also, be sure you understand the assumptions of the analysis you intend to use. Rarely do we expect the data to be normal. (Except in simple cases like for groups in a t test.) We might check if the data are approximately conditionally normal, for example by looking at the residuals.
Zoiya Naz this is an unresolved issue. As the sample size increases, normality tests lose power and this causes that it is recommended to use more than a test, a normality analysis, where in addition to the most powerful tests such as the Shapiro-Wilk test, graphs are used. However, I have seen articles where they report tests for large sample sizes, but they are not implemented in statistical software. It is best to analyze normality graphically using histograms and Q-Q (quantile-quantile) plots and complement it with the normality test. If the histogram conforms to a Gaussian curve, that is a first indication of normality. If there is a strong linear correlation between the quantiles of your data and the theoretical quantiles corresponding to a normal distribution, then it is very likely that your data are normal. Also, rely on kurtosis and standardized error as additional tools.
Zoiya Naz , it would fine to post your q-q plot and histogram and get people's opinions. But please also indicate what it is you are plotting. What statistical test are planning on using ? And are you plotting values for observations for a single group ? Or all the observations pooled ? Or residuals from an analysis ?
You haven't said what parameter that you are trying to measure. You can measure parameters with data that do not follow the normal distribution. Can you be more specific. But, assuming you are trying to do something like estimate the confidence interval for the mean, you could apply a bootstrap procedure. It will likely be similar to the one assuming normality. Note also that the standard errors for things like skewness printed in many textbooks assume normality so are not very useful for measuring asymmetry (Article Problematic standard errors and confidence intervals for ske...
).
Daniel Wright I am trying to find out median, standard deviation, checking the cause and its effect. I want to apply multivariate logistic regression but not sure if its completely applicable, if this data is apparently non normal, I have learned that multivariate logistic regression can do to test influence of one independent variable on multiple dependent variable and bootstrapping can be done on non normal data?
Zoiya Naz , it's difficult to give good advice because you haven't provided much information. Does your dependent variable have the values (1, 2, 3, 4) ? Are those ordinal categories ? (That is, is 4 > 3, 3 > 2, and so on.) Do you have only one grouping variable (cheatedon = yes / no) ? .... What nonparametric test are you using ?
Sal Mangiafico independent variable has 4 values strongly disagree ,disagree, agree and strongly agree, this is likert scale, yes only one grouping variable. Previously on other hypotheses I have applied ordinal logistic regression, Kruskal-Wallis test, . But please correct me if I am wrong ( I have been told that if the sample is above 300 one can use parametric test, based on CLI , but I see my data is not normal when I am checking perhaps due to the likert data , but I am interesting to show some of my analysis through parametric test.
Since you have an ordinal dependent variable with one independent dichotomous variable, appropriate tests include ordinal regression, Wilcoxon-Mann-Whitney, and Kruskal-Wallis.
It makes sense to calculate the median response. Probably use the interquartile range rather than the standard deviation.
Presenting the "histograms" tells the story. (They are really bar plots since the x-axis is categorical.)
It may also be helpful to calculate an effect size statistic like Vargha and Delaney's A, Cliff's delta, Glass rank biserial correlation coefficient. These are all related to the probability of an observation in one group being larger than an observation in the other group. There's also a "probability of superiority" statistic. These make sense for your kind of data.
With a DV with four ordinal categories, there's no reason to assess normality. And having a large sample doesn't justify using a "parametric" test like a t-test. It just doesn't make sense for this kind of data.
- Badges
- Science topic
- Similar topics
- Filing