If in doubt, stick to a nonparametric test.  You may lose a little power, but it is unlikely to be critical with this kind of sample size.

In general I tend not to perform tests of normality - such as the K-S comparison to the cumulative normal - but instead visually inspect the plots looking especially for outliers.  While many cookbook approaches suggest testing for normality, it's worth pointing out that the key assumption is not that the data are normally distributed but that the errors are normally distributed.  In fact, if you have a difference in means and plot the data for the two groups it will not be normally distributed (it will be bimodal).  If instead you do separate plots for the two groups this leaves you at the mercy of smaller samples.  One group may look roughly normal and the other not; one may be significantly different from normality and the other not.  Better to fit the two means and look at the distribution of the residuals.

Hope this helps.

These are really a lot of questions which are not answered with a couple of sentences. It may be helpful to contact a local statistician or at least have a look at a textbook. I recommend Andy Field - Discovering Statistics Using SPSS, since it is easy to grasp and it guides you through all SPSS dialogues and outputs. There is also a whole chapter covering assumptions such as normality and possible remedies in case of violation.

https://uk.sagepub.com/en-gb/eur/discovering-statistics-using-ibm-spss-statistics/book238032

I think  you should determinate which hypotheses to test. In general case you can test the null-hypothesis F(x)=G(x)  vs alternative F(G)G(x) with nonparameric Lehmann–Rosenblatt test (aka Lehmann's two-sample test), where F(x) and G(x) are distribution functions, x is continious random value.  If F(x) and G(x) are normally distributed and have the same variences, hypothesis F(x)=G(x) is reduced to hypothesis mean_1=mean_2. In this case you can use Student's test. Some mathematicians (for example, B. Yu. Lemeshko,  S.B. Lemeshko) show if the distribution of variable has not "very hard tails" we can still use parametric test for comparing means (Student's test, Welch test and etc) and comparing variences (F-test, C-Cochran test). I recommend to use parametric Welch test or nonparametric Wilcoxon-Mann-Whitney test.

If in doubt, stick to a nonparametric test.  You may lose a little power, but it is unlikely to be critical with this kind of sample size.

In general I tend not to perform tests of normality - such as the K-S comparison to the cumulative normal - but instead visually inspect the plots looking especially for outliers.  While many cookbook approaches suggest testing for normality, it's worth pointing out that the key assumption is not that the data are normally distributed but that the errors are normally distributed.  In fact, if you have a difference in means and plot the data for the two groups it will not be normally distributed (it will be bimodal).  If instead you do separate plots for the two groups this leaves you at the mercy of smaller samples.  One group may look roughly normal and the other not; one may be significantly different from normality and the other not.  Better to fit the two means and look at the distribution of the residuals.

Hope this helps.

You can test normality for two independent samples by using either graphical or analytical methods, the former requires to have the residuals in a new variable within your data set, that can be done easily, with the options of PROC GLM in the MODEL statement which allows you to get the RESIDUALS and the PREDICTED values.

Here I am using the principle that the ANOVA is an extension of the two independent samples t test; once you have the residuals for the two samples You can use the UNIVARIATE procedure, which allows You for performing the Shapiro-Wilk test.

The graphical alternative requires a histogram plot of the residuals, if the samples come from a normal distribution that plot should resemble a normal distribution; You can also do a normality plot of the residuals, if normality holds, you should get, from left to right going up, a nice straight line in your plot (read Neter, Kutner, Nachtsheim and Wasserman. 1996. Applied Linear Statistical Methods; on pages 106-107 for simple linear regression and 758-759, for one way ANOVA) .

 Note: The UNIVARIATE procedure will give both Shapiro-Wilk test as well as the normality plot if you request for them, remember under the null hypothesis, the t test assumes that the two samples arise from the same normally distributed population with unknown variance.

I have similar opinion with Denis William.Perform KS test of normality.Also conduct bartlety test or any variance test for independent populations.This will enable you to choose between models assumed normality assumption or not in comparing the two independent population.Size of samples is also a determinant.

Former researchers answer many information. Many tests for normality are developed for each variable. I guess you wish to discriminate your groups and image Fisher's asumption. There is no good test for the Fisher's assumption. I proposed the test for Fisher's asumption if number of misclassifications (NM) obtained by discriminunt functions become Minimum NM. See my several papers after2014, especially CPD (Cepahlo Pelvic Disproportion) data.

Kolmogorov Smirnov test is a non-parametric test that may be used to test normality for two independent groups.

You can use Kolmogorov Smirnov test for testing normality of two independent groups. When the test significant your data have not normal distribution and when the test is non-significant, your data have normal distribution.

I will like to talk about the third question, to test for homogeneity of variance, you can make use of Bartlett's test or Cochran's test. Meanwhile Cochran's test is used when the sample sizes are equal.

 Manar, why do you reply for 9 researchers answer?

Normality tests are not very powerful. I prefer instead visually inspect the plots, like Dennis suggested, looking for outliers and also for the symmetry.

I am more worried about heteroscedasticity.

 I am not familiar with SPSS. I agree Robert answer.

You try t-test there are many information in JUMP.

If you wish to discriminate your data, it is my research thema.

There are several papers after 2013.

I agre with t-test in case the n number is over 30. I use stata for that but are many other resources. Look in agreegroup.com they have many of them in excel 

I suppose that you want to compare two population means using a test, and that an estimation of a difference is not relevant for the moment. There are two rather than one question related to your problem: 1) concerning validity, 2) efficiency. 

To have a valid test based on sample means you must estimate the skewness coefficient of each of your populations. Cochran (Sampling Techniques, 1977, Wiley) suggests that the  skewness coefficient of the distribution of a sample mean should be at most 0.2 before you can hope to have a trustworthy normal distribution for a sample mean (simulation and re-sampling methods may help you gain confidence here). The kurtosis coefficient is important too, but usually not as critical as the skewness coefficient since kurtosis decrease as 1/n while skewness only as 1/root(n). If your samples show extreme difference of variances, I would prefer the Behrens-Fisher method since Welch's method tends to reject the null hypothesis too often. With the sample sizes which you state, I would not be surprised if these two tests would give the same result as with a t test. 

For efficiency, you may try a log transformation -- which often will stabilize variances. Other transformations may be relevant, but this is too sensitive a subject to venture in at this moment.

Thank you for all your replies.

Mr. Dennis,

You suggested to me to fit the two means and look at the distribution of the residuals. Did you mean to combine both groups and plot them as one group? How to check out the distribution of residuals?

Thank you again.

Compare the main variable of both group at base line through Explore and calculate the Shapiro-Wilk Test value, if the Shapiro-Wilk Test  p-value is more then .05 then your data is normal, for normal data you use parametric  Independent T test for group comperesion. Vice versa

In SPSS you can fit a General Linear Model and save the residuals.  The One Way ANOVA gives the same result as the t-test.  (In fact the F-value in the ANOVA is just the square of the t-value in the t-test)  You can then use the Graph function to plot the residuals against the predicted values.  Essentially the residuals for a t-test are just the difference from the group means.  The idea is these differences should be roughly normally distributed, with roughly the same variance. 

Here is the code generated by General Linear Model, Univariate:

UNIANOVA yvariable BY groupvariable

/METHOD=SSTYPE(3)

/INTERCEPT=INCLUDE

/SAVE=PRED ZRESID SRESID

/EMMEANS=TABLES(groupvariable)

/PLOT=RESIDUALS

/CRITERIA=ALPHA(.05)

/DESIGN=groupvariable.

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME="graphdataset" VARIABLES=PRE_1 SRE_1 groupvariable MISSING=LISTWISE REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource(id("graphdataset"))

DATA: PRE_1=col(source(s), name("PRE_1"))

DATA: SRE_1=col(source(s), name("SRE_1"))

DATA: VALID=col(source(s), name("groupvariable"), unit.category())

GUIDE: axis(dim(1), label("Predicted Value for yvariable"))

GUIDE: axis(dim(2), label("Studentized Residual for yvariable"))

GUIDE: legend(aesthetic(aesthetic.color.exterior), label("groupvariable"))

ELEMENT: point(position(PRE_1*SRE_1), color.exterior(groupvariable))

END GPL.

Most cookbook statistics books will recommend a test of normality but it's usually worthless.  You can get significant differences from normality that are not going to impact the test and you can also get non-significant differences when the data clearly demand a transformation or switch to a nonparametric method. 

Hope this helps.

Hello All

Lately found a query of my interest, responded to by the experts. Was wondering if Manar got answer to his query:

"You suggested to me to fit the two means and look at the distribution of the residuals. Did you mean to combine both groups and plot them as one group? How to check out the distribution of residuals? "

I have also the same query:

1. should we check the normality of each group separately. Then how to proceed if individually one group is normal / other is non normal.

2. Do we need to test the normality of both the groups taken together.

Seek advise.

@ Dennis William Lendrem @ Abdul Ghafoor Sajjad

In SPSS while checking for normality using shipiro wilk test do we enter both dependent and independent variable or dependent alone? its my confusion.please clarify if we should use residual how its done?

Thats so easy. You can use a kolmogorov smirnov test or Shapiro-Wilk Test. if the p value is higher than .05. the data are normal.

Ehsan Namaziandost well, if it would be so "easy", we wouldn't have any problems... but it isn't! KS and SW tests are dependent on power, i.e. sample sizes. With large sample sizes, both tests are very sensitive to slightest violations and will usually have p-values below .05, although the data/residuals are sufficiently normally distributed. So, I would say your answer is at least misleading! Visual inspection (e.g. histograms, PP/QQ plots, residuals vs predicted values) will singnifcantly improve the decison, if a distribution is normal or not. Additionally, this will help to asssess, what causes non-normality, i.e. outliers, skewed distributions etc. which will help to find an appropriate model or remedy for your data (e.g. generalized linear models). So, dont rely on significance tests to assess normality of your data!!

@ Rainer Duesing

Yes you are right Dear Duesing .\

Thank you for your nice critique.