Inferential Statistics to Evaluate Sample Data. Inferential

¶ … inferential statistics to evaluate sample data.

Inferential Statistics are used to determine whether one can make statements where the results reflect that would happen if we were to conduct the experiment again with multiple samples. With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone via inference. For instance, inferential statistics infer from the sample data what the population might think. Another example, inferential statistics can be used to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, inferential statistics make inferences from data to more general conditions; whereas descriptive statistics simply describe what's in the data.

When conducting research, inferential statistics that are useful in experimental research design or in program outcome evaluation. The simplest inferential test is used when comparing the average performance of two groups on a single measure to see if there is a difference. One might need to know whether eighth-grade boys and girls differ in math test scores or whether a program group differs on the outcome measure from a control group. Whenever one wishes to compare the average performance between two groups one should consider the t-test for differences between groups. The major inferential statistics come from a general family of statistical models known as the General Linear Model. This includes the t-test, Analysis of Variance (ANOVA), Analysis of Covariance (ANCOVA), regression analysis, and many of the multivariate methods like factor analysis, multidimensional scaling, cluster analysis, discriminant function analysis. Given the importance of the General Linear Model, it's a good idea for any serious social researcher to become familiar with its workings (Ader, et al., 2007).

7. Distinguish between the null hypothesis and the research hypothesis.

The null hypothesis means that the population means are equal, that the observed difference is due to random error. Research hypothesis is that the population means are not equal. NH states the IV had no effect, RH states the IV did have an effect. In short, a null hypothesis is a hypothesis that proposes no relationship or difference between two variables. In the standard hypothesis-testing approach to science one attempts to demonstrate the falsity of the null hypothesis, leaving one with the implication that the alternative, mutually exclusive, hypothesis is the acceptable one. Therefore, a null hypothesis is the hypothesis that there is no relationship between two or more variables, symbolized as H0. The alternate, or research, hypothesis proposes a relationship between two or more variables, symbolized as H1 (Fisher, 1966).

If a researcher was interested in examining the relationship between music and emotion, she may believe that there is a relationship between music and emotion. However, a more specific, testable proposition is needed for research purposes. After a review of the literature, the researcher forms a research hypothesis, as well as a null hypothesis. Thus, H1 (the research/alternate hypothesis): Music at a fast tempo is rated by participants as being happier than music at a slow tempo. H0 (the null hypothesis): Music at a fast tempo and at a slow tempo is rated the same in happiness by participants. Note that the two hypotheses we propose to test must be mutually exclusive; i.e., when one is true the other must be false. And we see that they must be exhaustive; they must include all possible occurrences. Lastly, the researcher must translate the research hypothesis into operational terms. The researcher goes on to operationally define fast tempo as being music at a tempo of 120 bpm (beats per minute) and slow tempo music as being music at a tempo of 60 bpm. In addition, a researcher has to specify how participants are going to rate the music for happiness (Hays, 1973).

8. Discuss probability in statistical reference, as well as the meaning of significance.

Probability is the likelihood of the occurrence of some event or outcome. A significant result is one that has a very low probability of occurring if the population means are equal. The probability required for significance is called the alpha level and is often .05. All results obtained by statistical methods suffer from the disadvantage that they might have been caused by pure statistical accident. The level of statistical significance is determined by the probability that this has not, in fact, happened. P is an estimate of the probability that the result has occurred by accident. Therefore a large value of P. represents a small level of significance (Moses, 1986).