# ***Can you justify a small sample size? My professor says no!***

#### Bdubz

##### New Member
I'm writing my dissertation and my research wasn't accepted because my sample size didn't meet my Committee Chair's desire for a double digit sample size. My research involves black and white students in a math class. There were 20 white students and 2 black. My research was rejected because of the sheer number of black students. I agree that typically this is a good assessment in predicting a confidence level, however I'm no statistician and have no idea how to present a justification. In layman's terms, I'm in Tucson where only 5% of the population is black. The school has a 59% white population (591 students), however only 3.4% of the school's student population is black (34 students). In that class it seems to me that there's actually more of the school's black student population represented in this class than there is white student representation. I have no idea if this actually makes sense statistically or how it could look in running a t-test, it just seems to me that when you have more than 50% of a population represented by a sample that the number's shouldn't defeat the research. My Chair tells me to go back to Fraenkel and come back with different literature to support a different study. How can I communicate this to my committee in an acceptable scholarly way that will make sense to seasoned researchers? My committee is made up of my Dept Head and my course coordinator, so I have to have support for my explaination, but I'm certain I'm right. Please help ASAP!!!!!! Thank you.

#### spunky

##### Doesn't actually exist
Unless you're keeping things at a purely and exclusive descriptive level, I'd also have a very hard time justifying a research design where one of the sub-groups has n=2. ESPECIALLY if one of those groups is one in which you're attempting to posit any kind of inferential claims.

On the other hand, though, there *are* such things as N-of-1 trials so if you're willing to change your design yo accommodate really, really small samples, that *could* potentially work. But it all depends on your research question, your methodology, etc.

#### Dason

I will say that I'm not a huge fan of how you worded all of this. You really should be asking *if* it's correct, what you can do with that data, etc.

It sounds like you aren't an expert in statistics but you still say you are convinced you are correct - why?

#### Bdubz

##### New Member
Unless you're keeping things at a purely and exclusive descriptive level, I'd also have a very hard time justifying a research design where one of the sub-groups has n=2. ESPECIALLY if one of those groups is one in which you're attempting to posit any kind of inferential claims.

On the other hand, though, there *are* such things as N-of-1 trials so if you're willing to change your design yo accommodate really, really small samples, that *could* potentially work. But it all depends on your research question, your methodology, etc.

#### Bdubz

##### New Member
Thank you Spunky. I am not married to my design; and I am seeking to use the student population to demonstrate that there has or has not been improvement since technology became a testing mechanism in the class. So I guess I am making a claim, but the data will only be used to support the claim and not to infer that it is or is not correct. There has been improvement made by both demographics in the class; one demographic just happens to be smaller than the other, but larger now than it was 8 years ago.

I think it's fair to say that initially my premise was to compare then two, however, as part of the revision, I now only need to see whether there has been movement made by both, and in what direction.

#### Bdubz

##### New Member
I will say that I'm not a huge fan of how you worded all of this. You really should be asking *if* it's correct, what you can do with that data, etc.

It sounds like you aren't an expert in statistics but you still say you are convinced you are correct - why?

#### Bdubz

##### New Member
Dason, thanks a bunch for your reply. NOOOO!!! I'm farrrrr from an expert. lol. I think you know that. My wording was very poor if that's what I portrayed. I'm a statistical dunce which is why I'm in this forum with you experts. I'm not convinced I'm correct, not at all...I really don't care to be correct. I simply think that there may be a way to save some research by justifying the small sample size due to the proportion of the population that it represents. I don't even know if I'm saying that right. Initially, I wanted to make a comparison now I want to use the same data to report progress or lack thereof. I just want to know if it's even worth the fight. I don't want to trash months of research because of the sample size. Its a limitation, it's a challenge, But I think that the change in use of the sample may strengthen my position in keeping it. Reporting the trend of a demographic instead of finding a significant difference between one and the other...is there a way to use the data given this shift? If I have to toss the research I will, but I feel that there is a justification...I just want to know if there is and what direction to go in, or who to read. Maybe I just muddied the water more, idk. Thanks again Dason.

#### GretaGarbo

##### Human
I'm writing my dissertation and my research
A dissertation! And it is research. OK!

My research involves black and white students in a math class.
Just because of curiosity, why did you choose that subject?

Don't you think that you could have found a less controversial subject? I am trying to figure out anything that could possibly be more contoversial.

If I have to toss the research I will, but I feel that there is a justification...
So, what is the justification?

#### Bdubz

##### New Member
GretaGarbo, I appreciate your reply. I know there's someone out there that can look at my spill and say, "oh, why don't you read Creswell & etc," or "there was a study that may help you understand your professor's point, look at http://www......?". Nevertheless, I will hopefully resolve your querries. Firstly, Yes, it's a dissertation, and it's research, and I FEEL there's a justification. The entire premise of my post was to see if any reader had any ideas or experience justifying generalizing a small sample to small population. I've received some feedback from another professor that inspired the feeling that there is more to this than meets the eye. I've also read something from some author stating that a sample of size of 5 can be justified, but I've read so many article and books over the past 5 years that I don't remember who it was. Speaking of 5 years, in response to your statement on my research focus. My message to anyone beginning a PhD journey is to do what moves you; do what interests you. Getting a PhD, you may know, I'm not trying to educate you on it, but it's a very long and tedious journey. The vast majority of those who start don't finish. I started with a focus that I knew would help people. Anyone paying 6 figures for an education should not go in avoiding controversy, but confronting insufficiencies with scientific data and research supported answers. I started to finish...my passion to understand more about a phenomenon of interest if the fuel that has gotten me to the finish line. Now I just need a little insight to cross it. GretaGarbo, I do appreciate your response.

#### GretaGarbo

##### Human
The entire premise of my post was to see if any reader had any ideas or experience justifying generalizing a small sample to small population.
I simply think that there may be a way to save some research by justifying the small sample size due to the proportion of the population that it represents.
So you do actually think of your investigation as infering something from a small sample to a population?

How large is the population? The town you live in? USA?

It is not just descriptive data as @spunky said?

Unless you're keeping things at a purely and exclusive descriptive level, I'd also have a very hard time justifying a research design where one of the sub-groups has n=2. ESPECIALLY if one of those groups is one in which you're attempting to posit any kind of inferential claims.

#### spunky

##### Doesn't actually exist
by justifying the small sample size due to the proportion of the population that it represents.
THIS right here is the problem. Although you *could* potentially do something like that, you would need to device a sampling plan, have probability weights and engage in a very careful data-collecting process for which you'd probably need to team up with a survey and sampling expert.

If the data that you have is just the data that you have now and you can't do anything else with it, then you need to be very careful and very mild with the type of claims you can make. For instance this, as stated:

I am seeking to use the student population to demonstrate that there has or has not been improvement since technology became a testing mechanism in the class.
cannot be supported with the data you have. And I think your Committee Chair knows that, just as we know it. If you cannot gather more data then your best bet is to say this is a descriptive, exploratory study where some trends might be suggestive of some conclusions but we don't actually know and people should perhaps spend more time and $$collecting more data in the future to see whether or not you were right. Either that or turning this into a more qualitative inquiry type study are your best bets if more data are not available. #### Bdubz ##### New Member So you do actually think of your investigation as infering something from a small sample to a population? Yes/No. I know that there the small sample infers upon the general population, there're national data to corroborate that, however, the confidence level of the small sample is not acceptable. How large is the population? The town you live in? USA? 600K, Tucson, AZ It is not just descriptive data as @spunky said? You are right...it was gathered for the purpose of inference using a comparative correlation methodology. However, I had actually considered revising my research under a descriptive methodology to save the data and time. I'm reading now to determine how feasible that is. I see now that it would be difficult to use the data, and I'm trying to stay away from increasing the level of difficulty. I greatly appreciate all the feedback that I've received, it's all been very helpful. #### Bdubz ##### New Member THIS right here is the problem. Although you *could* potentially do something like that, you would need to device a sampling plan, have probability weights and engage in a very careful data-collecting process for which you'd probably need to team up with a survey and sampling expert. If the data that you have is just the data that you have now and you can't do anything else with it, then you need to be very careful and very mild with the type of claims you can make. For instance this, as stated: cannot be supported with the data you have. And I think your Committee Chair knows that, just as we know it. If you cannot gather more data then your best bet is to say this is a descriptive, exploratory study where some trends might be suggestive of some conclusions but we don't actually know and people should perhaps spend more time and$$\$ collecting more data in the future to see whether or not you were right.

Either that or turning this into a more qualitative inquiry type study are your best bets if more data are not available.
I agree. Thanks for the suggestion, very helpful.