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essentials of statistics
Questions and Answers of
Essentials Of Statistics
Describe the terminology that is used for ANOVA, especially the terms factor and level, identify the hypotheses for this test, and identify each in the context of a research example.
Identify the circumstances in which you should use ANOVA instead of t tests to evaluate mean differences, and explain why.
Describe the F-ratio that is used in ANOVA and explain how it is related to the t statistic.
Identify the sources that contribute to the variance between-treatments and the variance within-treatments, and describe how these two variances are compared in the F-ratio to evaluate the null
Calculate the three SS values, the three df values, and the two mean squares(MS values) that are needed for the F-ratio and describe the relationships among them.
Dene the df values for an F-ratio and use the df values, together with an alpha level, to locate the critical region in the distribution of F-ratios.
Conduct a complete ANOVA to evaluate the differences among a set of means and compute a measure of effect size to describe the mean differences.
Explain how the results from an ANOVA and measures of effect size are reported in the scientic literature.
Describe the circumstances in which post hoc tests are necessary and explain what the tests accomplish.
Explain how the outcome of an ANOVA and measures of effect size are inuenced by sample size, sample variance, and sample mean differences.
Explain the relationship between the independent-measures t test and an ANOVA when evaluating the difference between two means from an independent-measures study
How many levels are there in a single-factor independent-measures design comparing depression scores of participants with and without treatment?a. 1b. 2c. 3d. 4
When is the distinction between the “testwise” alpha level and the“experimentwise” alpha level important?a. Whenever you do an analysis of varianceb. When the study is comparing exactly two
Which of the following accurately describes the F-ratio in an analysis of variance?a. The F-ratio is a ratio of two (or more) sample means.b. The F-ratio is a ratio of two variances.c. The F-ratio is
For an analysis of variance, the differences between the sample means contribute to the _________ and appears in the _________ of the F-ratio.a. variance between treatments, numeratorb. variance
What is suggested by a large value for the F-ratio in an ANOVA?a. There is a treatment effect and the null hypothesis should be rejected.b. There is no treatment effect and the null hypothesis should
An analysis of variances produces dfbetween treatments 5 2 and dfwithin treatments 5 24.For this analysis, what is dftotal?a. 26b. 27c. 28d. Cannot be determined without additional information
An analysis of variance is used to evaluate the mean differences among three treatment conditions. The analysis produces SSwithin treatments 5 20, SSbetween treatments 5 40, and SStotal 5 60.For this
A research study compares three treatments with n 5 5 in each treatment. If the SS values for the three treatments are 25, 20, and 15, then the analysis of variance would produce SSwithin equal to
A researcher uses analysis of variance to test for mean differences among four treatments with a sample of n 5 6 in each treatment. The F-ratio for this analysis would have what df values?a. df 5 3,
The following table shows the results of an analysis of variance comparing two treatment conditions with a sample of n 5 11 participants in each treatment.Note that several values are missing in the
A research report concludes that there are significant differences among treatments, with “F(2, 27) 5 8.62, p , .01, h2 5 0.46.” How many treatment conditions were compared in this study?a. 2b.
Under what circumstances are post hoc tests necessary after an ANOVA?a. When H0 is rejectedb. When there are more than two treatmentsc. When H0 is rejected and there are more than two treatmentsd.
An ANOVA finds significant treatment effects for a study comparing three treatments with means of M1 5 8, M2 5 4, M3 5
If Tukey’s HSD is computed to be HSD 5 2.50, then which of the treatments are significantly different?a. 1 vs. 2 and 2 vs. 3b. 1 vs. 2 and 1 vs. 3c. 1 vs. 3 and 2 vs. 3d. 1 vs. 2 and 1 vs. 3 and 2
Which combination of factors is most likely to produce a large value for the F-ratio and a large value for h2?a. Large mean differences and large sample variancesb. Large mean differences and small
If an analysis of variance is used for the following data, what would be the effect of changing the value of M2 to 30?a. Increase SSbetween and increase the size of the F-ratiob. Increase SSbetween
A researcher uses an ANOVA to evaluate the mean difference between two treatment conditions and obtains F 5 4.00 with df 5 1, 16.If an independentmeasures t statistic had been used instead of the
Calculate SStotal, SSbetween, and SSwithin for the following set of data:Treatment 1 Treatment 2 Treatment 3 n 5 10 n 5 10 n 5 10 N 5 30 T 5 10 T 5 20 T 5 30 G 5 60 SS 5 27 SS 5 16 SS 5 23 ΣX2 5 206
A researcher uses an ANOVA to compare three treatment conditions with a sample of n 5 8 in each treatment. For this analysis, find dftotal, dfbetween, and dfwithin.
A researcher reports an F-ratio with dfbetween 5 2 and dfwithin 5 30 for an independent-measures ANOVA.a. How many treatment conditions were compared in the experiment?b. How many subjects
A researcher reports an F-ratio with df 5 3, 24 from an independent-measures research study.a. How many treatment conditions were compared in the study?b. What was the total number of participants in
The following values are from an independent-measures study comparing three treatment conditions.Treatment I II III n 5 8 n 5 8 n 5 8 SS 5 35 SS 5 42 SS 5 70a. Compute the variance for each sample.b.
A researcher conducts an experiment comparing four treatment conditions with a separate sample of n 5 6 in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are
The following summary table presents the results from an ANOVA comparing four treatment conditions with n 5 10 participants in each condition.Complete all missing values. (Hint: Start with the df
A developmental psychologist is examining the development of language skills from age 2 to age 4.Three different groups of children are obtained, one for each age, with n 5 18 children in each group.
The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with a 5 .05 to determine whether there are any significant mean
The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with a 5 .05 to determine whether there are any significant mean
A research study comparing three treatment conditions produces T 5 20 with n 5 4 for the first treatment, T 5 10 with n 5 5 for the second treatment, and T 5 30 with n 5 6 for the third treatment.
The following values are from an independent-measures study comparing three treatment conditions.Treatments I II III n 5 8 n 5 8 n 5 8 SS 5 42 SS 5 28 SS 5 98a. Compute the variance for each
A research report from an independent-measures study states that there are significant differences between treatments, F(2, 36) 5 3.45, p , .05.a. How many treatment conditions were compared in the
A researcher used ANOVA and computed F 5 4.25 for the following data.Treatments I II III n 5 10 n 5 10 n 5 10 M 5 20 M 5 28 M 5 35 SS 5 1,005 SS 5 1,391 SS 5 1,180a. If the mean for Treatment III
The following data were obtained from an independentmeasures study comparing three treatment conditions.Treatment I II III n 5 6 n 5 6 n 5 6 N 5 18 M 5 1 M 5 2 M 5 6 G 5 54 SS 5 60 SS 5 65 SS 5 40
For the preceding problem you should find that there are significant differences among the three treatments.One reason for the significance is that the sample variances are relatively small. To
The following data summarize the results from an independent-measures study comparing three treatment conditions.Treatment I II III n 5 5 n 5 5 n 5 5 M 5 1 M 5 5 M 5 6 N 5 15 T 5 5 T 5 25 T 5 30 G 5
To create the following data we started with the same sample means and variances that appeared in problem 21 but doubled the sample size to n 5 10.Treatment I II III n 5 10 n 5 10 n 5 10 M 5 1 M 5 5
Use an ANOVA with a 5 .05 to check your prediction. Note: Because the samples are all the same size, MSwithin is the average of the three sample variances.b. Predict how the increase in sample size
An ANOVA produces an F-ratio with df 5 1, 34.Could the data have been analyzed with a t test? What would be the degrees of freedom for the t statistic?
The following scores are from an independentmeasures study comparing two treatment conditions.a. Use an independent-measures t test with a 5 .05 to determine whether there is a significant mean
Dene variability and explain its use and importance as a statistical measure.
Dene and calculate the range as a simple measure of variability and explain its limitations
Dene variance and standard deviation and describe what is measured by each.
Calculate variance and standard deviation for a simple set of scores.
Estimate the standard deviation for a set of scores based on a visual examination of a frequency distribution graph of the distribution.
Calculate SS, the sum of the squared deviations, for a population using either the denitional or the computational formula and describe the circumstances in which each formula is appropriate.
Calculate the variance and the standard deviation for a population.
Explain why it is necessary to make a correction to the formulas for variance and standard deviation when computing these statistics for a sample.
Calculate SS, the sum of the squared deviations, for a sample using either the denitional or the computational formula and describe the circumstances in which each formula is appropriate.
Calculate the variance and the standard deviation for a sample.
Dene biased and unbiased statistics.
Explain why the sample mean and the sample variance (dividing by n 2 1) are unbiased statistics.
Describe how the mean and standard deviation are represented in a frequency distribution graph of a population or sample distribution.
Describe the effect on the mean and standard deviation and calculate the outcome for each of the following: adding or subtracting a constant from each score, and multiplying or dividing each score by
Describe how the mean and standard deviation are reported in research journals.
Determine the general appearance of a distribution based on the values for the mean and standard deviation.
Explain how patterns in sample data are affected by sample variance
Which of the following is a consequence of increasing variability?a. The distance from one score to another tends to increase and a single score tends to provide a more accurate representation of the
What is the range for the following set of scores? Scores: 5, 7, 9, 15a. 4 pointsb. 5 pointsc. 10 or 11 pointsd. 15 points
For the following scores, which of the following actions will increase the range? Scores: 3, 7, 10, 15a. Add 4 points to the score X 5 3b. Add 4 points to the score X 5 7c. Add 4 points to the score
Which of the following sets of scores has the largest variance?a. 1, 3, 8, 12b. 12, 13, 14, 15c. 2, 2, 2, 2d. 22, 24, 25, 27
What is the variance for the following set of scores? Scores: 4, 1, 7a. 66 3 5 22b. 18c. 9d. 6
A set of scores ranges from a high of X 5 24 to a low of X 5 12 and has a mean of 18.Which of the following is the most likely value for the standard deviation for these scores?a. 3 pointsb. 6
What is SS, the sum of the squared deviations, for the following population of N 5 5 scores? Scores: 1, 9, 0, 2, 3a. 10b. 41c. 50d. 95
What is the standard deviation for the following population of scores?Scores: 1, 3, 9, 3a. 36b. 9c. 6d. 3
A population of N 5 8 scores has a standard deviation of s 5
What is the value of SS, the sum of the squared deviations, for this population?a. 72b. 24c. 8Ï3d. 9 8 5 1.125
Which of the following explains why it is necessary to make a correction to the formula for sample variance?a. If sample variance is computed by dividing by n, instead of n 2 1, the resulting values
Under what circumstances is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a sample?a. When the sample mean is a whole
What is the variance for the following sample of n 5 5 scores? Scores: 2, 0, 8, 2, 3a. 81 4 5 20.25b. 36 4 5 9c. 36 5 5 7.2d. Ï9 5 3
A researcher takes a sample from a population and computes a statistic for the sample. Which of the following statements is correct?a. If the sample statistic overestimates the corresponding
A researcher takes all of the possible samples of n 5 4 from a population.Next, the researcher computes a statistic for each sample and calculates the average of all the statistics. Which of the
All the possible samples of n 5 3 scores are selected from a population with m 5 30 and s 5 5 and the mean is computed for each of the samples. If the average is calculated for all of the sample
If a normal-shaped population with m 5 40 and s 5 5 is shown in a frequency distribution graph, how would the mean and standard deviation be represented?a. The mean is represented by a vertical line
If 5 points are added to every score in a population with a mean of m 5 45 and a standard deviation of s 5 6, what are the new values for m and s?a. m 5 45 and s 5 6b. m 5 45 and s 5 11c. m 5 50 and
A research study obtains a mean of 12.7 and a standard deviation of 2.3 for a sample of n 5 25 participants. How would the sample mean and standard deviation be reported in a research journal
For which of the following distributions would X 5 35 be an extreme score?a. m 5 30 and s 5 5b. m 5 30 and s 5 10c. m 5 25 and s 5 5d. m 5 25 and s 5 10
One sample is selected to represent scores in treatment 1 and a second sample is used to represent scores in treatment 2.Which set of sample statistics would present the clearest picture of a real
In words, explain what is measured by variance and standard deviation.
Is it possible to obtain a negative value for variance or standard deviation?
Calculate the mean and SS (sum of squared deviations)for each of the following sets of scores. Based on the value for the mean, you should be able to decide which SS formula is better to use.Set A:
For the following population of N 5 9 scores: 4, 2, 0, 5, 3, 2, 1, 7, 3a. Sketch a histogram showing the population distribution.b. Locate the value of the population mean in your sketch, and make an
Calculate SS, variance, and standard deviation for the following population of N 5 5 scores: 2, 13, 4, 10, 6.(Note: The definitional formula works well with these scores.)
Calculate SS, variance, and standard deviation for the following population of N 5 8 scores: 1, 3, 1, 10, 1, 0, 1, 3.(Note: The computational formula works well with these scores.)
Calculate SS, variance, and standard deviation for the following population of N 5 7 scores: 8, 1, 4, 3, 5, 3, 4.(Note: The definitional formula works well with these scores.)
Explain why the formula for sample variance is different from the formula for population variance.
For the following sample of n 5 6 scores:0, 11, 5, 10, 5, 5a. Sketch a histogram showing the sample distribution.b. Locate the value of the sample mean in your sketch, and make an estimate of the
Calculate SS, variance, and standard deviation for the following sample of n 5 8 scores: 0, 4, 1, 3, 2, 1, 1, 0.
A population has a mean of m 5 50 and a standard deviation of s 5 10.a. If 3 points were added to every score in the population, what would be the new values for the mean and standard deviation?b. If
Solve the following problems.a. After 6 points have been added to every score in a sample, the mean is found to be M 5 70 and the standard deviation is s 513.What were the values for the mean and
What were the values for the mean and standard deviation for the original sample?
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