Homework assignment topics 51-63 Georgina Salas Topics 51-63 EDCI Intro to Research 6300.62 Dr. A.J. Herrera
Topic 51 1. Which average is usually reported when the standard deviation is reported? The mean is usually reported. 2. What is meant by the term variability? It means the amount by which participants vary or differ from each other. 3. Is it possible for two groups to have the same mean but different standard deviations? Yes it is possible. 4. If all individuals in a group have the same score, what is the value of the standard deviation for the scores? The value of the standard deviation for the scores equals zero. 5. What percentage of the participants lies within one standard-deviation unit of the mean (i.e., on both sides of the mean) in a normal distribution? 68% of the participants lie within one standard-deviation unit of the mean. 6. The middle 68% of the participants in a normal distribution have scores between what two values if the mean equals 100 and the standard deviation equals 15? The two values would be 85 and 115. 7. If the mean of a normal distribution equals 50 and the standard deviation equals 5, what percentage of the participants have scores between 45 and 50? The percentage is 34%. 8. Does the 68% rule strictly apply if a distribution is not normal? No it does not strictly apply. The less normal it is, the less accurate the rule is. 9. If the standard deviation for Group X is 14.55 and the standard deviation for Group Y is 20.99, which group has less variability in its scores? Group X has less variability in its scores. 10. Refer to Question 9. Does Group X or Group Y have a narrower curve? Group X has a narrower curve.
Topic 52 1. If the median for a group of participants is 25.00, what percentage of the participants has scores above a score of 25.00? The percentage would be 50%. 2. Should the mean or the median be used with ordinal data? The median should be used with ordinal data. 3. How is the range of a set of scores calculated? The range is calculated by the highest score minus the lowest score. 4. Is the range or the interquartile range a more reliable statistic? Interquartile range is a more reliable statistic. 5. The interquartile range is the range of what? It is the range of the middle two quarters. 6. Suppose a researcher reported that for Group X, the median equals 55.1 and the IQR equals 30.0, while for Group Y, the median equals 62.9 and the IQR equals 25.0. Which group has the higher average score? Group Y has the higher average score. 7. On the basis of the information in Question 6, the scores for which group are more variable? Group Y the scores are more variable. 8. Which statistics discussed in this topic are measure of variability? Range or interquartile are measures of variability. 9. Which two statistics mentioned in this topic are averages (i.e., measures of central tendency)? One is median, and the second is interquartile. 10. When the median is reported as the measure of central tendency, it is customary to report which measure of variability? It is customary to report the interquartile range as the measure of variability.
Topic 53 1. Pearson r stands for what words? It stands for Pearson product-moment correlation coefficient. 2. When the relationship between two variables is perfect and inverse, what is the value of r? The value of the Pearson r would be 1.00. 3. Is it possible for a negative relationship to be strong? Yes it is possible for a negative relationship to be strong. 4. Is an r of -.90 stronger than an r of.50? Yes it is stronger. 5. Is an r of.75 stronger than an r of -.35? Yes it is stronger. 6. Is a relationship direct or inverse when those with high scores on one variable have high scores on the other and those with low scores on one variable have low scores on the other? It is direct relationship. 7. What does an r of 1.00 indicate? It indicates the relationship is perfect. 8. For a Pearson r of.60, what is the value of the coefficient of determination? The value is 36%. 9. What must be done in order to convert a coefficient of determination into a percentage? You need to multiply. 10. A Pearson r of.70 is what percentage better than a Pearson r of 0.00? The percentage is 49%.
Topic 54 1. What does the null hypothesis say about the difference between two sample means? The null hypothesis says there is no true difference between the means. 2. Are the values of t and df of any special interest to typical consumers of research? No they are not of any special interest to typical consumers of research. 3. Suppose you read that t=2.000, df=20, p>.05 for the difference between two means. Using conventional standards, should you conclude that the null hypothesis should be rejected? It would not be rejected. 4. Suppose you read that t=2.859, df=40, p>.01 for the difference between two means. Using conventional standards, should you conclude that the null hypothesis should be rejected? It would be rejected. 5. On the basis of the information in Question 4, should you conclude that the difference between the means is statistically significant? Yes because it has been rejected. 6. When a researcher uses a large sample, is he or she more likely or less likely to reject the null hypothesis than when a researcher uses a small sample? The researcher is less likely to reject the null hypothesis. 7. When the size of the difference between means is large, is a researcher more likely or less likely to reject the null hypothesis than when the size of the difference is small? The researcher is less likely to reject the null hypothesis. 8. If a researcher found that for a sample of 92 participants, r=.41, p>.001, would the researcher reject the null hypothesis? Yes the researcher would reject the null hypothesis. 9. Is the value of r in Question 8 statistically significant? No it is not.
Topic 55 1. ANOVA stands for what words? It stands for Analysis of Variance. 2. If a researcher compares two means for significance, will ANOVA and the t test yield the same probability? Yes it will yield the same probability. 3. If an ANOVA yields p<.05, should the null hypothesis be rejected? Yes it should be rejected. 4. If an ANOVA yields p>.05, is/are the difference(s) statistically significant? No it is not statistically significant. 5. If a researcher has four means on an achievement test for samples of students in four states, can he or she determine whether the set of differences, overall, is statistically significant by using a t test? Explain. The researcher cannot use a t test because it can only compare two means. 6. For the information in Question 5, could a researcher use an ANOVA for the same purpose? Yes, a single ANOVA can compare a number of means. 7. Should the typical consumer of research be concerned with the values of the degrees of freedom? No the consumer should not be concerned. 8. In an ANOVA table, which statistic is of greatest interest to the typical consumer of research? The typical consumer of research is only interested in the end result, which is the value of p. 9. If an overall ANOVA for three or more means is significant, it can be followed by what type of test to determine the significance of the differences among the individual pairs of means? The type of test is multiple comparisons tests.
Topic 56 1. Suppose a researcher drew random samples of urban, suburban, and rural children, tested them for creativity, and obtained three means. Should the researcher use a one-way or a twoway ANOVA to test for significance? Explain. The researcher should use a two-way ANOVA to test for significance because it compares the means of the tests. 2. Do the following means on a performance test indicate an interaction between type of reward and age? Yes it indicates an interaction between type of reward and age. 3. Do the means for Question 2 indicate a main effect for type of reward? No it does not. 4. Do the following means on an achievement test indicate an interaction between the method of instruction (A vs. B) and the aptitude of the students (high vs. low)? Yes it indicates an interaction. 5. Do the means for Question 4 indicate a main effect for method of instruction? Yes it does because it shows method A worked better. 6. Do the means for Question 4 indicate effect for aptitude? Yes it does because it show method A was successful. 7. If p>.05 for an interaction in an analysis of variance, should the researcher reject the null hypothesis? No the researcher should not reject the hypothesis.
Topic 57 1. Is it possible for a small difference to be statistically significant? Yes it is possible. 2. This topic describes how many types of considerations for determining practical significance? There are five considerations. 3. If the cost is very low, might a very small statistically significant difference be of practical significance? Yes it can be of practical significance. 4. Does a crucial difference need to be numerically large to be of practical significance? No it does not need to be numerically large. 5. According to this topic, should the acceptability of a treatment to the clients be considered when determining practical significance? Yes the treatment should be considered. 6. According to this topic, ethical considerations should play no role in the interpretation of the results of a study. Is this statement true or false? This statement is false. 7. Should determining the practical significance of a study s results be a mechanical process? No it should not.
Topic 58 1. In this topic, which experimenter had the smaller range of possible raw scores? Explain. Experimenter A had the smaller range of possible raw scores. They used a 20 item true/false scale with a possible raw score from 0to 20. 2. In this topic, the raw-score differences between the means (5 for Experimenter A and 10 for Experimenter B) were standardized by dividing each of them by what statistic? They were divided by the size of the standard-deviation unit. 3. When comparing the results of two experiments, is it possible for the experiment with the smaller raw-score difference to have a larger difference when the differences are expressed as d? No, it cannot have a difference higher than 3.00. 4. Suppose a researcher obtained a value of d of 2.95. Should this be characterized as representing a large difference? Explain. Yes, because 3.00 is the highest the value can get. 5. Suppose you read that the mean for an experimental group is 20.00 and the mean for the control group is 22.00. On the basis of this information alone, can you calculate the value of d? Explain. Yes because you have the two means to divide with. 6. Suppose a researcher conducted an experiment on improving algebra achievement, and the experimental posttest raw-score mean equaled 500.00 (sd=100.00), and the control group rawscore mean equaled 400.00 (sd=100.00). What is the value of the effect size for the experiment? The value is 0.5. 7. What is the definition of effect size? Effect size is the magnitude (i.e., size) of a difference when it is expressed on a standardized scale.
Topic 59 1. Are there universally accepted standards for describing effect sizes? There are no universally accepted standards for describing effect sizes. 2. What is the effective range of standard deviation units on both sides of the mean? Explain. The effective range of standard-deviation units is only three on each side of the mean. 3. If the value of d for the difference between two means equals 1.00, the experimental group s mean is how many standard-deviation units higher than the control group s mean? It is 2.00 units higher. 4. What value of d is associated with the label extremely large? The value of d for extremely large is 1.40+. 5. According to Cohen, what label should be attached to a value of d of 0.80? The label should be large. 6. Under what circumstance will a negative value of d be obtained? A negative is obtained when the control group s mean is higher than the experimental group s mean. 7. Should a test of statistical significance be conducted before or after computing d and interpreting its value using labels? It should be conducted before computing d.
Topic 60 1. According to this topic, what are the two measures of effect size that are very widely reported? The two measures of effect size that are widely reported are effect-size r and correlation coefficients. 2. Correlation coefficients are expressed on a standard scale that always ranges from -1.00 up to what value? 1.00 3. A value of r should be interpreted by doing what? A value of r should be interpreted by first squaring them (r2). 4. A value of r equals to 0.40 is what percentage of the distance above zero? 20% 5. If there is one group of participants and a researcher wants to determine the strength of the relationship between two sets of test scores, which measure of effect size would typically be more appropriate? The measure used should be r and r2. 6. A value of d of 1.20 corresponds to what value of r2? It corresponds to 0.264. 7. A value of r of 0.600 corresponds to what value of d? It corresponds to 1.50.
Topic 61 1. What is the meaning of the prefix meta as used in this topic? Meta means occurring later and/or being later and more highly organized. 2. Meta-analysis is a set of statistical methods for doing what? It is a set of statistical methods for combining the results of previous studies. 3. Two types of random errors tend to be canceled out in the process of conducting a metaanalysis. What are the two types of random errors discussed in this topic? The two types of errors are random sampling errors and systematic errors. 4. In the report of a meta-analysis, the main thrust of the conclusions is based on what? It is based on a mathematical synthesis of the statistical results of the previous studies. 5. Very briefly state the second important characteristic of meta-analysis. The second important characteristic is that it typically synthesizes the results of studies conducted by independent researchers. If one researcher makes a systematic error, the errors of his erroneous result will be moderated when they are averaged with the results obtained by other independent researchers who have not made the same error.
Topic 62 1. According to this topic, is it easy to find perfectly strict replications of previous studies? No it is not easy. 2. What is one very important way that various studies on a given topic differ? One very important way that various studies on a given topic often differ is that various researchers frequently use different measures of the same variable. 3. Computing a mean difference across studies that used measurement scales with different possible numbers of score points is meaningless. What is suggested in this topic to overcome this problem? The solution to the problem being considered is to use a measure of effect size. 4. What should usually be done when the studies to be used in a meta-analysis have different sample sizes? The two values of d can be averaged by adding the two values and then dividing by two. 5. Is d the only standardized measure of effect size used in meta-analytic studies? Explain. No it is not. The value of r can be averaged while weighting the average to take into account varying sample sizes.
Topic 63 1. What was the sample size for the meta-analysis of the 162 studies mentioned in this topic? The sample size was 109,654. 2. According to this topic, is a meta-analysis or a review consisting of a narrative discussion of the literature more objective? A review consists of a narrative discussion of the literature more objective. 3. Even if a meta-analysis yields highly reliable results based on objective mathematical procedures, are its results necessarily valid? Explain. No, because the meta-analysis can have serious methodological flaws resulting in a lack of validity. 4. What is the name of the final potential weakness of meta-analysis? It is called publication bias. 5. What is a partial solution to the problem you named in your response to Question 4? A partial solution to this problem is for those conducting meta-analysis to search for studies that might be reported in dissertations, convention papers, government reports, and other nonjournal sources, where there might not be as much bias against studies with statistically insignificant results.