One-Way ANOVA Quiz

PDF page 789: analysis of variance also referred to as ANOVA; a method of testing whether the means of three or more populations are equal The method is applicable if

PDF page 789: one-way ANOVA a method of testing whether the means of three or more populations are equal; the method is applicable if

PDF page 789: The test statistic for analysis of variance is the F ratio.

PDF page 789: The test statistic for analysis of variance is the F ratio

PDF page 789: • all populations of interest are normally distributed,

PDF page 789: • Each population from which a sample is taken is assumed to be normal.

PDF page 789: • there is one independent variable and one dependent variable.

PDF page 789: Analysis of variance extends the comparison of two groups to several, each a level of a categorical variable (factor). Samples from each group are independent and must be randomly selected from normal populations with equal variances. We test the null hypothesis of equal means of the response in every group versus the alternative hypothesis of one or more group means being different from the others. A one-way ANOVA hypothesis test determines if several population means are equal. The distribution for the test is the F distribution with two different degrees of freedom.

PDF page 790: hypothesis test is the F distribution with two different degrees of freedom.

PDF page 790: dfbetween = df(num) = k – 1

PDF page 789: Analysis of variance compares the means of a response variable for several groups. ANOVA compares the variation within each group to the variation of the mean of each group. The ratio of these two is the F statistic from an F distribution with (number of groups – 1) as the numerator degrees of freedom and (number of observations – number of groups) as the denominator degrees of freedom. These statistics are summarized in the ANOVA table.

PDF page 790: dfwithin = df(denom) = n – k

PDF page 789: Analysis of variance compares the means of a response variable for several groups. ANOVA compares the variation within each group to the variation of the mean of each group. The ratio of these two is the F statistic from an F distribution with (number of groups – 1) as the numerator degrees of freedom and (number of observations – number of groups) as the denominator degrees of freedom. These statistics are summarized in the ANOVA table.

PDF page 789: Analysis of variance compares the means of a response variable for several groups. ANOVA compares the variation within each group to the variation of the mean of each group. The ratio of these two is the F statistic from an F distribution with (number of groups – 1) as the numerator degrees of freedom and (number of observations – number of groups) as the denominator degrees of freedom. These statistics are summarized in the ANOVA table.

PDF page 789: The graph of the F distribution is always positive and skewed right, though the shape can be mounded or exponential depending on the combination of numerator and denominator degrees of freedom. The F statistic is the ratio of a measure of the variation in the group means to a similar measure of the variation within the groups. If the null hypothesis is correct, then the numerator should be small compared to the denominator. A small F statistic will result, and the area under the F curve to the right will be large, representing a large p-value. When the null hypothesis of equal group means is incorrect, then the numerator should be large compared to the denominator, giving a large F statistic and a small area (small p-value)

PDF page 789: The graph of the F distribution is always positive and skewed right, though the shape can be mounded or exponential depending on the combination of numerator and denominator degrees of freedom. The F statistic is the ratio of a measure of the variation in the group means to a similar measure of the variation within the groups. If the null hypothesis is correct, then the numerator should be small compared to the denominator. A small F statistic will result, and the area under the F curve to the right will be large, representing a large p-value. When the null hypothesis of equal group means is incorrect, then the numerator should be large compared to the denominator, giving a large F statistic and a small area (small p-value)

PDF page 789: • samples (not necessarily of the same size) are randomly and independently selected from each population.

PDF page 789: • All samples are randomly selected and independent.