complete the word document. I have attached a statistics PDF as a resource.
Starting Statistics: A Short, Clear Guide Introducing Hypothesis Testing In: Starting Statistics: A Short, Clear Guide By: Neil Burdess Pub. Date: 2013 Access Date: May 18, 2021 Publishing Company: SAGE Publications Ltd City: London Print ISBN: 9781849200981 Online ISBN: 9781446287873 DOI: https://dx.doi.org/10.4135/9781446287873 Print pages: 127-137 © 2010 SAGE Publications Ltd All Rights Reserved. This PDF has been generated from SAGE Research Methods. Please note that the pagination of the online version will vary from the pagination of the print book. https://dx.doi.org/10.4135/9781446287873 Introducing Hypothesis Testing Chapter Overview This chapter will: • Define hypothesis testing as the procedure to work out how likely it is that a specific prediction about the population is correct. • Show how the first step is to develop a null hypothesis and an alternative hypothesis. • Show how the second step is to locate the sample in the sampling distribution. • Show how the final step is to decide whether to reject or retain the null hypothesis using a predetermined benchmark or significance level. As well as estimating population characteristics, researchers use another major type of data analysis, called hypothesis testing. This chapter introduces hypothesis testing, and the following chapters look in more detail at hypothesis testing for categorical data (Chapter 14), numerical data (Chapter 15), and combinations of the two (Chapter 16). In these chapters, a hypothesis is a specific, testable prediction about the population. Hypothesis testing is the procedure used to work out how likely it is that the prediction is correct. A very simple example will help to explain the basic hypothesis-testing procedure. A man in a bar claims to have powers of psychokinesis – that he can control the movement of inanimate objects with his mind. As a good researcher, you are sceptical of his claimed psychokinetic powers. You ask him for evidence to allow you to test his claim. By some incredible chance, the bar has a lottery drum containing equal numbers of black and white balls. You ask the man to use his powers to influence the movement of the balls in the drum. He agrees, and says that he will use psychokinesis to draw out balls of the same colour. Behind the Stats The term psi (pronounced ‘sigh’) refers to two broad types of psychic or paranormal phenomena: (i) psychokinesis, which includes controlling inanimate objects and your own or other people's bodies (e.g. levitation, miraculous cures); and (ii) extra sensory perception, which includes telepathy and clairvoyance. The mainstream scientific SAGE 2010 SAGE Publications, Ltd. All Rights Reserved. SAGE Research Methods Page 2 of 15 Introducing Hypothesis Testing http://methods.sagepub.com/book/starting-statistics/n14.xml http://methods.sagepub.com/book/starting-statistics/n15.xml http://methods.sagepub.com/book/starting-statistics/n16.xml community is generally highly critical of psi. The few high-profile supporters, such as Brian Josephson, winner of a Nobel Prize for Physics, are publicly derided (e.g. McKie 2001). The problem, of course, is the difficulty of explaining psi with current scientific thinking. For example, the Princeton Engineering Anomalies Research project found that subjects influenced results from a random event generator several days after the running of the machine (McCrone 1994: 37)! In his lifetime, the man could try to influence the results from millions of rolls of the drum. This is the ‘population’, of which the few rolls of the drum he does with you are just a small sample. In line with your initial scepticism, your hypothesis about the population is that it will show no evidence of psychokinesis. If your hypothesis is right, your sample is from this population. Only if the sample result warrants it will you support an alternative hypothesis that the man does have psychokinetic powers. The next step is to get a sample result. The man concentrates on the drum, you roll it, and a white ball appears. You replace it, spin the drum a second time, and another white ball appears, then a third white ball, then a fourth and a fifth white ball; however, on the sixth roll a black ball appears. The man then says that he can feel his psychokinetic powers fading for the evening, refuses to continue the experiment – and demands a large whisky from you. The sample result, therefore, is 5 white balls and 1 black ball. You use this small set of sample data to test your hypothesis statistically. Figure 13.1 (based on Figure 12.1) shows the sampling distribution from randomly sampling 6 balls from equal numbers of black and white balls. In other words, it shows the number of black and white balls expected when the only influence on the results is chance (i.e. not psychokinesis). Overall, 11% of all results (7 of 64) have 5 or more white balls. SAGE 2010 SAGE Publications, Ltd. All Rights Reserved. SAGE Research Methods Page 3 of 15 Introducing Hypothesis Testing http://methods.sagepub.com/book/starting-statistics/n12.xml#f85 Figure 13.1 All possible sample results: sampling 6 balls from a population with equal numbers of black and white balls You then think back to what the man agreed to do – to draw out balls of the same colour. He did not specify whether they were black or white balls. Thus, if there had been 5 black balls in the sample rather than 5 white, he would similarly have used the result to back up his claim. Figure 13.1 also shows that there are 7 ways of getting at least 5 black balls in 6 draws – another 11% chance. Thus, without any psychokinetic ability whatsoever, the man has a 22% (11 + 11) chance of getting 5 balls of one colour in 6 draws. You now need to make a decision about your initial hypothesis that the man does not have psychokinetic abilities. Does the result suggest that your initial scepticism might be wrong? Drawing 5 balls with the same colour from 6 draws occurs by chance alone 22% of the time. In other words, there's a better than 1 in 5 chance of this result occurring without psychokinesis. You will probably decide that this result is not unusual enough for you to abandon your initial scepticism. So you retain your hypothesis that the man has no psychokinetic abilities. The psychokinesis example shows that there are three basic steps in hypothesis testing: 1 Make a hypothesis, or specific testable prediction, about the population. 2 Take a sample and locate it in the relevant sampling distribution. 3 Decide whether to reject or retain the hypothesis. SAGE 2010 SAGE Publications, Ltd. All Rights Reserved. SAGE Research Methods Page 4 of 15 Introducing Hypothesis Testing The following sections look more carefully at each of these steps. They use an example of research into participation in student organisations. Researchers have a hunch that there is a difference between male and female students in terms of their participation in student groups. To test this hunch, they find the gender breakdown of candidates for a sample of elections for positions on the boards of management of various student clubs and societies. The results show that of 140 candidates, 60% are women and 40% are men. University records show that 50% of students are women and 50% are men. Make a Hypothesis About the Population Always remember that a hypothesis is a specific, testable prediction about the population. In this example, the population consists of all candidates for student elections. The prediction is that there is a difference in participation rates of men and women. However, it is not this prediction that you test directly, but rather its opposite – that the sample is from a population in which there is no difference in the participation rates of men and women. At first glance, this approach seems a bit bizarre. But how, for example, can you prove the hypothesis that ‘All grizzly bears are brown’? Basically, you can't. No matter how long and hard you look and find only brown grizzly bears, the next could be another colour. However, it is much easier to disprove the hypothesis that ‘All grizzly bears are brown’. All you need is one bear that is not brown. You now need to translate this general prediction that there is no difference in the participation rates of men and women into a specific, testable hypothesis. Recall that you need to test the prediction that there is no difference in the participation rates of male and female students. If this prediction is true, you would expect 50% of all election candidates to be women. This is because university records show that 50% of all students are women. In other words, you predict that because there is no difference in the participation rates of male and female students, 50% of the population of all election candidates will be women. (Similarly, if 75% of all students were women, you would predict that women make up 75% of election candidates.) This specific, testable prediction is the null hypothesis, from the Latin word nullus, meaning ‘no’ or ‘none’. Behind the Stats Much of the southern part of Australia is made up of a plain called the Nullarbor, meaning ‘no trees’. Edward John Eyre was the first European to cross the Nullarbor, in 1841. He wrote in his journal that the area included some of ‘the wildest and most inhospitable wastes of Australia’ (Eyre 1845: 2), though that could have been because his expedition was marred by supply problems, mutiny, theft, and murder (Dutton 2006). Edward Eyre is not to be confused with Henry Ayers, a local politician after whom the 335 metre (1100 SAGE 2010 SAGE Publications, Ltd. All Rights Reserved. SAGE Research Methods Page 5 of 15 Introducing Hypothesis Testing feet) high sandstone rock in central Australia is named. Ayers Rock is now also known by its traditional Aboriginal name, Uluru. What if the evidence is strong enough to allow you to reject the null hypothesis? You need an alternative hypothesis. The simplest and best advice is to make the alternative hypothesis the direct opposite to the null hypothesis. Thus, if the null hypothesis is that there is no difference, the alternative is that there is a difference. At this point, don't specify the direction of any difference (i.e. that women participate more than men, or that men participate more than women). In this example