StatsCast: What is a t-test?

welcome to stats cast the purpose of this series is to explain statistical concepts in a way that is clear and simple even if you don't have any previous experience with stats this video explains the purpose of t-tests how they work and when to use them in another set of videos I'll show you how to use an interpreter test on some popular software programs so what does the t-test do well it's very simple a t-test checks the averages or means of two groups are reliably different that's all it does you may ask well why not just look at the means looking at the means may tell us if there's any difference at all but that doesn't tell us if the difference is reliable for example if you and I both look a coin 100 times and you get heads 52 times and I get heads 49 times does that mean you reliably get more hits than me are you somehow more likely to get heads in the future now there's no real difference it's only chance this leads us to the difference between descriptive and inferential statistics a descriptive statistic only describes the sample we have it doesn't tell us if our results are likely to happen again in contrast a t-test is what we call an inferential statistic inferential statistics don't just describe our sample they tell us what we can expect in new samples that we don't even have inferential statistics allow us to generalize our findings to a whole population beyond the sample that we're testing that can be very powerful let's take an example researchers have developed a new drug they hope will lower cholesterol let's call it D test role they take two groups of people and give the drug to one group for a month that's the treatment condition the other group gets an empty pill that's the control or placebo condition after that month has gone by the researchers measure cholesterol for both groups they find that the control group which didn't receive the drug now has a mean cholesterol score of 36 the treatment group which did receive the drug now has a mean cholesterol score of 34 descriptively these two means are different but does the drug actually work or was this just chance when a similar result happen again with a new sample that's why we need inferential and not just descriptive stats the t-test will tell us how likely this difference is to be reliable or whether it's just due to chance well how does the t-test do this how does it work well I won't go into the full formula but basically it measures the difference between the groups and compares it to the difference within the groups the t-value is just 2 ratio of these two numbers variance between groups over variance within groups a t-value of three into two groups are about three times as different from each other as they are within each other that also means that if groups have wider more scattered scores it will be harder to detect a real difference between the groups and if they had narrow tightly clustered scores you can think of it as the signal-to-noise ratio the signal that's the difference is easier to detect when there's less noise that's the scanner in our example with the cholesterol drug the difference between groups is about two while the difference within the groups is about six two over six gives us a T value of one-third which is not big enough to be reliable based on these results we can't save the drug actually helps lower cholesterol but how do we know if it's big enough each T value has a corresponding p value the p value is the probability that the pattern produced by our data could be produced by random data in other words it tells us whether the difference between our groups is real or if it's just a fluke so a p-value of 0.05 means there's only a 5% chance we would get these results with random data a p-value of 0.01 means there's only a 1% chance we would get these results with random data while point 1 means there's a 10% chance in most research the cutoff for what we consider reliable or a statistically significant is a p-value of 0.05 or below the exact p-value associated with the t-value depends on how many people are in your sample bigger samples make it easier to find statistically significant differences for example with two groups of five a t-value of 2 has a p-value of 0.05 when you increase the sample size to two groups of 10 that same T value of 2 now has a p-value of 0.03 bigger samples are helpful but the benefit diminishes as the sample size increases a good guideline is to try and have at least 20 to 30 data points in each group if your sample is too small you may not have the statistical power to detect differences that really are their sample sizes represented through number called degrees of freedom for T tests the DF is the sample size minus 1 there are three main types of t-test the independent samples prepared samples and the one sample test the most common type is the independent samples t-test this is when you have two different groups you want to compare our cholesterol experiment is an example this type of test let's take another example t-test were first developed in the early 1900's to check for differences in quality and batches of Guinness beer that's another example of an independent samples t-test if you need to test two different groups this is the test you need just to make things confusing there are a few different names other than independent samples t-test they're also called between samples or unpaired samples t-test however they all mean the same thing another type of t-test is the paired-samples t-test this is we have one group that is measured at two different times for example we could test the quality control team at Guinness and test their balance before and after they test their batches of beer in a paired samples t-test each score is paired with another score usually because the measurements come from the same subject this is different from an independent sample t-test where scores between groups are not related this pairing gives us more statistical power as it reduces possible variability between subjects however it's also susceptible to ordering effects again paired samples t-tests have a few different names they're also called within subjects repeated measures or dependent samples t-tests again it all means the same thing the last type of t-test is the one sample t-test this is when we only have one group and we want to compare it to a hypothetical value or a known population mean for example the mean IQ is 100 you could test if your co-workers average IQ differs from that by using a one sample t-test like most stats there are some limitations that go a t-test first you can only generalize to a population that resembles your sample if our cholesterol experiment was only tested on adults we can't rightfully say the results also apply to children second your sample and population should be roughly normal in their distribution this means the scores resemble a bell curve around the meet if the distribution is skewed your p-values may be inaccurate thankfully t-test can handle a fair amount of departure from normality before they start to break down third you should have close to the same number of scores in each group comparing a large group to a small group can lead to inaccurate results fourth your data point should be independent of each other that means the outcome on one score should not influence the outcome on another score fifth your data should be at least interval level or close to it this means that one unit of your score is equal to any other unit if you're using ranks like first second third your results may be inaccurate if your data is unruly and breaks some of these rules you do have a few options you can do a Monte Carlo simulation to test whether it is safe to use the t-test you can also use another kind of test instead like a man Whitney you test they can take more abuse but statistically if there was powerful finally let's go for how to read and write a t-test let's go back to our cholesterol example Styles may vary but this is a typical way you may see t-test presented first the name of the test is given then each of the statistical values the T value tells us the size of the difference and the p value tells us if this is reliable if the p value is less than 0.05 and the difference is considered reliable or statistically significant the number in parentheses is the degrees of freedom which is the sample size minus 1 here since the DF is 99 that tells us there were 100 people in the sample finally the mean scores of each group are given in this case there is no significant difference but if there was a significant difference this is how we would write it out when you have a significant difference the means are especially important as they show the reader which group is bigger well that's all for this video in future stats cast videos we'll learn how to do t-test using a computer bye for now and happy computing

Channel: StatsCast

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Keywords: StatsCast, statistics, stats, t-test, t-tests, what is a t-test?, how do t-tests work?, Student's T-test, Statistics (Field Of Study)

Id: 0Pd3dc1GcHc

Length: 9min 56sec (596 seconds)

Published: Sun Aug 22 2010