Chap 13

EXAMPLE: THE t AND F TESTS(2)

-Degrees of Freedom To use the table in the text we have to determine the degrees of freedom for the test. The degrees of freedom is calculated by N1+N2-2 so in our example 10+10-2= 18. You do not need to know what degrees of freedom is or means just know how to calculate it. -One-Tailed Versus Two-Tailed Tests In the table you need to choose a critical t for the situation in your research. Either (1) you have a specified direction of difference between the groups (e.g. group 1 will be greater than group 2) OR (2) You did not previously predict a direction of the different (e.g. group 1 will differ from group 2). Situation 1 is called a one-tailed t-test and situation 2 is called a two-tailed test. Look at figure 13.1 to see the difference. -The F-Test or analysis of variance is an extension of the t- test. F-test we use to ask if there is a difference among three or more groups or to evaluate the results of factorial designs. When there is 1 IV with 2 groups the F test is identical to the t-test. The F-test is a ration of systematic variance and error variance. -Systematic variance (between-group variance) - is the deviations of the group means from the grand mean or the mean score of all individuals. This is small when the differences between groups is small and increases as the group mean differences increase. -Error variance (within-group variance)- the deviation of individual scores in each group from their respective group means. The larger the f-ration the more likely it is that the results are significant.

Significance Testing

-In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone The p-value, gives you the probability of getting the results you did (or more extreme results) given that the null hypothesis is true-

INFERENTIAL STATISTICS

Allows researchers to make inferences about the true difference in the population on the basis of the sample data Gives the probability that the difference between means reflects random error rather than a real difference

MULTIPLE Regression

Applying to grad school you are evaluated on College grades Scores on GRE Scores on psych GRE Letters of recommendation. R2 is similar to r2 in that R2 tells us the percentage of variability in the criterion variable that is accounted for by the combined set of predictor variables

REGRESSION EQUATIONS

Calculations used to predict a person's score on one variable (criterion) when that person's score on another variable (predictor) is already known General Form: Y=a + bX Y = Score we wish to predict X = Score that is known a = constant b = weighing adjustment ( slope of the line created with this equation) We must first show that there is a high correlation between the criterion and predictor variables and then we can use the regression equation to predict the score we are interested in.

TYPE I AND TYPE II ERRORS

Decisions to reject the NULL are based on probability and NOT on the the TRUE SCORES in the population. Due to this the decision may be correct or errors may result from the inferential statistics. There are 2 possible decisions -reject null - Accept null There are 2 possible truths about the population - null is true - the null is false A correct decision is made when we reject the null and the research hypothesis is true in the population or if the null is accepted and the null is true. Errors can be made. Type I Errors Made when the null hypothesis is rejected but the null hypothesis is actually true. OR we decide the population means are not equal when they are . They occur when we Obtain a large value of t or F by chance. There is still a 5% chance of error The probability of type 1 error is determined by the significance level or alpha level we choose. So if we choose .05 then there is a 5% chance we will make a type 1 error. Sometimes we use a .01 level which is a 1% chance of type 1 error.

EXAMPLE: THE t AND F TESTS

Different statistical test let us use probability to decide to reject the null. The t-test is the most commonly used to look at if 2 groups are significantly different from each other. In the aggression experiment, we could use a t-test because we want to see of the mean of the no-model group differs from the mean of the model group. Before we use a statistical test we must first clearly specify the null and research hypotheses ...in the modeling experiment they were WHAT? And we must also decide a significance or alpha level to reject the null...we use .05

EFFECT SIZE

Effect size is the General Term that Refers to the Strength of Association Between Variables Pearson r Correlation Coefficient is One Indicator of Effect Size Advantage of Reporting Effect Size is that it Provides a Scale of Values that is Consistent Across All Types of Studies Effect size is another type of coefficient that ranges from 0 to 1 we do not worry about the direction or sign here.

NULL AND RESEARCH HYPOTHESES

Inferential Statistics begins with an statement of the null hypothesis. The Null Hypothesis: Population Means are Equal or in other words that the observed differences between groups is due to random error. The Research Hypothesis is that the Population Means are Not Equal The NULL HYPO states that the IV had no effect while the RESEARCH HYPO states that the IV did have an effect. In the aggression study we discussed last class - write the variables on board. Ho The population mean of the no-model group is equal to the population mean of the model group H1 The population mean of the no-model group is not equal to the population mean of the model group. The idea here is that if we can show that Ho is incorrect than we can accept that the Research hypothesis is is correct. If we accept the research hypothesis this means that the IV an effect on the DV. The Null Hypothesis is rejected only when there is a low probability that the obtained results can be due to random error. This is what is mean by statistical significance. statistical significance - a significant result has a very low probability of occurring if the population means are equal. In other words a significant result means that there is a low probability that differences between the means in the sample (control vs. exp) was due to random error. Significance is based on probability.

CHOOSING A SIGNIFICANCE LEVEL

Researchers traditionally have used either a .05 or a .01 significance level in the decision to reject the null hypothesis Researchers generally believe that the consequences of making a Type I error are more serious than those associated with a Type II error. If the null is falsely rejected, this might lead to publishing the results of a study and the results are not indicative of the actual population.

IMPORTANCE OF REPLICATIONS

Scientists attach little importance to results of a single study Detailed understanding requires numerous studies examining same variables Researchers look at the results of studies that replicate previous investigations

THE EVERYDAY CONTEXT OF TYPE I AND TYPE II ERRORS

There are 2 possible decisions -reject null - Accept null There are 2 possible truths about the population - null is true - the null is false

TYPE I AND TYPE II ERRORS (2)

Type II Errors Made when the null hypothesis is accepted although in the population the research hypothesis is true. OR the population means are not equal but the results do not lead to that decision. The probability of type 2 errors is called beta and a study should be designed to keep this low. Factors related to making a Type II error -Significance (alpha) level - a low significance level to decrease type 1 errors will increase type 2 error. If we make it hard to reject the null the chances of accepting it incorrectly increases. -Sample size - the smaller the sample size the greater the chance of type 2 error -Effect size - the larger the effect size the less likely a type 2 error.

SAMPLES AND POPULATIONS

We use inferential statistics to determine if we can make statements that the results reflect what would happen if we were to conduct the experiment again and again with multiple samples. Allows conclusions on the basis of sample data