Hi

First thing why not t test why anova ?

Every time you conduct a t-test there is a chance that you will make a Type I error. This error is usually 5%. By running two t-tests on the same data you will have increased your chance of "making a mistake" to 10%. The formula for determining the new error rate for multiple t-tests is not as simple as multiplying 5% by the number of tests. However, if you are only making a few multiple comparisons, the results are very similar if you do. As such, three t-tests would be 15% (actually, 14.3%) and so on. These are unacceptable errors. An ANOVA controls for these errors so that the Type I error remains at 5% and you can be more confident that any statistically significant result you find is not just running lots of tests.

next your question is how to check 

1) The one-way ANOVA is considered a robust test against the normality assumption. This means that it tolerates violations to its normality assumption rather well. As regards the normality of group data, the one-way ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate. However, platykurtosis can have a profound effect when your group sizes are small. This leaves you with two options: (1) transform your data using various algorithms so that the shape of your distributions become normally distributed or (2) choose the nonparametric Kruskal-Wallis H Test which does not require the assumption of normality.

so you can check the normality by shapiro wilk test or by Kolmogorov-smirnov test.

2) There are two tests that you can run that are applicable when the assumption of homogeneity of variances has been violated: (1) Welch or (2) Brown and Forsythe test.

So first try to use parametric test , by making your data normal if it is not.

But still if you found that it can't be converted into normal then go for Non parametric alternative i.e. Kruskal-Wallis H Test.

I hope this helps.

Thanks

Hi

Anova is just the extension of t test, because t test is for comparison of two groups only and anova is used when we are going to compare the means of more than 2 groups.

So, in this case anova is applicable not t test. or you can pairwise compare the groups also, to see which groups are statistically significantly different.

But before applying anova, just check the normality condition and equality of variances which are the assumoptions of anova.

If that will not be fulfilled go for the Non-parametric alternative.

i hope it helps. Thanks

Hi Ravi,

thank you so much for your answer. How can I check the  normality condition and equality of variances?

Thank you again.

Hi

First thing why not t test why anova ?

Every time you conduct a t-test there is a chance that you will make a Type I error. This error is usually 5%. By running two t-tests on the same data you will have increased your chance of "making a mistake" to 10%. The formula for determining the new error rate for multiple t-tests is not as simple as multiplying 5% by the number of tests. However, if you are only making a few multiple comparisons, the results are very similar if you do. As such, three t-tests would be 15% (actually, 14.3%) and so on. These are unacceptable errors. An ANOVA controls for these errors so that the Type I error remains at 5% and you can be more confident that any statistically significant result you find is not just running lots of tests.

next your question is how to check 

1) The one-way ANOVA is considered a robust test against the normality assumption. This means that it tolerates violations to its normality assumption rather well. As regards the normality of group data, the one-way ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate. However, platykurtosis can have a profound effect when your group sizes are small. This leaves you with two options: (1) transform your data using various algorithms so that the shape of your distributions become normally distributed or (2) choose the nonparametric Kruskal-Wallis H Test which does not require the assumption of normality.

so you can check the normality by shapiro wilk test or by Kolmogorov-smirnov test.

2) There are two tests that you can run that are applicable when the assumption of homogeneity of variances has been violated: (1) Welch or (2) Brown and Forsythe test.

So first try to use parametric test , by making your data normal if it is not.

But still if you found that it can't be converted into normal then go for Non parametric alternative i.e. Kruskal-Wallis H Test.

I hope this helps.

Thanks

@ Silvia Caprari

(reedited after 6 hours)

I would like to understand your problem a little bit more. Can you please explain:

- how many colonies do you have on ONE plate, at least approximtely;

- how many pairs are measured on ONE plate; perhaps - just the closest, but then: what is the rule of choosing the closest pairs?

- what is the distance between two chosen colonies? is this the distance between two closest points of the boundaries?

- is the number of colonies varying in time?

Thanks in advance,

Joachim

Hi, thanks for your help. Answers to your question

-The number of the colonies is quite variable between the replicates. I can count approximately 50-60

-approximately 10 pairs

-yes, it is the distance between two closest points of the boundaries

-yes, the  number varies in time

Hi, Silvia,

Thanks a lot! Now remains the rule of choosing the circa 10 pairs, and  new questions:

- is the substance carrying the antibiotics some kind of gel/liquid filling the whole plate?

- is the antibiotic addd to the plate afer the colonies are already developed? or before and then the bacteria put on the plate?

- how about the standard evolution of one colony - is its size/diameter decreasing/increasing, and shouldn't be the size not taken into the statistical analysis? Especially important, if some bacteria colonies disappear within 3 days!

The question I am asking are important for building an appropriate mathematical model of the evolution of the population(s) of bacteria coloniesl, with the next aim to suggest a statistical algorithm allowing to discover the quantitative impact of the antibiotic. Any standard procedure, not supported by a model in great degree looses the information of detailed measurements.

Of course, if someone needs fastly numerically calculated parameters, then some standard procedure can be OK. But then the core phenomena are obviously missed:(

Best regards, Joachim

Hi Joachim, thank you so much.

- the antibiotic (in solution )has been added to the liquid LB agar before pouring it into the plate. So it is evenly spread in the whole plate

-before, during the plates preparation

 its size/diameter decreases over the time.. I did not consider this, actually. but yes, it might be important to include. The colonies don't disappear after days.

I don't understand the experiment well. Noting that the average distance is different is most likely a result of a different number of colonies... 

You have two aspects that influence the minimum disances:

- the number of colonies and

- the size of the colonies

both can be affected to a different degree by the treatment (antibiotics).

When you measure the minimum difference, you cannot dissect these two things.

There can also be some cluster-effect that determines the distances between colonies. Imagine a gene transfer of survivors that leads to dense clusters of colonies with larger distances between clusters. This is also something your method won't detect (at least not efficiently).

I would think it's more useful to determine three things:

- the center distances of the colonies

- the number of colonies

- the size of the colonies

I would use an image processing software (like JImage) to get that data for the entire plate(s). You could then do some network analysis on the colonies (find clusters, determine the desities etc) and see if this changes due to the treatment.

Under the assumption of a spatially uniform distribution of the colonies, the distances will have an exponential distribution. You can test so test the hypothesis that the colonies are uniformely distributed (the alternative is that there are clusters) by testing the observed distribution against the exponential model.

Observing the plates over several days would add

- the growth rate of the colonies

as another factor in the model. Maybe the groth rate is different in colonies that are in larger clusters etc.

That could be an interesting project, but it will require good data. I am afraid that having 10 distances of a randomly selected subset of colonies won't be enough to tackle interesting questions. But as I said: I don't understand the project well. 

Hi, I attached a picture. Maybe it explains better the experiment. I have one colony of a bacterial species (blue circle) in the middle of the plate. After 24 hours I measure the distances between the edge of this colony and the centre of the satellite colonies grown on the plate (light green circles). This measure is repeated for all the colonies grown.The reason why I am considering the edge of the blue colony is because the growth of satellite colonies is especially due to the bacteria at the edge (according to what I am studying). After 48 hours, I measure the distance between the edge of the blue colony and new satellite colonies grown further (orange colonies) without considering   the light green colonies. After 72 hours, I measure again the distance between the edge of the blue colony and new satellite colonies grown further (red colonies) without considering all the other colonies. However, although the new colonies grown after 48 and 72 hours are further than those at 24 hours, their number diminishes with the time (see the picture). So the distances I can measure at 48 hours and 72 hours are less than 24 hours.  For each concentration of antibiotic tested I have three replicates and the concentrations tested were 4. So, in total 36 plates. I hope the experiment is clearer, Thanks so much

Ok, that's really different to what I thought :)

At the time you measure the distances, the cells that were responsible to build new satellite colonies were not located at the adge of the mother colony, but somewhere inside (the mother colony grew after the satellite grounders have left their mother). So I am still not convinced that the edge-to-edge distance is a good measure.

How can identify the mother colony? Any new colony at d2 can be an offspring of the center colony or of one of the d1 satellite colonies (or of some other tiny colony you missed to see at d1).

I am still not sure about the purpose of that experiment. I would now think that you aim to model the "colony diffusion behaviour"?

Dear Madam,

You have done excellent work on antibiotics concentrations on different plates, measured distances between colonies in three days. chemical point of view please mention the chemical name of antibiotic, it is more useful for study in the formation of satellite colonies related to the chemical structure of antibiotics. in this regard i will help you for development of research work.

with regards 

Dear Rajeshwar, thank you  very much. The antibiotic is the Ampicillin

I worked on ampicillin and published a paper, which is uploading, i wish to improve research work on chemical point of view using quantum chemistry. if you are interested, i will continue collaboration with you.

still i am working on various antibiotics like benzylpenicillin, cephapirin, phenethecillin, methicillin etc. please see

As the distances mesured at each time points,and concentrations might be correlated observations, it will be better to use the statistical method considering it.

So, I suggest to use repeated measured ANOVA, MANOVA or linear mixed effect model.

However, applying these methods, you would better to consider these statistical method should satisfy with  the assumptions such as normality, sphericity...