 ## Silagra Thus buy discount silagra 100mg online erectile dysfunction young, you should always compute a measure of effect size for any significant result 50mg silagra mastercard erectile dysfunction doctor visit, because this is the only way to determine whether your independent variable is important in influencing a behavior buy genuine silagra on-line erectile dysfunction doctor visit. In fact buy silagra cheap impotence doctor, the American Psychological Association requires published research to report effect size. Effect Size Using Cohen’s d One way to describe the impact of an independent variable is in terms of how big a difference we see between the means of our condi- tions. For example, we saw that the presence/absence of hypnosis produced a differ- ence in recall scores of 3. However, the problem is that we don’t know whether, in the grand scheme of things, 3 is large, small, or in between. We need a frame of reference, and here we use the estimated population standard deviation. Recall that the standard deviation reflects the “average” amount that scores differ from the mean and from Describing the Relationship in a Two-Sample Experiment 281 each other. Individual scores always differ much more than their means, but this still provides a frame of reference. For example, if individual scores differ by an “average” of 20, then we know that many large differences among scores occur in this situation. Therefore, a difference of 3 between two samples of such scores is not all that impres- sive. Because smaller differ- ences occur in this situation, a difference between conditions of 3 is more impressive. Thus, we standardize the difference between our sample means by comparing it to the population standard deviation. This is the logic behind the measure of effect size known as Cohen’s d: It measures effect size as the magnitude of the difference between the conditions, relative to the population standard deviation. The formulas for Cohen’s d are: Independent-samples t-test Related-samples t-test X1 2 X2 D d 5 d 5 s2 s2 3 pool 3 D For the independent-samples t-test, the difference between the conditions is meas- ured as X1 2 X2 and the standard deviation comes from the square root of the pooled variance. For the related-samples t-test, the difference between the conditions is measured by D and the standard deviation comes from finding the square root of the estimated vari- ance 1s2. First, the larger the absolute size of d, the larger the impact of the independent variable. In fact, Cohen1 proposed the following interpretations when d is the neighborhood of the following amounts: Values of d Interpretation of Effect Size d 5. Second, we can compare the relative size of different ds to determine the relative impact of a variable. Others think of d as the amount of impact the independent variable has, which can- not be negative. Effect Size Using Proportion of Variance Accounted For This approach measures effect size, not in terms of the size of the changes in scores but in terms of how consistently the scores change. Here, a variable has a greater impact, the more it “causes” everyone to behave in the same way, producing virtually the same score for everyone in a particular condition. This then is an important variable, because by itself, it pretty much controls the score (and behavior) that everyone exhibits. Thus, in an experiment, the proportion of variance accounted for is the pro- portional improvement achieved when we use the mean of a condition as the predicted score of participants tested in that condition compared to when we do not use this approach. Put simply it is the extent to which individual scores in each con- dition are close to the mean of the condition, so if we predict the mean for someone, we are close to his or her actual score. When the independent variable has more con- trol of a behavior, everyone in a condition will score more consistently. Then scores will be closer to the mean, so we will have a greater improvement in accurately pre- dicting the scores, producing a larger proportion of variance accounted for. On the other hand, when the variable produces very different, inconsistent scores in each condition, our ability to predict them is not improved by much, and so little of the variance will be accounted for. In Chapter 8, we saw that the computations for the proportion of variance accounted for are performed by computing the squared correlation coefficient. For the two-sample experiment, we compute a new correlation coefficient and then square it. The squared point-biserial correlation coefficient indicates the propor- tion of variance accounted for in a two-sample experiment. This pb can produce a proportion as a low as 0 (when the variable has no effect) to as high as 1. In real research, however, a variable typically accounts for between about 10% and 30% of the variance, with more than 30% being a very substantial amount. Statistics in Published Research: The Two-Sample Experiment 283 The formula for computing r2 is pb 1t 22 2 obt rpb 5 2 1tobt2 1 df This formula is used with either the independent-samples or related-samples t-test. Then, for independent samples, df 5 1n1 2 12 1 1n2 2 12 For related samples, df 5 N 2 1. Hypnosis is not of major importance here, because scores are not consis- tently very close to the mean in each condition. Therefore, hypnosis is only one of a number of variables that play a role here, and, thus, it is only somewhat important in determining recall. Further, fewer other variables need to be considered in order to completely predict scores, so this is an important relationship for understanding phobias and the therapy. We also use the proportion of variance accounted for to compare the relationships from different studies. Thus, the role of therapy in determining fear scores (at 67%) is about three times larger than the role of hypnosis in determining recall scores (which was only 22%). Thus, a published report of our independent-samples hypnosis study might say, “The hypnosis group (M 5 23. Obviously, you perform the independent-samples t-test if you’ve cre- ated two independent samples and the related-samples t-test if you’ve created two related samples. In both procedures, if tobt is not significant, consider whether you have sufficient power. If tobt is significant, then focus on the means from each condition so that you summarize the typical score—and typical behavior—found in each condition. Use effect size to gauge how big a role the independent variable plays in determining the behaviors. Finally, interpret the relationship in terms of the underlying behaviors and causes that it reflects. For either, the program indicates the at which tobt is significant, but for a two-tailed test only. It also computes the descriptive statistics for each condition and automatically computes the confidence interval for either 1 2 2 or D. Two samples are independent when participants are randomly selected for each, without regard to who else has been selected, and each participant is in only one condition. The independent-samples t-test requires (a) two independent samples, (b) normally distributed interval or ratio scores, and (c) homogeneous variance. Homogeneity of variance means that the variances in the populations being represented are equal. The confidence interval for the difference between two ms contains a range of differences between two s, one of which is likely to be represented by the difference between our two sample means. Two samples are related either when we match each participant in one condition to a participant in the other condition, or when we use repeated measures of one group of participants tested under both conditions. The confidence interval for mD contains a range of values of D, any one of which is likely to be represented by the sample’s D. The power of a two-sample t-test increases with (a) larger differences in scores between the conditions, (b) smaller variability of scores within each condition, and (c) larger ns The related-samples t-test is more powerful than the independent-samples t-test. Effect size indicates the amount of influence that changing the conditions of the independent variable had on the dependent scores. Cohen’s d measures effect size as the magnitude of the difference between the conditions. The proportion of variance accounted for (computed as r2 ) measures effect pb size as the consistency of scores produced within each condition. The larger the proportion, the more accurately the mean of a condition predicts individual scores in that condition. All other things being equal, should you create a related-samples or an independent-samples design? We study the relationship between hot or cold baths and the amount of relaxation they produce. The relaxation scores from two independent samples are Sample 1 (hot): X 5 43, s2 5 22. We investigate if a period of time feels longer or shorter when people are bored compared to when they are not bored. Using independent samples, we obtain these estimates of the time period (in minutes): Sample 1 (bored): X 5 14. A researcher asks if people score higher or lower on a questionnaire measuring their well-being when they are exposed to much sunshine compared to when they’re exposed to little sunshine. A sample of 8 people is measured under both levels of sunshine and produces these well-being scores: Low: 14 13 17 15 18 17 14 16 High: 18 12 20 19 22 19 19 16 (a) Subtracting low from high, what are H0 and Ha? A researcher investigates whether classical music is more or less soothing to air- traffic controllers than modern music. She gives each person an irritability question- naire and obtains the following: Sample A (classical): n 5 6, X 5 14. We predict that children exhibit more aggressive acts after watching a violent television show. The scores for ten participants before and after watching the show are Sample 1 (After) Sample 2 (Before) 5 6 4 4 7 3 2 1 4 3 (a) Subtracting before from after, what are H0 and Ha?  