When performing a one-way analysis of variance, which statistical test is used?
F test
The correct answer is F test.
One-way Analysis of Variance (ANOVA) uses the F-test to determine whether the means of three or more independent groups differ significantly. The test statistic is computed as the ratio of the between-group variance (Mean Square Between) to the within-group variance (Mean Square Within):
\(F = \dfrac{MS_{between}}{MS_{within}}\)
This ratio is then compared against the critical value from the F-distribution with the appropriate degrees of freedom. A large F-value indicates that group means differ more than would be expected by chance, leading to rejection of the null hypothesis of equal means.
Why not the others: The z-test and t-test compare means of only one or two groups, not multiple. The χ² (chi-square) test is used for categorical data (goodness-of-fit or independence), not for comparing means of continuous variables across groups.
Similar Questions
If α is the level of significance and if (1 − α) is increased, then the width of the confidence interval of mean:
The analysis of variance technique was introduced by:
The power of a test is:
The term ‘Analysis of variance’ was introduced by:
Which of the following can be applied as a goodness-of-fit test?
For two-way classification, let number of treatments and blocks be 5 and 5, respectively. It is given that SSTR (sum of squares due to treatments) = 18.5335, SSE (sum of squares due to error) = 3.545 and SST (total sum of squares) = 46.9335. The value of F-statistic for testing equality of effectiveness of five treatments is:
In a survey, it is found that out of 301 women, 24 women had impaired fasting glucose (IFG). If null hypothesis to be tested is that 6.3% have IFG and alternative hypothesis is that percentage is more than 6.3, then the value of test statistic is:
The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and standard deviation (sd) of 10, while IQs of 14 students from another area of the city showed a mean of 112 and sd of 8. The null hypothesis to be tested is that there is significant difference between IQs of the two groups. The distribution with degrees of freedom and value of test statistic assuming that null hypothesis is true, are:
In two-way classification, how many factors affect the values of the response variable?
In a one-way classified data analysis with 'v' number of treatments and 'n' number of experimental units, then the number of degrees of freedom for the sum of squares due to error is:
Important Questions from Hypothesis testing
Which of the following statements relating to Tests of Hypothesis are correct ? Select the correct code.
Statement I: Type-I error occurs when true null hypothesis gets rejected by the test.
Statement II: Beta value denotes the power of the test.
Statement III : To test the significance of the goodness of fit of a distribution, F-test is applied.
Statement VI: When H0: μM > μF, two-tailed test is applied for testing the hypothesis.
Statement V: The critical value of Z-statistic for two-tailed test at 5% level of significance is 1.96.
Match the items of List-II with the items of List-I and denote the code of correct matching:
List-I
List-II
(a) Testing the goodness of fit of a distribution (i) Z-test (b) Testing the significance of the differences among the average performance of more than two sample groups (ii) Chi-square test (c) Testing the significance of the difference between the average performance of two sample groups (Large-sized) (iii) F-test
Codes:The sequence of steps involved in testing a hypotheses are:
A. Select a suitable test statistic
B. Establish critical or rejection region
C. State the null and alternative hypothesis
D. State the level of significance (α)
E. Formulate a decision rule to evaluate the null hypothesis
Choose the correct answer from the options given below
If α is the level of significance and if (1 − α) is increased, then the width of the confidence interval of mean:
The analysis of variance technique was introduced by:
