Chapter 12 - Analysis of variance. In this chapter, the learning objectives are: List the characteristics of the F distribution, conduct a test of hypothesis to determine whether the variances of two populations are equal, discuss the general idea of analysis of variance, organize data into a one-way and a two-way ANOVA table, conduct a test of hypothesis among three or more treatment means,. | Analysis of Variance Chapter 12 GOALS List the characteristics of the F distribution. Conduct a test of hypothesis to determine whether the variances of two populations are equal. Discuss the general idea of analysis of variance. Organize data into a one-way and a two-way ANOVA table. Conduct a test of hypothesis among three or more treatment means. Develop confidence intervals for the difference in treatment means. Conduct a test of hypothesis among treatment means using a blocking variable. Conduct a two-way ANOVA with interaction. The F Distribution Uses of the F Distribution test whether two samples are from populations having equal variances to compare several population means simultaneously. The simultaneous comparison of several population means is called analysis of variance(ANOVA). Assumption: In both of the uses above, the populations must follow a normal distribution, and the data must be at least interval-scale. Characteristics of the F Distribution There is a . | Analysis of Variance Chapter 12 GOALS List the characteristics of the F distribution. Conduct a test of hypothesis to determine whether the variances of two populations are equal. Discuss the general idea of analysis of variance. Organize data into a one-way and a two-way ANOVA table. Conduct a test of hypothesis among three or more treatment means. Develop confidence intervals for the difference in treatment means. Conduct a test of hypothesis among treatment means using a blocking variable. Conduct a two-way ANOVA with interaction. The F Distribution Uses of the F Distribution test whether two samples are from populations having equal variances to compare several population means simultaneously. The simultaneous comparison of several population means is called analysis of variance(ANOVA). Assumption: In both of the uses above, the populations must follow a normal distribution, and the data must be at least interval-scale. Characteristics of the F Distribution There is a “family” of F Distributions. A particular member of the family is determined by two parameters: the degrees of freedom in the numerator and the degrees of freedom in the denominator. The F distribution is continuous F cannot be negative. The F distribution is positively skewed. It is asymptotic. As F the curve approaches the X-axis but never touches it. Comparing Two Population Variances The F distribution is used to test the hypothesis that the variance of one normal population equals the variance of another normal population. Examples: Two Barth shearing machines are set to produce steel bars of the same length. The bars, therefore, should have the same mean length. We want to ensure that in addition to having the same mean length they also have similar variation. The mean rate of return on two types of common stock may be the same, but there may be more variation in the rate of return in one than the other. A sample of 10 technology and 10 utility stocks shows the same mean rate
