This is a five-section course as part of a two-course sequence in Research Methods in Psychology. This course deals with experimental methods whereas the other course dealt with descriptive methods.

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From the course by Georgia Institute of Technology

Experimental Research Methods in Psychology

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Georgia Institute of Technology

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This is a five-section course as part of a two-course sequence in Research Methods in Psychology. This course deals with experimental methods whereas the other course dealt with descriptive methods.

From the lesson

Evaluating Causal Claims

- Dr. Anderson D. SmithRegentsâ€™ Professor Emeritus

School of Psychology

Hello. Anderson Smith here. We are talking about ways that we can evaluate

Â a causal claim that there is a difference in

Â the independent variable that is causing a difference in the dependent variable.

Â And often we have to use statistics to do that and we use

Â inferential statistics to tell

Â us whether the manipulation of

Â the independent variable(s) significantly affect(s) the dependent variable(s).

Â So the statistical procedures that we can use is

Â if we get a difference whether that difference is a real difference or not.

Â So we have a difference between the effect of

Â one level of the independent variable and the other level of the independent variable.

Â So we want to know is there really a difference between those two means,

Â and is that difference significant?

Â That is the difference are not the same, they are unequal.

Â But if we see that difference it might be

Â that in fact the difference that we are observing is simply due to chance.

Â That is the two means are really the same

Â significantly not found a difference, they are the same.

Â And that is often called the null hypothesis.

Â So if we want to find out if it is significant or is due to chance.

Â We often use a standard of 5%,

Â that is if it is significant,

Â the probability of getting that difference is < 5%.

Â And if it is due to chance the probability of getting that difference is > 5%.

Â That is an arbitrary standard,

Â that it is a standard that we use.

Â So let's say we have a difference where the difference is > 5%.

Â That could mean there are no difference,

Â that is a null hypothesis. They are equal.

Â The difference that we are observing is not a significant difference,

Â that could mean that but it could also mean that there is a difference,

Â but in fact the means are not the

Â same but we can't find it because we don't have a powerful enough experiment.

Â This is why testing in null hypothesis is very

Â difficult because we have null hypothesis because there really is no difference.

Â Others are different so we just can't detect it because have a sloppy experiment or

Â we don't have enough power in a statistical procedure to really see the difference.

Â Power: Probability of detecting a difference really depends upon sort of

Â the expected relationship whether we expect to have

Â a large difference or a small difference and that means the sample size.

Â We expect to see a small difference.

Â We got to have a much larger sample to see the difference.

Â If we have a big difference then we can have a smaller sample to see the difference.

Â So the number of people that we test really determine the power that we have in

Â detecting the differences of getting that p < 5%.

Â So we have two kinds of error;

Â we have type 2 error,

Â which is the probability of accepting the null hypothesis,

Â that is there is no difference when the difference is really present.

Â And remember, the power that we expect to have is

Â usually the standard is just like the p < 5%.

Â The power needs to be about 0.80 or higher,

Â and again that is a statistical finding which tells us the sample size

Â and expected difference to get

Â what the power of the experiment is detecting the difference.

Â So to achieve a power of 80, for example,

Â if we expected the difference to be large then we need about 52 subjects.

Â If we expect it to be a sort of a medium difference,

Â we need 128 subjects and if we really think it is a small difference

Â but a meaningful one then we have to have 788 subjects.

Â When we look it up in tables from the textbook,

Â in fact these sort of numbers actually come from one of your readings.

Â It is just another way of saying the p that we get,

Â is it powerful enough to really detect the difference?

Â That is we are trying to do in making causal claims.

Â We want to say we believe that

Â this independent verbal manipulation is causing this difference of

Â the dependent variable and that result really depends upon the power of the test.

Â Let's talk about that significance test,

Â the test that tells us whether the p < 5% or > 5%.

Â Is it significant or is it due to chance?

Â Well, if we only have two means that we are comparing,

Â a very simple experiment just one variable and

Â two means we can use this statistic called the t-test which simply

Â tells us whether or not the difference between the two means based on

Â the variability found in the experiment are significantly different or not,

Â less than p < 0.5.

Â If we have more than two means so we are testing maybe

Â more than one variable or more than one mean then would use Analysis of Variance.

Â Again it is a test that we use when we have more than

Â just one comparison to tell us whether there

Â is a difference among any of the means in the experiment.

Â The t Statistic: When we have several comparisons of two means,

Â that is the independent sample t-test

Â and we are just comparing one mean to the other

Â and we have to also understand is it one-tail test or two-tail test?

Â We have two means.

Â Now, is it possible that this mean is higher than the other mean?

Â And that is the only direction that can occur.

Â Or is it possible that the test can be higher or be lower?

Â That is a two-tail test.

Â So we want to know whether it is significantly lower or significantly

Â higher in the same test that is two-tail.

Â If we know the difference has to be in one way,

Â that is a one-tail test.

Â So, what do we need to do to have this kind of test?

Â We need two sample means,

Â we need to have an estimates of variance or two standard deviations and we need to

Â have a sample size which is determined by how big do we expect the difference to be.

Â So a t-test is really this formula.

Â It's the difference between the two means divided by the variance which is the square of

Â the standard deviation divided by

Â the number of subjects we have in

Â the square root because it is variance standard deviation,

Â a squared, so we take a square root of that and that gives us the t which is the test.

Â And when you look that up in the statistics table and

Â tell us whether that t with that degrees of

Â freedom that in size really is powerful enough to give us a significant difference.

Â Let's use an example. This is an example again

Â from the texts how psychologists want to know if

Â calorie estimation for people that eat

Â junk food is different from people to eat non-junk food, healthy food.

Â Is the calorie estimation different?

Â Are we good at estimating the number of calories?

Â So here is the results from the junk food eaters, eight of them,

Â they guessed that the food that is in front of me in a picture is 180 calories,

Â 220 calories, 150, 85, 200.

Â So different estimates, different guesstimates I should say

Â made by the people that eat junk food of

Â the number of calories in that food group that is shown in the picture.

Â The non-junk food eaters have this estimates,

Â we only have seven of those.

Â So within the t-tests,

Â we take the difference of

Â the two means and we divide it by the standard deviation squared,

Â divided by the n,

Â n of 8, n of 7.

Â Then we look up the t-test that result is 2.42,

Â then we can look that up in a table that you can

Â find on the internet a t-test calculator or you can find it in

Â any statistics textbook and you look

Â up t-score of 2.42 that is the t score of that comparison.

Â Degrees of freedom it is 1 minus the degrees of freedom so (8-1) + (7-1)=13.

Â And we know it is a two-tail test because we believe that

Â the junk food is a going to estimate more calories or estimate

Â less calories and we get a p=0.0306 and that is less than 0.05.

Â So our different between the two means is significant, there is a difference,

Â they are not equal and we can talk about that

Â there is a causal relationship between junk food eaters,

Â independent variable and non-junk eaters and

Â their estimation of calories of dependent variable.

Â If we have more than two means,

Â we have to use an Analysis of Variance which is a much more complicated statistic.

Â And in fact, even though it is used when we had more than two means it

Â really is based on lots of different designs.

Â What we are testing is that the null hypothesis where all the means are

Â equal and expectation is going to be differences in the means,

Â that all the means are not equal.

Â And that test unlike the t-test is called The F distribution so is an F-test.

Â So the statistic we are looking for is an F. Then we can look at F value given

Â the degrees of freedom up in a table or on the internet and come up with a p,

Â the F statistics that is significant at p < 0.05.

Â As I said there are different tests for different kinds of designs.

Â But basically what you are doing in

Â all Analysis of Variance designs is you are

Â getting a computation of the variance between groups,

Â the variability between the groups that you are studying and the variance within groups

Â that is within a single group and then you

Â comparing that as a ratio and that gives you the F statistic.

Â I am not going into details about the statistics,

Â this is not a statistics course but I want to point

Â out that they are statistics that tell us that there are differences,

Â influential statistics there are differences among the means.

Â And just like t,

Â F tables can be used to determine the p for that particular experiment.

Â As I mentioned, there are many different Analysis of Variance

Â used to repeated measures design,

Â used for factorial designs but they all have

Â that same common way of looking at significant differences.

Â Analysis of Variance will only tell us that the means are different.

Â It won't tell us what means are different,

Â what other means and so we have to use

Â something called multiple comparison tests or post-hoc tests,

Â which didn't tell us any individual mean Analysis of Variance is different from

Â any other individual mean and that is often what we

Â have to do when we have multiple variables for example.

Â So, statistics used to analyze the design.

Â The data analysis are used to come up with

Â whether or not the inferences that we are making

Â about relationships between variables are significant.

Â And then the interpretations and conclusions are based on this analysis,

Â A is better than B,

Â that means we have done a test to show that in fact

Â the probability of getting A better than B in our experiment is < 5%.

Â In the next fed back into the research literature which then allows us to

Â increase body of knowledge about the relationship that we are interested in research.

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