Parametric Statistics - Science topic

I have six ecosystems in two substrate categories (Triplicates essentially). I have determined shannon wiener index values for each ecosystem and also for the two categories separately. I have done this for two separate sets of data that were sampled in two separate years. Is it possible to statistically compare the development of the biodiversity between each of the categories i.e., the development of biodiveristy in ecosystem 1 between the two years, using the shannon wiener values somehow? Are there any other tests that could work? I am aware of the hutcheson t test however, some of my data is not normally distributed.

I would really appreciate some help!

Is it very literally subbing in shannon wiener index values instead of species abundances?

In a causal model (such as multiple IVs and single DV) with presence of a mediator or moderator, do we have to consider such mediator or moderator when assessing the parametric assumptions or do we have ignore them and consider only the IV/s and DV in the model?

Hi, 

I have a general question regarding weather or not one can use cronach's alfa for measuring scale reliability? As far as I understand alfa is only used for metric data, right ? 

Thanks 

Davit 

In determining the number of social research subjects, there are many opinions that the data must be more than 30 as a condition to be tested for parametric statistics. What theory underlies this?

I a comment to one of members on researchgate re normalising data using Normal Quantile Transformation which is as follows: “… If you want to run a three factor ANOVA model with interactions, I recommend using normal quantile transformation first, followed by a regular three factor ANOVA on the normal scores. This is a robust ANOVA procedure….” . I have a survival data-set for my study in which I have 5 vitamin levels x 2 heat levels x 2 genders. The 2 dependent variables that I am trying to analyse are: 1- The day I got 50% survival 2- the day I got 90% survival I have used Kaplan Meier analysis to generate survival curves (all good with that). I want to run a 3 way Anova to look for interactions between the independent variables (vitamin, gender and heat) but my data are not normally distributed even though I tried to normalise them using Log10, Square Root, and normal quantile transformation that were suggested. I was wondering if: 1- there is another 3 way anova for nonparametric vales? 2- there is another way to transform my data (other than the 3 types I tried) to normalise my data to parametric valued so that I can use 3way anova in parametric statistics ?

Majority of our questions were in Likert scale (from 5 very frequent to 1 never), and we use a pretest-posttest methodology. To compare the pretest and the posttest, we wanted to use paired sample t-test. However, this is a parametric test wherein the data should be normally distributed.

I have also read in the work of Norman, G. (2010) that parametric statistics can still be used with Likert data even with non-normal distributions.

What would be the best option here? Should we proceed in using the paired sample t-test, or go for Wilcoxon tests since the data is not normal? Thank you for answering in advance.

Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances in health sciences education, 15(5), 625-632.

I have large sample (just one sample with 1100 cases) and I want to test a hypothesis about comparing mean of my sample in the two groups (each group has 550 cases).

Some statisticians told me "you can use formal student t-test because the data are normal, based on Central Limit Theorem".

I'm confused, the Central Limit Theorem is about "mean of sample means". for example, if we have a data with 100,000 cases which is not normal then we can take 100 samples. In this case, the average of 100 sample means would be normal. Now I can use the t-test.

Would you please share your kind opinion regarding this issue?

Hi,

We received a statistical reviewer comments on our manuscript and one of the comments goes as follows: '... Note that common tests of normality are not powered to detect departures from normality when n is small (eg n<6) and in these cases normality should be support by external information (eg from larger samples sizes in the literature) or non-parametric tests should be used.'

This is basically the same as saying that 'parametric tests cannot be used when n<6', at least without the use of some matching external data which would permit accurate assumption of data distribution (of course in real life such datasets do not exist). And this just doesn't seem right. t-test and ANOVA can be used with small sample sizes as long as they satisfy test assumptions, which according to the reviewer cannot be accurately assumed and thus cannot be used...

I see two possible ways of addressing this:

For every dataset in the paper, I assume data distribution by identifying outliers (outliers - >Q3 + 1.5xIQR or < Q1 - 1.5xIQR; extreme outliers - > Q3 + 3xIQR or < Q1 - 3xIQR), testing normality assumption by Shapiro-Wilk’s test and visually inspecting data distribution using frequency histograms, distribution density and Q-Q (quantile-quantile) plots. Homogeneity of variance was tested using Levene’s test.

Datasets are usually n=6 and are exploratory gene expression (qPCR) pairwise comparisons or functional in vivo and in vitro (blood pressure, nerve activity, response magnitude compared to baseline data) repeated measures data between 2-4 experimental groups.

Choice of parametric statistical methods used in analysis of non-parametric data is often criticize due to lack of fulfillment of assumptions, for example, homogeneity of variance and normality of distribution. Some literature says that one can use parametric statistical procedures when the sample size is 'large enough'. What is this size which is 'large enough'? I will appreciate your input. Please provide relevant journal articles. Thank you for reading this question.

I am going to examine the effectiveness of an intervention study. My advisor wants me to use parametric tests when testing the effectiveness of the intervention. Based on the central limit theory, I need to assign more than 30 people to intervention and control groups to be able to use parametric tests. In these circumstances, I must lead at least three intervention groups. Can I take 10 people instead of 30 people in the experimental group and bootstrap to analyze the data using parametric tests?

I have two datasets of equal size and characteristics, I'm looking for metrics to compare these data. I'm using the Python language associated with Pandas and Sklearn.

In general term, Bayesian estimation provides better results than MLE . Is there any situation, Where Maximum Likelihood Estimation (MLE) methods gives better results than Bayesian Estimation Methods?

Hello, I'm struggling to find out which non-parametric test I need to use to compare the VO2 Max scores between physically active women and physically inactive men.

Aka, gender and physical activity are two independent(?) variables. I need a non-parametric test because I ran the data through normality tests and it says it's not normally distributed. I've looked at a Mann-Whitney U test but I don't think it's appropriate as it only lets me select one grouping variable?

Sorry I'm still really new at all this, any help would be appreciated.

Hello,

I have data (size of neuronal soma area for two different mouse genotype) which are lognormally distributed.

In order to be able to use parametrical statistical analysis (ttest, ANOVA,...) I transformed my data with the log() function. Now perfect, the log(data) follow a normal distribution, so I can run my stats.

My problem is now how do I make figure with it?

Should I represent my histogram with the mean of the data, or of the log(data)? How do I calculate the percentage change between my two groups (based on data or log(data))? etc

Because if I represent the log(data) on my graph, the scale should be a logarithmic one, and it is not the more intuitive way to catch up the difference.

But am I authorized to represent the mean and sem of my data, if the statistical test was done on their log()?

Thank you for your help, my coming figures (and my mental health) will gain from it!

Hi all,

Just a quick question. 2 of my groups when compared do not demonstrate normal distrubution (ND), so in order to compare group differences I chose a sign test (previously failed assumptions of ND so cannot run paired t-test or non-parametric wilcoxan-signed rank). The other two groups in which I am looking to compare do show normal distrubution (as will as fulfilling the other assumptions) warranting use of the paired t-test. My question is to what extent can I comment on the results of both tests (as t-test considers means ,whereas sign considers median) in relation to each other ?

Thanks in advance!

Hello,

I'm currently analyzing my survey data for my master thesis and my advisor suggested to do a one-sided t-test. However, I'm not quite sure if I can really do this or if I should use a test of proportion or a binominal probability test?

I had questions with three options (only one could be chosen). Let's say A, B, C. I generated a new variable in Stata, called x. For each subject, let x=0 if he/she answered C. Furthermore, let x=1 if the subject answered A or B. Thus, x is a binary variable, with the mean x_m telling us how many percentage of subjects in the sample did not choose C.

He then said: "Now, we would like to test whether the population mean of x (say, mu_x) is larger than 0.5 (50%). By construction of x, we can employ a one-sided t-test for this (Note that x satisfy the distributional assumptions; if we could keep drawing samples from the population, then x_m would follow a normal distribution with mean mu_x). Thus, you can simply employ a t-test to test whether the mean is significantly larger than 0.5."

Can I really use a one-sided t-test here? How is this data normally distributed?

I'm not sure about the non-parametric options that I could use instead...

What I have found was a one-sample test of proportion. In stata I would then type "prtest x == .5". Another option would be the binominal probability test "bitest x == .5".

I'm quite new to these statistical tests and have never done it. Thank you so much for any help!!

Why is the T-Test the only parametric statistical method that can be used with small samples? Minimum 10 persons

Hi. OK we all know the well used effect size criteria for Pearson correlation coefficents of .1 = small, .3 = medium and .5 = large. However, I've picked up over some time another criteria related to correlations of small = .1, medium = .24 and large = .37. This is largely based on the fact that commonly cited benchmarks for r were intended for use with the biserial correlation rather than  point biserial and that for a point-biserial correlation the .1, .24, .37 criteria correspond more closely to the value for d. Also from reading the Pearson Product moment is of mathematical equivalence to point-biserial. Therefore could one use the .1, .24, .37 as effect size criteria for Pearson product moment correlation coefficients. Or is there something different about the point biserial correlation from Pearson's r  (regardless of the mathematical equivalence) that doesn't allow that criteria to be used.

Hi all,

I've been reading up on parametric survival analysis, especially on accelerated failure time models, and I am having trouble wrapping my head around the family of distributions.

I am aware that there are the exponential/weibull/log-normal/log-logistic distributions. But what I can't seem to find a clear and consistent answer on is which of the following is the one that is actually assumed to follow one of those distributions? Is it the survival time T, the log survival time ln(T), the hazard function h(t), the survival function S(t), or the residuals ε?

Thanks in advance.

I am writing a non-parametric/parametric statistical analysis paper on three Independent data sets. (Human Development Index, Gini Index, US Aid) for 10 countries, annually over the last 10 years. I want to find out whether the Gini index can be described as a predictor for the country's Human Development, and whether US Aid impacts this.

I want to know which tests I should conduct to find an inference for my data.

It's a weighted least-squares polynomial regression, so it's based on assuming normal errors, and the normal probability model is parametric. However, in some statistics book and online statistics resources lo(w)ess is often termed a non-parametric method, and in some software (e.g. in STATA), lo(w)ess is found under "non-parametric analyses". I think this is wrong, as "(non-)parametric" refers to the probability model, not to the functional model (describing the relationship between the expectation of the response depending on the predictors). What do the experts say?

I'm wondering what test to use.

I have 9 IVs and 1 repeated DV (measured twice). The 9 IVs measure different aspects of identity, and include 2 composite scales and 7 subscales between them.

Initially, I had intended to median split each IV and conduct 2x2 mixed ANOVAs, i.e. High vs. Low IV on the DV. The issue is the inflation of Type 1 error (I hadn't factored that in when designing the experiment).

Is there another test that could include all IVs that wouldn't inflate the error rate?

Dear to whom it may concern,

I would like to ask people who are interested in univariate analysis in metabolomics. Now, I am proceeding my metabolomics data using univariare analysis, namely p-values and FDR-adjusted p-values.

However, as far as I know, the calculation of a p-value for each feature depends on two factors: (a) distribution of each feature and (b) variance of each feature between case and control group. To be more specific, the first step is that we need to apply a statistical tool (I do not know which tool can help me to check this issue) to check whether one examined feature is normally distributed in both these groups or in only one of them, and of course, there are two scenarios as follows:

1. If this feature is normally distributed in both these group, we proceed to use F-test as a parametric test to check whether the variance of this feature in both these groups is equal or unequal. If it is equal, we can do a t-test assuming equal variance, otherwise, a t-test with unequal variance must be taken into account.

2. If not, a non-parametric test will be applied to obtain a p-value for this feature. In this case, may you please show me which tests are considered as non-parametric tests?

I am unsure that what I mention above is right because I am a beginner in metabolomics. In case, this procedure is right, that means that each feature will be processed under this step by step one to obtain a p-value because all features are expressed differently in the distribution and variance way between these groups (case and control).

I hope that you may spend a little time correcting my idea and give me some suggestions in this promising field.

Thank you so much.

Pham Quynh Khoa.

Hi there,

I am carrying out a study on factors affecting electric vehicle adoption. I am using a likert scale format (from strongly disagree to strongly agree) for all of the predictor variable such as price or range anxiety and then a continuous dependent variable (the likelihood they believe they will adopt EVs).

I would assume to treat it strictly as ordinal and non-parametric but I have seen some sources say you can use parametric tests if your DV is continuous.

I have to bear in mind i am doing a second regression analysis where I add in demographic variables on top of predictors . Could anyone assist me with what is preferred in statistics in my case?

Thank you in advance

Hello,

I have the challenging issue that many meta-analyses are having since I have my data on advertisement-level instead of user-level. This means that my sample size is small (11) but each observation has over a milliion impressions. The data is averaged of all of these impressions. I have tried using non-parametric analysis, like Spearman Rho, but lately I have been trying to weight my cases.

When cases are weighted, the sample size suddenly is increased to 30K. When running analyses, should I use non-parametric statistics since my data originally is non normally distributed, or can I use parametric statistics since my sample size is large enough?

I would like to hear your opinions.

Thanks in advance

Any advice would be welcome regarding where I can look to formulate my argument regarding this point. I know there is debate around Likert scales being used in parametrig testing, is it likely that this belief is the rationale for the the use of parametric tests in this scenario?? Thank you in advance.

Suppose that my sample size is greater than 30. However, it does not follow a normal distribution. Should I use a parametric statistical test or a non-parametric statistical test?

Definition and examples, please.

IF I HAVE A METRIC AND NON NORMAL DATA (SHAPIRO-WALK TEST <.001), CAN I USE PARAMETRIC STSTISTICS WITH A RELATIVELY LARGE DATASET (N=144).

There are three groups from different professions. Data is not normal. Since ANOVA comes under the category of parametric statistics, this can not be applied. What to do now?

In most research works, the word parametric analysis have been used for correlation between two variables. Whereas the variables could have failed in test of normality and homogeneity, can it also be called parametric analysis?

if the normality test and associated parametric assumptions are not fulfilled, should bi-variant analysis be termed as parametric?

Some scholars , especially that have psychology backgroung argue that likert type scales are interval scales so that we can use parametric statistics. Some other scholars argue that likert type scales are ordinal scales so that we cannot use parametric ones. I want scholars to clarify this issue to have clear understanding and application in my research endeavours? I thank you in advance for your suggestions!

I opted for non-parametric test because the data is skewed and I have varying number of data in each group (90-400).

From reading, it seems to me that there is no hard rule on such situation. Some statisticians advocate the usage of parametric tests, stating that the skewness of the data will be minimised due to large sample size. Some advised to go with the Wilcoxon test anyways, and that the maximum size of 20 is just a rule of thumb.

Can anyone please advise me? Thank you very much!

I have one variable (out of six) that doesn't adhere to the assumption of homogeneity of variance for ANOVA. I don't really want to perform data transformation. Is there any way around this? I am performing 2-way ANOVA and don't know of a good non-parametric equivalent.

Hi everyone, was wondering if I could drop a query to all of the statisticians out there?

I'm comparing gene expression of biomarkers between control and treated samples, most of my data was nonparametric so I have log transformed the values so as to induce normal distribution. Despite this, there are a few instances where one of my groups ( either control or treated) holds normally distributed data, but the other group will show nonparametric data; despite log transformation. I have also transformed using square root, squared and inverse values, but have found logging values usually giving the best results.

I was wondering what statistical test would normally be used in situations like this?

Many thanks in advance and I look forward to hearing from you.

I found someone say:

"There are few consequences associated with a violation of the normality assumption, as it does not contribute to bias or inefficiency in regression models.  It is only important for the calculation of p values for significance testing, but this is only a consideration when the sample size is very small.  When the sample size is sufficiently large (>200), the normality assumption is not needed at all as the Central Limit Theorem ensures that the distribution of disturbance term will approximate normality."

Is this true, so could i say that if my sample size larger than 200 then normality assumption is not needed??!!

I am comparing 2 variables both of which were answered using a likert scale type questions. I was considering doing a Mann Whitney U and a Chi square? Is it worth doing them both?

The plasma potassium concentration in general healthy population is in a range of 3.5-5.5 mmol/L. If it is assumed that plasma K fit into a normal distribution, based on the data that presented the mean and std of plasma K from a sampling, what methods or formulars can I take to calculate the sample size by which the data collected satisfies with the normal distribution?

I had a data sample. I used the Shapiro-Wilk test for normality. But, now, I have a doubt. Can one always use the Shapiro-Wilk test? Should I have use other tests? How can you understand what test you have to use? What are the vantages and advantages of each test for normality?

Drug Abuse Screening Test -20 are answered with No and Yes and is coded with 0,1 called dichotomous but as a whole scale this scale has also been classified like ordinal scale i.e. Low drug abused 1-5 scores, Intermediate drug abused 6-10 scores, Substantial drug abused 11-15 scores, Severe drug abused 16-20 scores but again this was converted into as a whole scale as Likert Scale.Can we consider it interval scale and consider it for Parametric Statistics.

-should I interpret them whatever the loadings are? if yes, what will be the interpretation?

-If I need to do treatments? if yes, please suggest what should be done ?

Murphy et al. described in their article that they made two special regressors by convolution of time and dispersion derivatives with time series of pupil size.

I know that we get canonical HRF using SPM function "spm_hrf". But, I don't know how we get temporal and dispersion derivatives to convolve these derivatives with a certain time series like pupil size.

How do we get temporal and dispersion derivatives on SPM?

Establishment of Reference Values is a very important aspect of Diagnostic Research. I want to know the minimum sample size required when data is parametric or non-parametric. 

In Teitz Text of Clinical Chemistry 120 is the minimum sample size given for Non-Parametric data but statisticians do not agree and say it is very small. Unfortunately they do not give their own formulae, so our projects are delayed.

Prof Aamir Ijaz, FCPS, FRCP (edin)

HOD Chemical Pathology and Endocrinology, AFIP Rawalpindi Pakistan

I am trying to conduct a meta-analysis using the difference in mean change between intervention and control groups.  I have one study with data on mean (SD) for baseline, after and change in both intervention and control groups. Therefore, I want to calculate the mean change and its corresponding standard deviation to be used in meta-analysis; for this, I will need to use the paper which reported the mean and standard deviation values for baseline, after and change to calculate the correlation r and use it to calculate the mean (SD) for change for other papers. Is it valid to calculate correlation r for just one study and use it for all other studies included in meta-analysis? If no, how many papers are reasonable?

I have a matrix with species as columns and sites as rows and it contains counts of individuals per site per species. It was suggested that due to the high variability in counts (they go from 0 to ~3000), I should transform my matrix. Basically, I am doing multivariate statistics to find differences in community compositions among bioregions.

My knowledge of stats is by no means great, but I do know transformations are used to normalize your data and perform parametric statistical analyses, and you can check if the transformation applied does this by doing a test (e.g., Shapiro-Wilks). But, this is different to what I want to do and I don't understand why and when transformations should be applied to your data and how do I decide that the transformation chosen is the correct one or most suited for my data and research question. Is there like a rule of thumb for the application of transformations (e.g., if the SD is over 2 or the counts vary by more than two orders of magnitude, etc. the data should be transformed)?

I have not been able to find information about this, so I would really appreciate your help.

Thanks!

This question is in the context of aproach paramétric to analyse the data obtained in a experimental study.

- Sample Size = 134

- Shapiro Wilk Statistics all >.90, but also statistically significant.

- LOG10 transformation --> still not-normal distributed

My PhD thesis contain a cross-culture research between two nationalities witch requires me to standardized my data to avoid the issue of responses type a cross-cultures for that i did the Z-score to standardized my data in Spss. So my question is: is it right to run T-test and Correlations directly to the standardized data or is it just for raw data?

Under what circumstances may parametric tests be used for non-normal data?

Please provide article or texts I may review to substantiate your response.

I am doing some literature review on non parametric regression techniques.

I would like to ask those familiar with the topic if you may know the disadvantages and advantages of ANNs compared to other non parametric regression techniques like :

- MARS (Multiple Adaptive Regression Spline)

- Projection Pursuit Regression

- Gaussion Process Models (?)

- Additive Models

Is There Anyone who has a comparative literature on it?

Your Contribution will be of great help.

I'm going to use Pearson's correlation coefficient in order to investigate some correlations in my study. I've tested my data and I'm pretty sure that the distribution of my data is non-normal. My data are the cumulative incidence cases of a particular disease in 50 wards. Can I use Pearson's coefficient or not? (Link me to references if there be.)

Kindly, How to use maximum likelihood method or any other method to parametrize a mathematical model to discuss risk analysis?

If you are given a parametric surface, possibly non smooth, what is the best way of finding its global minimum with related matlab commands?

I have seen researchers use Pearson's correlation coefficient (r) or coefficient of determination to evaluate performance of developed models. So what is the difference between them? 

Can the Pain Intensity Numerical Rating Scale be treated as an interval scale to use a parametric statistical analysis such as ANOVA?

I have carried out impedance spectroscopy of my sample in the temperature range of 303-373 k, in complex impedance spectra I try to feet my data with using equivalent R-C circuit and evaluating the value of R and C. All the nyquist plot consist of 3 depressed semi-circle from higher to lower frequencies. So first circle at higher frequency I assigned as a bulk resistance and bulk capacitance. generally the value of bulk resistance is decreased with  increase in temperature but in my case the bulk resistance gives random value for different temperature. so what are the reasons for such type of behavior. My nyquist plots also consist series resistance.

If we have an experimental design with control and experimental group, and we run a normality test (i.e., Kolmogorov-Smirnov) for each group and it show that one group has a normal distribution and the other has not. Should we use a parametric test or non-parametric test?

Thank you

Which different methods are used for parametric optimization of EDM? Which is the best suited?

What is the advantages, limitations and difference between different methods of optimization of EDM like taguchi, regression analysis, genetic algorithm, gauss elimination, ANOVA etc...

I have come across many articles where gender has been used as a moderating variable or as a control variable in the model applying multiple regression (standard/step-wise) and gender has been coded as 1,2. one of the assumptions of parametric statistics like Pearson Correlation or regression analysis is having data on continuous scale/interval scale. How to justify including gender and coding it as 1,2 in the model.

I want to compare data from four independent groups (as part of a three-way ANOVA in SPSS). The data are not normally distributed, so I want to apply a transformation so that I can run parametric statistical tests. However, some groups are skewed positively and some negatively. As there are different transformations for different issues, I could apply the relevant transformation, but then I wouldn't be able to compare the groups.

Should I transform it, or should I simply run the ANOVAs and report on the violations? Or should I not transform it and run non-parametric tests?

I have a sample (n=30) of surveys which were completed pre and post a training day. All people involved in the training day completed the questions pre training on a 5 point (strongly disagree to strongly agree) scale. They then completed the same questions post training. 

Can i use a parametric statistic (paired samples t test), or should i use a non parametric alternative (Wilcox signed rank test)? Or something completely different???

Thanks

Hi everyone,

I want to do a survey research on the cosmetics companies in Malaysia,and using parametric method to analyze data. Unfortunately, the number of cosmetics companies is less than 20 so my total target population is less than 20. How to sample?and  what is appropriate sampling method to used?do i have to change my research design from quantitative to qualitative?

We have two techniques/methods/algorithms. One produces results that follow normal distribution; however, distribution of the results of the other is not known. If we want to arrive at some conclusion on performance comparison, whether two systems are same, different, or one is better than other, which statistic-test or sequence of statistic-tests need to be performed?

Is there any  study (references) about estimating the scale parameter of Laplace distribution with assuming that, the Location parameter is unknown?. Any good references/sources to have a look please? Many thanks in advance for any help.

 

Hello. I´m looking for a paper using this statistical test: canonical correlation analysis with optimal scaling. I perform this test in SAS and SPSS and i get different kind of result.

And another question for SAS users or in the sense of parametric statistic. Are variable on Likert scale useful to do such analysis and can it be mixed with variable on ratio scale

I welcome any paper with those types of analysis... REGARDS

In inferenctial statistics we consider the significance result if the statistical test value (e.g t stat.) is above the critical value, why in non-parametric test, the value supposed to be below the critical value to be considered significant?

Many statistical textbooks state that parametric significance tests require a normal distribution of the samples' data points.

Norman and Streiner write: "It seems that most people who have taken a stats course forget [a] basic idea when they start to worry about when to use parametric statistics such as t tests. Although it is true that parametric statistics hang on the idea of a normal distribution, all we need is a normal distribution of the means, not of the original data." (My italics.) (Norman GR, Streiner DL (2003) PDQ Statistics, 3rd ed., BC Becker Inc., Hamilton, London.)

I am not enough of a mathematician to verify this statement. What are your thoughts?

I am trying to perform a mixed ANOVA to compare the effects of two teaching methods on a group of students at three different points in time. I have read that parametric tests must not be used on ordinal data. However, after testing my variables using Shapiro-Wilk test, all of them meet the criteria for a normal distribution.

Would I concur in a methodological mistake if I performed a Mixed ANOVA?

The model is y_i = x_i'*beta + n_i'*f+epsilon_i, where beta is the parametric coefficient regression of vaiables X1,..., Xp; f is the functional form of the nonparametric curve (an spline); and epsilon_i is the error term.

Hi everyone. I've run the Wald test for zero interactions and found out that there is an interaction effect in my regression model. Then, I tested my model for Multicollinarity using VIF and found that those variables with interaction terms have a high VIF > 10. So, I'm wondering should I take out these variables (assuming that there is no interaction effect, which by the way would mean that there are omitted variables in my regression). Any suggestions on this will be greatly appreciated.

Thanks

What are the best methods to analyse nominal, ordinal, interval, and ratio data in Life Sciences / Agricultural Sciences with reference to  Non-parametric & parametric tests?

Do you've a taxonomic illustration for statistical analytic methods according to type of data, Parametric/Non-parametric, Uni-variate/Multivariate tests.

Sample is attached.

Need explanation with simple example.

I am trying to find statistical differences between two lists of values, where the 1st list is smaller and generally shows Gaussian distribution and the 2nd list is much larger and generally non-parametric. Is it still appropriate to use the Mann Whitney U test here?

Secondly, Can you use the Mann Whitney U test on Parametric data? In some cases I have two lists which are both Gaussian, but as most of my data is non-parametric, is it okay to use Mann Whitney (for consistency)?

What is the difference between parametric and non parametric research?

Definition and examples, please.

I'm looking for references which nicely explain something like "evolution of regression analysis from SLR (Simple Linear Regression) to NPR (Non-Parametric Regression)".

Please let me know your suggestions.

The distribution of values in the samples should provide a good estimate of the population distribution. If this is skewed we are often told to avoid using parametric statistics. However, doesn't the central limit theorem (CLT) contradict this? The central limit theorem states that provided the samples are not tiny, the sampling distribution will always be normal even if the population distribution (estimated by the distribution within the study sample) is skewed. Hence it seems wrong to not use parametric statistics, which are, of course, carried out on the (normal) sampling distribution.

Normality test may be easier to establish in ideal conditions but in real life working conditions, say in industrial-type organizations, such a test does face some challenges. Data collection for my study is based on stratified sampling i.e closeness of fit to the population. If the respondents do not have much time, nor do they have every opportunity to be to be sampled, it could be more practical to pre-select the respondents due to their availablility. Under such conditions, the results of a normality test could be less than 0.05 and the data may not be normal. Could this be accepted or should countermeasures be carried out? Are there exceptions for not carrying out normality tests or how could this problem be addressed to meet the 0.05 requirement? E.g. transform the data, parametric test? What are your views?