Advanced Statistics - Science topic

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Hi Abraham,

I think this has been previously adressed in various epi oriented papers.

A good reference and tutorial to do it on several software is:

Genders TS, Spronk S, Stijnen T, Steyerberg EW, Lesaffre E, Hunink MG. Methods for calculating sensitivity and specificity of clustered data: a tutorial. Radiology. 2012 Dec;265(3):910-6. doi: 10.1148/radiol.12120509. Epub 2012 Oct 23. PMID: 23093680.

I hope this helps!

Depending on the structure of the data (how much pre-processing has been already done), I would be ready to conduct the meta-analysis as well. Please feel free to reach out by PM.

You can see www.Stats4Edu.com

Carlos Parra-López this sounds interesting. I'm interested, but if you like, we can have a preliminary discussion earlier.

The assumption on normality only matters for a model with normally (Gaussian) distributed errors (LMM). Meaning the residuals of the model are from your side to approximate normality and this assumption is reasonable. Assuming that you use the word GLMM, you have selected a model with a different distribution and link function? If these words sound like gibberish, it might provide some help to search the terminology I just used or find a few introductory articles or books. Best

Ravisha Jayawickrama dont thank , but chatGPT, you could have gotten the same answer yourself.

As the temperature range is too extreme to use an external reference source to test your measurement system, the next best thing is to simulate thermocouple response.

There is data available on relationship between temperature and voltage for the different thermocouple types. A standard multi-calibrator tool can generate voltages to simulate specific temperatures. Simply disconnect the thermocouple, simulate the thermocouples response to temperature using the multi-calibrator and compare your read out to the expected value.

As thermocouple responses tend to be curved rather than linear, there may be bigger errors at certain parts of the measurement range depending on how accurately the relationship can be expressed as an equation.

Adnan Majeed Thank you for extensive answer. I am searching for Quantitative Comparison solution. I need to find similarity between shape formed by two curves on one 2D space compared to shape formed by other two curves on second 2D space.

Calculating area between two curves is not a suitable solution as the shape is not taken into consideration.

There is ongoing debate in the scientific community about the validity of p-values in scientific research. Many scientists and statisticians are calling for abandoning statistical significance tests and p-values. The only way to avoid p-hacking is to not use p-values. You should make scientific inference based on some descriptive statistics and your domain knowledge (not p-values).

IYH Dear Vivian Parker

Ch. 19 Muthén, B. Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In D. Kaplan (ed.), Handbook of quantitative methodology for the social sciences. Newbury Park, CA: Sage.

Although this ref do not exclusively concentrate on two-time-point cases, it does contain discussions revolving around multiple latent variables and multiple indicators for those latent constructs. https://users.ugent.be/~wbeyers/workshop/lit/Muthen%202004%20LGMM.pdf

It contains rich content concerning latent growth curve models and elaborates on multivariate implementations.

While conceptually broader, it present crucial components necessary for building and applying two-time-point, multivariate latent change models.

Hi Hsin-Yuan Chen ,

That indeed does seem to be the case. Thank you for your answer!

Check these.

What could your "political inclinations" possibly have to do with the scientific issues discussed on this website?

The precision of a class must be defined by specifications, which define the RMS and the instruments to be used. If there are no specifications, then people involved in such a class get together and decide about the specifications for the class.

The number of digits also characterizes the precision of an instrument. If a theodolite measures an angle with a direct reading of one second, its precision is one second. If you want to test it you measure several times the three angles of a triangle, and you see how much the closing error is.

In any case, you define precision by specifications; you test precision by statistical analysis of measurements of a well-designed experiment.

Check this link.

The pooled standard deviation is a method for estimating a single standard deviation to represent all independent samples or groups in your study when they are assumed to come from populations with a common standard deviation. The pooled standard deviation is the average spread of all data points about their group mean (not the overall mean). It is a weighted average of each group's standard deviation.

Attached is the formula.

Zubaida Abdul Sattar Thanks a lot for sharing detailed information.

You have 1000 replicate measurements from each subjects. These 1000 values are correlated and they should not be analyzed as if they were independent. So your model is wrong and you should identify a more sensible model. Eventually, the test of the difference between your groups should not have more than 98 degrees of freedom (it should have less, since a sensible model will surely include some other parameters than just the tow means). Having 1000 replicate measurements seems an overkill to me if there was no other aspect that should be considered in an analysis (like a change over time, with age, something like that). If there is nothing else that should be considered, the simplest analysis is to average the 1000 values per patient and do a t-test on 2x50 (averaged) values.

If you had a sample of independent thausands of samples per group, estimation would be mor interesting than testing. You should then better interpret the 95% confidence interval of the estimate (biological relevance) rather than the (in this respect silly) fact whether it is just in the positive or in the negative range.

An age-old and widely debated question: there is no univocal and precise answer.

There should be a causal effect of the independent variables on the dependent variable in regression analysis. Primary data gathered through questionnaire for the dependent variable would be influenced by the current happenings while the independent variables based on secondary data was influenced by past or historical happenings. Therefore, there would not true linkages between independent variables and the dependent variable. Therefore, running a regression with both Secondary and primary data in the same model would not give you best outcome.

A mean is a model. It is an assumption that barring other effects every member of a population will exhibit the mean value. Variation about the mean can be normally distributed (i.e., the difference between the model and the real measurements) exhibits an exponentially decreasing frequency that is symmetric on either side of the mean. It can be log-normal, exponential, triangular, uniform, or 'other'. For normal and log-normally distributed error about the mean we can employ parametric tests (e.g., t-test, or F-test) to compare with an assignable probability the difference between one or more populations. These are parametric tests. There are no similar simple tests for the other distributions. These parametric tests also let you set a confidence interval on the model parameters (i.e., the mean +/- t(alpha, df)*std dev). When the model is more complex you can distribute the confidence intervals to all the parameters of the model (e.g., to the slope and intercept of a line). Most non-parametric tests (e.g., Chi-squared, Mann-Whitney, Kolmagorov-Smirnov) require that you bin the error (i.e., create a histogram of the error) to compare two or more populations. The act of binning the data converts the error from a continuous to a discrete distribution. Discrete distributions include Poisson, bi- and multi-nomial distributions, Chi-squared, etc. Ultimately, when comparing two or more models. Creating an ROC curve, ultimately based on true vs. false positives can also be used.

This means that Shital has no idea whether the information and advice in the answer is right or wrong, helpful or misleading. And they don't care.

Discriminant function technique involves the development of selection criteria on a combination of various characters and aids the breeder in indirect selection for genetic improvement in yield. In plant breeding, the selection index refers to a linear combination of characters associated with yield.

Thank you for your reply, David. Best Regards. David Morse

Nonparametric regression techniques, including kernel and local regression, can be used in psychology research. While they may not be as commonly employed as other regression methods in psychology, they can be valuable in certain contexts where the assumptions of parametric regression models may not hold or when researchers are interested in exploring non-linear relationships.

Kernel regression, also known as kernel smoothing or kernel density estimation, is a nonparametric method that estimates the conditional expectation of a dependent variable given an independent variable. It can be particularly useful when the relationship between variables is not expected to be linear and no specific functional form is assumed. Kernel regression uses a kernel function to weight the data points around the target point, producing a smoothed estimate.

Local regression, often referred to as locally weighted scatterplot smoothing (LOWESS) or LOESS, is another nonparametric regression technique that allows for the flexible modeling of relationships. It fits a separate regression model to each data point by giving more weight to nearby points and less weight to distant points. Local regression can capture non-linear patterns and is suitable for situations where the relationship between variables may change across the range of the independent variable.

While there may be less literature specifically focused on the application of kernel regression and local regression in psychology research compared to parametric methods, it does not necessarily mean they are not useful. The choice of regression technique often depends on the specific research question, the nature of the data, and the assumptions that can be reasonably made. Parametric regression models, such as linear regression or generalized linear models, are more commonly used in psychology due to their simplicity and interpretability. However, nonparametric regression techniques can be valuable when exploring complex relationships or when assumptions of parametric models are not met.

It's worth noting that the application of nonparametric regression techniques in psychology research may be influenced by factors such as the availability of specialized software, the familiarity of researchers with these methods, and the specific research traditions within the field. Nonetheless, when appropriate, nonparametric regression approaches can offer valuable insights into relationships that may not be captured by parametric models.

There are several statistical analysis techniques available, and the choice of method depends on various factors such as the type of data, research question, and the hypothesis being tested. Here is a step-by-step guide on how to approach hypothesis testing:

First, to change the reference level You can specify the order of items in categorical array

categorical(A,[1, 2, 3],{'red', 'green', 'blue'}) or

categorical(A,[3, 2, 1],{'blue', 'green', 'red'})

Second, You can specify the correct hypothesis matrix for coefTest function for comparison between every pair of categories.

In the Seurat R package for analyzing single-cell RNA-seq data, "power" and "myAUC" are both functions used for selecting the most informative features or genes in the dataset. However, they employ different approaches and criteria to achieve this.

In summary, the "power" function identifies highly variable genes based on their expression dispersion relative to mean expression, while the "myAUC" function ranks genes based on their ability to discriminate between two predefined groups or conditions using the area under the ROC curve. Both functions aim to identify genes that are potentially important for distinguishing between different cell types, states, or experimental conditions, but they use different statistical and computational approaches to achieve this goal.

Ravisha Jayawickrama

7.7.3.2 Obtaining standard deviations from standard errors and (cochrane.org)

also, there is useful calculator in the attached Excel file from Cochrane.

PSPP has the same look and feel as SPSS but is less good for printed output. But it's free, and there are workarounds to offset its limitations.

At the same time，Collect two variables data,As a sample,After collecting N samples over time,erform data regression analysis on them,The correlation coefficient will be obtained.

It is randomization, if they are the same or different randomization, I see no problem. Regards.

Oh that makes sense, thank you! I only have limited statistics teaching behind me so this has been a struggle.

Go with the test of association (chi-square test )

I've only glanced quickly at those two resources, but are you sure they are addressing the same thing? Yates' (continuity) correction as typically described entails subtraction 0.5 from |O-E| before squaring in the usual equation for Pearson's Chi2. E.g.,

But adding 0.5 to each cell in a 2x2 table is generally done to avoid division by 0 (e.g., when computing an odds ratio), not to correct for continuity (AFAIK). This is what makes me wonder if your two resources are really addressing the same issues. But as I said, I only had time for a very quick glance at each. HTH.

Dear Thuy,

In our last publication, we had the same problem with CCD and the alpha being generating negative values, so I inserted the levels in terms of alphas and it worked perfectly.

You can check our publication

Kind regards

It depends, but first, why did some people not answer some? Were these not presented to them by some random mechanism, or were they the last few (and perhaps easier or harder than others), or did people see them but decide not to answer because they thought they would miss them or it would take to long to answer them, or etc. Second, I am not sure what the three categories means. Is it that they got say 5 items on math, 5 on reading, and 5 on science? or that there were three groups? The choice of statistic will depend on this. Third, what research questions do you have? And finally, Mann-Whitney is usually used for two categories of people (i.e., two groups).

Shubh Yadav Type I and Type II mistakes are both dangerous and, depending on the circumstances, can have catastrophic repercussions.

A Type I mistake, often known as a false positive, happens when a statistical test rejects the null hypothesis yet finds it to be true. This can result in inaccurate inferences and improper actions being done as a result of such findings. A Type I error might arise, for example, if a medical test is meant to identify a certain disease and the test wrongly suggests that a patient has the condition when they do not. This might lead to the patient receiving needless and perhaps hazardous therapy.

A Type II mistake, often known as a false negative, arises when a statistical test fails to reject the null hypothesis despite the fact that the null hypothesis is wrong. This can also lead to erroneous assumptions and improper behaviors. For example, if the same medical test indicated above wrongly suggests that a patient does not have the disease while, in reality, they do, the patient may not receive the appropriate therapy.

Making a Type I error may be more dangerous in some instances, while making a Type II error may be more significant in others. In the end, it is determined by the context and the potential implications of each sort of error.

@ Ravisha Jayawickrama. Most sources accept value for standardised factor loadings above 0.4

A scale reliability of .39 (and even .53!) is very low. Even if your main focus is not on the psychometric properties of your measures, you should still care about those properties. Inadequate reliability and validity can jeopardize your substantive results.

My recommendation would be to examine why you get such a low alpha value. Most importantly, you should first check whether each scale (item set) can be seen as unidimensional (measuring a single factor). This is usually done by running a confirmatory factor analysis (CFA) or item response theory analysis. Unidimensionality is a prerequisite for a meaningful interpretation of Cronbach's alpha (alpha is a composite reliability index for essentially tau-equivalent measures). CFA allows you to test the assumption of unidimensionality/essential tau equivalence and to examine the item loadings.

Also, you can take a look at the item intercorrelations. If some items have low correlations with others, this may indicate that they do not measure the same factor (and/or that they contain a lot of measurement error). Another reason for a low alpha value can be an insufficient number of items.

Yes. You can use the Friedman Test in order to determine the statistical version of significant differences of means within the sessions in a group, if the data is not normally distributed and is of ordinal type.

Selecting the best algorithm for calculating the child nodes from the parent nodes using GeNIe software can depend on several factors, including the specific characteristics of your data, the computational resources available to you, and the desired properties of the resulting model. Some general considerations to keep in mind when choosing an algorithm include:

To help you decide which algorithm is best for your particular needs, you may want to consider consulting documentation or literature on the algorithms available in GeNIe software, as well as experimenting with different algorithms on your data to see which one performs best.

Yes, you can run such a model (with all variables included simultaneously) within the framework of path analysis using programs for structural equation modeling such as Mplus, lavaan (in R), and AMOS. In the free workshop below, I show how to run path analysis in Mplus: https://www.goquantfish.com/courses/path-analysis-with-mplus

You wrote: "For context, one variable is weight, and one is a behaviour score. The groups are receiving various treatment and I want to test if weight change influences the behaviour score differently in each group."

I'm not sure this is best tested with a correlation coefficient. This sounds like an interaction hypothesis (or moderation if you prefer). What you need I think is the interaction of weight change by group. This is usually tested by the regression coefficient for the interaction. You can standardize this to scale it similarly to a correlation coefficient (though that's actually best done outside the model for interactions).

You can compare correlations but that isn't necessarily sensible because you risk confounding the effects of interest with changes in SD of the variables across groups (and there seems no rationale for needing that).

A further complication is including weight change without baseline weight as a covariate might be a poor choice. Even if groups are randomized including baseline weight may increase precision of the estimates of the. other effects.

* Create a toy dataset to illustrate.

NEW FILE.

DATASET CLOSE ALL.

DATA LIST LIST / A B C D E (5F1).

BEGIN DATA

1 0 0 0 0

0 1 0 0 0

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

1 1 0 0 0

0 1 1 0 0

0 0 1 1 0

0 0 0 1 1

1 0 2 0 0

END DATA.

IF A EQ 1 and MIN(B,C,D,E) EQ 0 AND MAX(B,C,D,E) EQ 0 severity = 1.

IF B EQ 1 and MIN(A,C,D,E) EQ 0 AND MAX(A,C,D,E) EQ 0 severity = 2.

IF C EQ 1 and MIN(B,A,D,E) EQ 0 AND MAX(B,A,D,E) EQ 0 severity = 3.

IF D EQ 1 and MIN(B,C,A,E) EQ 0 AND MAX(B,C,A,E) EQ 0 severity = 4.

IF E EQ 1 and MIN(B,C,D,A) EQ 0 AND MAX(B,C,D,A) EQ 0 severity = 5.

FORMATS severity (F1).

LIST.

* End of code.

Q. Is it possible for any of the variables A to E to be missing? If so, what do you want to do in that case?

Ange, I think the easiest way for you to find an answer to your question would be to google something such as "SPSS recode variables YouTube". You'll probably find several sites that demonstrate what you want to do.

All the best with your research.

The "technique" leaves the time it finds.

Have you drawn a representative sample from a population?

Did you submit a structured questionnaire to the sample units?

Good: start analyzing the data that describe the phenomenon you are studying and the rest will come by itself.

for the second part of your problem, you can try vcf2gwas pipeline, that is very easy to run as a docker image

If there aren't too many censored values on the low end (< LLOQ), what precise values these take shouldn't matter much in the analysis. (Or, we shouldn't do an analysis where the precise values of these observations matter much). If there are many < LLOQ values, then you might consider a different analysis.

Just thinking about it, I'm not sure what to do with values censored at the high end (> HLOQ). I would be wary of replacing them some kind of random distribution with no upper limit, since it's possible to get a really high value by chance. I have done analyses where I replaced > HLOQ with just HLOQ; because there weren't that many values, it didn't really affect the overall conclusions.

Section 4.7, VALUES BELOW DETECTION LIMITS, of the following (USEPA, 2000) has some simple advice about values less than the detection limit. They say, if there < 15 % of values below the detection limit, "Replace nondetects with DL/2, DL, or a very small number." They have more involved methods when Non-detects are 15%–50% of observations.

For observations < LLOQ, maybe random values from a uniform distribution would make more sense than from a normal distribution.

As far as I understand your problem, you first need a mathematical relation between the instructions and rank. For instance, Rank x should correspond to some instruction value as y and vice versa; it means you require a mathematical function.

So there are various methods/tools to find a suitable (as accurate as you want) to find mathematical function based on given discrete values like curve fitting methods or the use of ML.

Further, Once you obtain the mathematical function, run your code a few times, and you will get a set for various combinations of (instruction, rank). These set values will work as the feedback for your derived function. Make changes based on the feedback, and you will get a much more accurate function.

I hope you are looking for the same.

Sorry, Jianhing. But I think you have misunderstood something in the lecture. Frequentist statistics, which is an interpretation of probability to be assigned on the basis of many random experiments.

In this setting, on designs functions of the data (also called statistics) which estimate certain quantities from data. For example, the probability p of a coin to land heads is given from n independent trials with the same coin and just counting the fraction of heads. This is then an estimator for the parameter p.

Each estimator should have desirable properties, as unbiasedness, consistency, efficiency and low variance and so on. Not every estimator has these properties. But, in principle one can proof, whether a given estimator has these properties.

So, it is not a characteristics of frequentist statistics, but a property of an individual estimator based on frequentist statistics.

David will likely think this is complete rubbish, but here is what one librarian had to say about Z-Library.

<quote>

So there are outright “We pirate stuff’ sites like Mobilism and ZLibrary. These are places that are basically set up to pirate things and have no veneer of legality to them.

</quote>

Source: https://www.librarian.net/stax/5103/ask-a-librarian-what-is-the-deal-with-free-ebook-sites/

I agree with Yongkang Stanley Huang and Michel Charifzadeh. Because ESG score is not a periodic data ( such as contineous data) rather a score usually provied with symbols such as A, B and C...

اذا اردنا t-teast للفروق بين المجموعتين

او اذا اردنا استخدام معامل الاتبارط بيرسون @

اذا لم نقوم باستعمال الادوات الاحصائية الدقيقية لهذا المجال بالنسبة للمتغيرات البحث سوف يؤدي الى الى اخطاء احصائية في دقة النتائج ولكن ممكن استخدام في بحثين منفصلين كمتغير تابع @

Hi Maria, In general if you have a strong theoretical framework that justifies the decision to include these DVs, then include the DVs. This is your hypothesis. Although you could remove variables based on the p-value, AIC, BIC then you specific hypothesis: nursing duration ~ rank + mothers' age*infants' age + (1| weather) is not addressed. By sequentially removing values based on p>.05 you inflate your error rate and by removing them based on AIC and BIC you are not addressing your hypothesis. If p [of any DV] is not < .05. Then you simply have not obtained enough data to address this as evidence against H0. Then repeat the study with a larger n (never add more data to the study after you see p<.05).

I am in favor of simpler models (in the sense of less DVs, as they are easier to understand and address), although I have created horrible models in the past. I luckily seemed to have learned from this (I hope). Note that your model is not all that complex. Also, I removed mothers' age + infants' age as R considers this automatically using *. And if you run the model consider given the point and interval estimates for future repetition/replication (e.g., using the parameters package https://easystats.github.io/blog/posts/parameters_new_models/).

Good luck.

Useful books are:

https://hastie.su.domains/ISLR2/ISLRv2_website.pdf (only Chapters 1-3 for the basics)

https://www.discoveringstatistics.com/books/dsus/ (not free)

(extremely well written, not free)

(note that any book has it weaknesses and strengths, and you often only use a particular chapter)

---------------------

Some additional useless information. From a Popperian view "simplicity" of the model has it preference (Logic of Scientific Discovery, Chapter 7). He describes simplicity as that the argumentation can be easily rejected, it has to be "testable" (easy to "reject" or "invalidate"). In your case this would be the "complex" model, as any of the assertions made on the DVs in the model: rank + mothers' age*infants' age (which is not a bad thing, it is a good thing!). Note also that Popper did not really tried to define of find the essence of word "simplicity".

It is just coincidental

I suggest using mosaic plots rather than (stacked) barplots to visualize your data.

The chi²- and p-values can be calculated simply via chi²-tests (one for each ABA conc) -- assuming the data are all independent (again, please note that seedlings on the same plate are not independent). If you have no possibility to account for this (using a hierarchical/multilevel/mixed model), you may ignore this in the analysis but then interpret the results more carefully (e.g., use a more stringent level of significance than usual).

A binomial model (including genotype and ABA conc as well as their interaction) would allow you to analyse the difference between genotypes in conjunction with ABA conc. However, due to the given experimental design (only three different conc values) this is cumbersome to interpret (because you cannot establish a meaningful functional relationship between cons and probability of germination).

You should use the model that makes more sense, practically and/or theoretically. A high R² is not in indication for the "goodness" of the model. A higher R² can also mean that the model makes more wrong predictions with a higher precision.

Do not build your model based on observed data. Build your model based on understanding (theory) and the targeted purpose (simple prediction, exptrapolation (e.g. forecast), testing meaningful hypotheses etc.)

Removing a variable from the model changes the meaning of the intercept. The intercepts in the two models have different meanings. They are (very usually) not comparable. The hypothesis tests of the intercepts of the two models test very different hypotheses.

PS: a "non-significant" intercept term just means that the data are not sufficient to statistically distinguish the estimated value (the log odds given all X=0) from 0, what means that you cannot distinguish the probability of the event (given all X=0) from 0.5 (the data are compatible with probabilities larger and lower 0.5). This is rarely a sensible hypothesis to test.

Kishalay Adhikari, you might find some useful information in Chapter 12 of the following book:

Hair, J. F., Babin, B. J., Anderson, R. E., & Black, W. C. (2019). Multivariate data analysis (8th ed.). Cengage.

I think that some of this chapter could have been written a bit more effectively, but overall it is helpful in drawing distinctions between scales and indexes.

All the best with your research.

Marco Marini as far as I know, you must have two conditions both verified for a partial mediation hypothesis to be confirmed:

1 - the indirect effect must be significant (X -> M -> Y) *

2 - the direct effect must be significant (X -> Y)

If both conditions are satisfied, then you have a partial mediation. If condition 1 is satisfied, but not condition 2, then you have a full mediation (i.e., your mediator entirely explains the effect of X over Y).

As Christian Geiser suggested: "Partial mediation simply means that only some of the X --> Y effect is mediated through M".

To my knowledge, the ratio between direct and indirect effect has no role in distinguishing between partial vs. full mediation.

* Please note: "the indirect effect must be significant" doesn't mean that path a and b must both be significant. All you need is path a × b significant (better if bootstrapped).

I think you have answered your question: "It should be noted that when I plot the data, very very few participants chose yes in response to the neutral and positive images. Almost all yes responses were given in response to the negative images."

This is what you'd expect even in a simple 2x2 design. If the probability of a yes response in the positive condition is very high and the probability very low in the negative condition then the OR could be high as its the ratio of a big probability to a very low one.

This isn't unnatural unless the raw probabilities don't reflect this pattern. (There might still be issues but not from what you described).

Hi David Morse,

Thank you very much for your answer. It is really helpful and makes sense.

I do not think I will include these estimated means and SDs in the meta-analysis, but I can definitely report them in the narrative synthesis, as they will add additional evidence (with all the precautions due to the assumptions) to the findings.

Thanks again David, I very much appreciated your help.

Hello Paul,

The first question to address is, how do you characterize the strength/scale of your DVs? Nominal? Ordinal? Interval? The second question is, do you really aim to interpret the results multivariately (that is, for the vector of values on rated competence and rated employability), or is it more likely that your attention will be focused in these individually? If individually, then run univariate analyses, one for each DV; otherwise, go multivariate.

Interval / Multivariate:

Multivariate regression or Manova (either would involve a repeated measures factor having four levels: condition)

Interval / Univariate:

Regression or mixed (two-between, one-within) anova

Ordinal / Univariate:

Ordinal regression or an adaptation of aligned ranks anova

Nominal / univariate (Depends on number of levels of the nominal variable)

Possibly logistic regression (if two levels of DV, such as "Satisfactory/Unsatisfactory")

Good luck with your work.

I made a mistake in my answer. I gave you the information for the COntingency coefficient. For the Cramer V, there is a table of effect size which depend on the degree of freedom of the Cramer V. See: https://www.real-statistics.com/chi-square-and-f-distributions/effect-size-chi-square/

Mr a. D.

The ECT(-1)os always the lagged value of your dependent variable.

Regards