1SPSS 2 Hypothesis Testing and Inferential Statistics Tutorial Goal: Building and testing hypotheses using inferential statistics in SPSS. This workshop covers parametric and nonparametric tests, concentrating on correlation, regression, chi-square, t-tests, and ANOVAs. Participants learn how to understand, analyze and report results. Ok, let’s review somewhat from our last workshop. What is statistics? First, what is statistics? “Statistics is the science and practice of developing knowledge through the use of empirical data expressed in quantitative form (http://www.answers.com/topic/statistics-2?method=6).” So, you are basically posing a question about something in the Social Sciences and using numbers to answer it. Some examples of these questions are: • Do countries with stricter gun control laws have fewer deaths by firearms? • What are the best methods for teaching? • What factors cause a disease to spread from one place to another? • Do religious views and class affect opinions about euthanasia? You can answer these questions by using numbers. For statistics, there are four kinds of levels of measurement for the variable. All your analyses extend from what kind of level your variable is. They are NOIR. (N)ominal (O)rdinal (I)nterval (R)atio Let’s talk about each one. Nominal means that the number simply represents a category of objects. There is no measured different among the objects or people. Some examples are giving states numbers (N.Y. 1, Connecticut 2, R.I. 3), assigning a number for gender (male 1, female 2), or designating college major (History 1, Business 2, Sociology 3). You are just assigning a number to something. Ordinal means the larger number for the object is truly larger in some sort of amount. This typically means rank. Some examples are 1st, 2nd, and 3rd places in a contest, or preferences for different movies. However, there is no exactly measured difference among the objects. We don’t know definitively how much larger or better 1st is compared to 2nd. We just know 1st is somehow larger than 2nd. Interval means, like Ordinal, that there is a rank for the objects or people, but there is also a measurement for the ranking. Some examples are degrees Celsius or Fahrenheit. We know that the different between 98 and 99 degrees is the difference of the amount of mercury in a thermometer. Also, the difference between 42 and 43 degrees is the same amount between 98 and 99. However, there is no true zero, which stands for a complete lack of the object being measured. 0 degree does not mean there is no mercury, for example.Ratio means, like Interval, that there is a measurement for the ranking, but there is also a true zero. A true zero means that there is lack of the quality being measured. Some examples are income, where the difference between $10,000 and $11,000 is known and zero means complete lack of income. These levels are very important and we will be discussing them more as we go on. Nominal and Ordinal are called Nonparametric Data, and Interval and Ratio are called Parametric Data. The statistical analyses that you can use are dependent on what level your data are. Specifically, if you can make a logical mean using your data, then you can use parametric data. In this tutorial, we are interested in Inferential Statistics. This form of statistics tries to make conclusions about a whole group from one sample from that group. So, we have two important concepts. First, population means the entire group of whatever you’re studying. Second, a sample is a subset of the population. If you’re trying to do research, studying a whole population is probably out of the question. A sample is easier to obtain and you can use the sample to surmise how the whole population behaves. Of course, it has to be a random sample, which means that anyone or anything from the population has an equal chance of falling into the sample. If not, then you have bias, which means that the sample is not an accurate picture of the whole population. Sample Population Ok, now that we understand what a population and sample are, we need to know what probability theory is. Probability Theory is “the branch of mathematics that studies the likelihood of occurrence of random events in order to predict the behavior of defined systems” (http://www.answers.com/probability+theory&r=67). So, we want to apply the theories of probability on this sample to infer what the whole population does. The best way to understand this is by looking at dice and how they behave. If you rolled one die, what is the chance you’d get a five? 1/6 2If you rolled two dice, what is the chance you’d get 2 fives? 1/36 Ok, now look at our sample set, which is all possible outcomes. If you have two dice, the following chart has all the 36 possible outcomes: Result Probability2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36 (http://www.edcollins.com/backgammon/diceprob.htm) So, the more chances you have for that outcome, the higher the probability you’ll have to get that outcome. For example, from all our possible outcomes, the possible outcome of “7” is 1/6, whereas the possible outcome of “2” is only 1/36. A good graphic for this probability is seen at a web site called Introduction to Probability Models. Here you can run a simulation of rolling two dice. The right panel below shows the result of the dice on the X axis and the number of times on the Y axis. The first chart shows the result from rolling two dice ten times. 3Rolling two dice twenty times. And finally, rolling two dice one hundred times. (http://www.math.csusb.edu/faculty/stanton/m262/intro_prob_models/intro_prob_models.html) You can see that the outcomes with more probability, numbers 6, 7, and 8, build up more quickly. You can also see that this builds up as a bell-shaped curve. If it’s considered a normal distribution, you should see this kind of curve. So, the numbers with more probability are in the middle and those without a high probability are on the extremes. This is what statistics is all about. It’s about seeing what number has a high probability of occurring and what doesn’t. Subsequently, two important ideas from distribution of outcome are central tendency and variance. Let’s explore these essential ideas for a moment.