C82MCP Diploma Statistics School of Psychology University of Nottingham 1 Overview of Lecture Independent and Dependent Variables Between and Within Designs Statistical Hypotheses One & Two Tailed Tests Errors in Hypothesis Testing

C82MCP Diploma Statistics School of Psychology University of Nottingham 2 Independent Variables The essence of the experimental method can be stated quite simply: Manipulate the independent variable, and hold all other conditions constant. Any observed changes can be attributed to the manipulation of the independent variable.

C82MCP Diploma Statistics School of Psychology University of Nottingham 3 Dependent Variables The dependent variable is the thing that we measure. When we choose a dependent variable we have to be fairly convinced that it will measure the effect that the independent variable is supposed to be producing.

C82MCP Diploma Statistics School of Psychology University of Nottingham 4 Confounding Variables We might find that all the people who are in the high motivation group are older than all the people in the low motivation group. How do we know that it isn't age that is leading to this result and not motivation? The answer is that we don't. We have confounded two variables, motivation and age.

C82MCP Diploma Statistics School of Psychology University of Nottingham 5 Between Group & Within Subjects Designs. There are two forms of manipulation of the independent variable. All the conditions can be applied to the same subject All the conditions applied to different groups of subjects. In a situation where different groups of subjects do different things then we have a between group design. In a situation where the same group of subjects do different things then we have a within subjects design

C82MCP Diploma Statistics School of Psychology University of Nottingham 6 Statistical Hypotheses. The name of the game in using statistical tests is to make inferences about populations on the basis of measure taken of samples. There are two statistical Hypotheses that we can make The Null Hypothesis The Alternative Hypothesis

C82MCP Diploma Statistics School of Psychology University of Nottingham 7 The Null Hypothesis The null hypothesis simply states that the different samples we look at come from the same population For parametric statistics, the null hypothesis states Ho: All the means are equal. For non-parametric statistics, the null hypothesis states Ho: All the distributions are the same. In other words if there is no effect of the independent variable, then there will be no differences on the scores obtained at the different levels of that variable.

C82MCP Diploma Statistics School of Psychology University of Nottingham 8 The Alternative hypothesis The alternative hypothesis is the logical opposite to the null hypothesis. The relationship between the null and alternative hypothesis is fairly simple: they are mutually exclusive. Only one of them can be true. They cover all the possible outcomes in the experiment. For parametric statistics the alternative hypothesis is Ha: Not all the means are equal. For non-parametric statistics the alternative hypothesis is: Ha: Not all the distributions are the same.

C82MCP Diploma Statistics School of Psychology University of Nottingham 9 Reject and Failing to Reject the Null Hypothesis There is a very simple decision rule. If the statistical test that we use suggests that the samples do not come from the same population then we reject the null hypothesis. If the statistical test that we use does not support the conclusion that the samples do not come from the same population we fail to reject the null hypothesis.

C82MCP Diploma Statistics School of Psychology University of Nottingham 10 A Plan For Designing and Analysing Experiments Design the experiment. identify independent & dependent variables. identify between or within design. Select a statistical test. Specify the statistical hypotheses the null hypothesis the alternative hypothesis. Collect the data. Calculate the test statistic. Reject or fail to reject the null hypothesis.

C82MCP Diploma Statistics School of Psychology University of Nottingham 11 Test Statistics & Probability Distributions. We reject the null hypothesis when the probability of null hypothesis beginning true is only p=0.05 (i.e. 1 in 20). We do this by calculating a test statistic. The test statistic has known probabilities associated with its values.

C82MCP Diploma Statistics School of Psychology University of Nottingham 12 Test Statistics & Probability Distributions. Each test statistic we calculate has a probability distribution associated with it. We reject the null hypothesis when the test score is in the critical region.

C82MCP Diploma Statistics School of Psychology University of Nottingham 13 One Tailed & Two Tailed Tests When we compare two different treatments there are two different possible outcomes when the null hypothesis is rejected. Scores of Group 1 > Scores of Group 2 Scores of Group 1 < Scores of Groups 2 Given a significance level of p=0.05 there is a 1 in 20 chance of getting either of the above possible outcomes. But there is only a 1 in 40 chance of obtaining one of the two possible outcomes.

C82MCP Diploma Statistics School of Psychology University of Nottingham 14 One Tailed & Two Tailed Tests In the first graph the rejection region (p=0.05) is on one side of the distribution. This is the equivalent of predicting the outcome of the experiment. This is known as a one tailed hypothesis

C82MCP Diploma Statistics School of Psychology University of Nottingham 15 One Tailed & Two Tailed Tests In the second graph there are two rejection regions of (p=0.025) one at either end of the distribution. This is the equivalent of not predicting the outcome of the experiment in terms of the direction of the result. This is known as a two-tailed hypothesis.

C82MCP Diploma Statistics School of Psychology University of Nottingham 16 Errors in Hypothesis Testing The procedures we follow in hypothesis testing do not guarantee that a correct inference will be drawn. Whenever we decide to reject the Null Hypothesis we can make a mistake. There are two basic kinds of errors. Type I Error Type II Error

C82MCP Diploma Statistics School of Psychology University of Nottingham 17 Errors in Hypothesis Testing Type I Error Rejecting the null hypothesis when it is true Type II Error Failing to reject the null hypothesis when it is false