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P-Values and the null hypothesis…. A very brief explanation of basic statistics. Two delicious studies…. Study A and study B both measure the correlation between in-class rewards and student attentiveness among FLED 104 students.
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P-Values and the null hypothesis… A very brief explanation of basic statistics
Two delicious studies… Study A and study B both measure the correlation between in-class rewards and student attentiveness among FLED 104 students. • In both studies, participants’ regular levels of participation are measured. (How many times do students raise their hands to answer questions in a typical class?) • During the next class, students receive oreos for correct answers. Again, students’ participation levels are measured.
Judging results • Results of study A: 50% more students’ hands went up when oreos were given as rewards than when no oreos were given. • Results of study B: a significantly larger number of students raised their hands when given oreos for correct answers than when they were not given oreos (p <.05). Which study provides more reliable results? Why?
The issues of reliability and probability… • Group A: In the normal class measured, there are four hands raised. In the oreo-as-reward class, six total hands are raised. • WOW!!! We can say that the total improvement here is 50%! • Based on these data, is it possible to generalize the data for all FLED 104 students? Why or why not? What other factor might be at play here?
Issues of reliability and probability… • There are two possible reasons for study A’s results: • There is a real difference between the attentiveness of FLED 104 students + oreos and FLED 104 students without oreos. • There is no difference between the attentiveness of FLED 104 students + oreos and FLED 104 students without oreos…The results are a coincidence of random sampling.
Judging results… • Study B’s results are more reliable than those of study A…. • Study A’s results have the problems you just mentioned…. • A p-value (present in study B’s results) helps to get around these problems… What, then does a p-value probably measure? P-value: the probability that the differences between two samples’ means are actually a result of random sampling…
Probability • A p-value is a number between 0 and 1. • 1=100% probability that differences are coincidental. • 0= 0% probability that differences are coincidental. What, then, does it mean if the results of study B are significant at the value of p< .05? Make this statement in terms of the goals of the given experiment.
The p-value in the context of the null hypothesis… • Hypothesis: Boğaziçi students who study while listening to classical music will receive significantly higher test scores than Boğaziçi students who study while listening to other kinds of music… To show evidence in support of this hypothesis at the level of p<.05, you need to show that B.U. students listening to classical music will outperform their classmates who do not listen to classical music more than ______% of the time if this test were repeated hundreds of times. 95
The p-value in the context of the null hypothesis… • Now re-state the previous directional hypothesis as a null hypothesis…. • To support the null hypothesis, no difference must be seen between classical music listeners and other types of music listeners more than 95% of the time if the study is repeated hundreds of times….
The p-value in the context of the null hypothesis… • Rejecting the null hypothesis… • Based on the previous percentage (+95%) for supporting the null hypothesis, what percentage is needed to reject the null hypothesis? Only +5% of the replications need to show no evidence of the null hypothesis in order to reject it…
The p-value in the context of the null hypothesis… • So, then, based on the previous discussion, why do researchers often choose to implement a null hypothesis instead of directional or non-directional hypotheses? Rejecting a hypothesis requires far less evidence than supporting a hypothesis. Rejecting a null hypothesis is much easier than supporting the directional hypothesis.
New Study: Touching toes • I believe that the ability to touch one’s toes (while one has straight legs) is correlated with gender. • Hypothesis: A significantly larger number of female B.U. FLED students between the ages of 18 and 22 will be able to touch their toes while standing with straight legs than male B.U. FLED students of the same age.
Let’s test the hypothesis… • What is the average for male students? • What is the average for female students? • Is this enough information to draw conclusions? No, we need to test more FLED students to achieve a representative sample. Also, we need more male FLED students so that we can compare them to the females.
So, then, let’s find some more participants! • You have five minutes. Leave the classroom and find some FLED students. Look at their ability to touch their toes while standing with their legs straight. (Look for MALE FLED students especially; we hope their number is the same as the female participants.) • Record: • Name • Gender • Year in the department • Then come back and tell us your findings!
Data analysis • What is the total number of male participants whose hamstring flexibility was analyzed? • Out of them, how many were able to touch their toes? • What is the total number of female participants whose flexibility was analyzed? • Out of them, how many were able to touch their toes?
The question of significance • From the averages found earlier, calculate the percentage of difference between the two groups’ scores. • Can we say that this difference is significant? Why or why not? No, we cannot say that it’s significant because no statistics have been used.
Then let’s apply statistics. • Why do we use statistics? To look at the reliability of the given results…. For a given result to be significant, similar results have to appear over hundreds of tests of the same hypothesis. This means that we have to perform this test over and over again, but we have no time for this. Statistics simulate hundreds of replication studies.
The numbers • If I actually did this test hundreds of times, what percentage of the time would I have to find a difference between males and females for it to be significant? Over 95% of the time is the p-value is set to p<.05
The numbers… • This hypothesis would definitely be rejected if this result occurred what percentage of the time? More than five percent of the time. 100%-95% = 5%
Partner Work • What is the null hypothesis of the early hypothesis? • How many times is it necessary to show a difference, so that it’s possible to reject the null hypothesis? There will be no correlation between gender and FLED 104 students’ ability to touch their toes while they are standing with straight legs. Over 5% of the time, p>.05 (to be able to show that the p-value will not be able to reach 95% or above) In this way, it is far easier to reject a null hypothesis than to support a directional hypothesis.
