1 Group workAnswer the following questions in small groups.Five sets of identical twins were selected at random from a population of identical twins. One child was selected at random from each pair to form an “experimental group.” These five children were sent to school. The other five children were kept at home as a control group. At the end of the school year the following IQ scores were obtained.Pair Experimental group Control group1 110 1122 125 1203 139 1284 142 1355 127 126Which of the tests that we have considered so far in DATA2002 can be applied here? Why might you use one instead of the other?If you were to proceed with a Wilcoxon signed rank test, calculate the test statistic.Under the null hypothesis of no difference in the mean IQ score between the experimental and control group, what is the expected value of the Wilcoxon signed rank test statistic?Let’s say we are testing a one sided alternative, i.e. the researchers hypothesised that the experimental group that were sent to school had higher IQs than the control group. If you had to guess which of the following p-values looks most reasonable for this example?0.00010.96630.09380.4367Don’t perform the test in R, just think about the observed test statistic, the expected test statistic and the sample size.
Question
1 Group workAnswer the following questions in small groups.Five sets of identical twins were selected at random from a population of identical twins. One child was selected at random from each pair to form an “experimental group.” These five children were sent to school. The other five children were kept at home as a control group. At the end of the school year the following IQ scores were obtained.Pair Experimental group Control group1 110 1122 125 1203 139 1284 142 1355 127 126Which of the tests that we have considered so far in DATA2002 can be applied here? Why might you use one instead of the other?If you were to proceed with a Wilcoxon signed rank test, calculate the test statistic.Under the null hypothesis of no difference in the mean IQ score between the experimental and control group, what is the expected value of the Wilcoxon signed rank test statistic?Let’s say we are testing a one sided alternative, i.e. the researchers hypothesised that the experimental group that were sent to school had higher IQs than the control group. If you had to guess which of the following p-values looks most reasonable for this example?0.00010.96630.09380.4367Don’t perform the test in R, just think about the observed test statistic, the expected test statistic and the sample size.
Solution
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The tests that can be applied here are the paired t-test and the Wilcoxon signed rank test. Both tests are used to compare two related samples, in this case, the experimental group and the control group. The paired t-test is used when the differences between the pairs follow a normal distribution, while the Wilcoxon signed rank test is a non-parametric test used when the differences between the pairs do not follow a normal distribution.
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To proceed with a Wilcoxon signed rank test, we first need to calculate the differences between the pairs. Then, we rank these differences in ascending order, ignoring the signs. The test statistic is the sum of the ranks of the positive differences.
Differences: 112-110=2, 125-120=5, 139-128=11, 142-135=7, 127-126=1 Ranks: 1, 2, 3, 4, 5 Test statistic: 1+2+3+4+5 = 15
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Under the null hypothesis of no difference in the mean IQ score between the experimental and control group, the expected value of the Wilcoxon signed rank test statistic is n(n+1)/4, where n is the number of pairs. In this case, n=5, so the expected value is 5(5+1)/4 = 7.5.
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Given that we are testing a one-sided alternative, i.e., the researchers hypothesized that the experimental group that were sent to school had higher IQs than the control group, we would expect a low p-value if this hypothesis is true. Looking at the given options, 0.0001 seems to be the most reasonable p-value for this example. This is because the observed test statistic (15) is much higher than the expected test statistic (7.5), suggesting a significant difference in IQ scores between the experimental and control groups.
Similar Questions
Similar intelligence test scores for identical twins reared apart are taken as evidence for the:
Identical twins who were brought up in dramatically different social environments score quite differently on intelligence tests. This supports which of the following?Multiple choice question.the impact of socialization on human developmentthe influence of heredity on intelligencethe impact of "nature" on intelligencethe failure of environmental factors to influence intelligence
Some research suggests that first born children may have higher IQ scores than their later born siblings. Do first-born identical twins have higher IQ scores than their second-born sibling? Data from a 1998 study were analyzed to determine whether first-born identical twins have higher IQ scores than their second-born siblings. Ten pairs of adult identical twins were assessed and their Full Scale IQ scores were calculated.Source: M. J. Tramo, W. C. Lodtus, T. A. Stukel, R. L. Green, J. B. Weaver, and M. S. Gazzaniga. “Brain Size, Head Size, and Intelligence Quotient in Monozygotic Twins.” Neurology 50, 1246–52.The following hypotheses were tested:H0: μd = 0Ha: μd < 0The following is the (edited) output for the test:SampleNMeanStDevSE MeanFirst-born10112.914.74.65Second-born10108.711.33.57Difference104.113.44.2395% lower bound for mean difference: −4.36t-test of mean difference = 0 (vs. > 0): t-value = 0.97, p-value = 0.179Which of the following is an appropriate conclusion based on the output? The data provide sufficient evidence to reject H0and, thus, conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins. The data do not provide sufficient evidence to reject H0. We therefore conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins. The data provide sufficient evidence to reject H0. We therefore conclude the data do not provide evidence to conclude that the mean Full Scale IQ scores for first-born identical twins is higher than that of second-born identical twins. The data do not provide sufficient evidence to reject H0. In other words, based on the data we cannot conclude that the mean Full Scale IQ scores for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.
The observation that each generation has a significantly higher IQ than the last is called:Question 7Select one:a.Generation biasb.IQ biasc.Testing effectsd.Flynn effecte.None of the above
Dr. Jamie is a personality expert who studies the impact that personality traits have on intelligence. For the purposes of her current research project, she is interested in examining the IQ scores of people who score highly in each of the five 'Big Five' personality factors. Personality traits are inherent to each person, so random assignment to personality type cannot be used. Participants would initially be assigned to groups based on their personality assessment scores across each of the five personality factors. Which type of experiment would this be?Group of answer choicesQuasi ExperimentTrue ExperimentBoth
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