EDUC 856 Exam 2
A researcher wished to discover whether a special course called "Attacking the SATs" reduced anxiety levels about taking the test. A random sample of 30 high school seniors was selected and their anxiety levels were ranked from 1 to 3 where 1 = low anxiety, 2 = no anxiety, 3 = high anxiety). They then took the three week course on attacking the SAT. Afterward, their anxiety levels were measured.
Data are on the ordinal scale of measurement. Therefore, the researcher should use the Wilcoxon Signed-Rank test.
A researcher interested in the effects of marijuana on pulse rates. A group of 20 college students was randomly selected and their pulse rates recorded. They were given (and smoked) one marijuana cigarette and 30 minutes later their pulse rates were taken again. The pulse rates were found to be skewed. Therefore, the interval scores are converted to ordinal ranks.
Data were converted to the ordinal scale of measurement. Therefore, the researcher should use the Wilcoxon Signed-Rank test.
Assume that a researcher wishes to discover whether there is a co-occurrence between gender and altruism (kindness). The researcher uses Conners' Altruism Device (CAD) as the dependent measure. Scores on the CAD are presented as T scores (M = 50, SD = 10) which are on the interval scale of measurement. A random sample of 90 undergraduates are administered the CAD (45 males, 45 females).
Gender is a nominal variable. Therefore, we would use the point-biserial coefficient to calculate the correlation.
A researcher wants to determine whether, among elementary school children, there is a significant association between height (measured in inches) and running speed (measured in seconds). A random sample of 60 children is selected. Each child is measured for height and time in the 40-yard dash.
Use the Pearson correlation coefficient.
A researcher for the Registry of Motor Vehicles became interested in whether recidivism among convicted drunken drivers is affected by the judicial outcome. A random sample of convicted drunken drivers was selected. The drivers were then randomly divided into two groups. The members of Group A received heavy fines and temporarily lost their licenses. The members of Group B were not fined but were placed in a six-month rehabilitation program and temporarily lost their licenses. Two years later, all subjects were checked for repeat convictions. The groups were compared on the basis of the number of subjects in each group found to have and not have repeat convictions. Thus, data were on the nominal scale of measurement. This is experimental research, between-subjects. The independent variable (whether subjects go into the rehabilitation program) is manipulated by the researcher. The potential for uncovering a causal relationship is thus available. The dependent variable (repeat convictions versus no repeat convictions) is measured in nominal form.
This is a 2 x 2 Chi-Square.
A psychologist wants to decrease the number of tantrums displayed by her two year-old. Whenever the child is in public, the child cries, jumps up-and-down, and runs away from the parents. The psychologists learn that the parents often give the child what he wants in order to stop the tantrums. The problem is that the behavior has only become worse. The behavior does not occur at home. The psychologist helps the parents develop a program of planned ignoring. This takes much work and the psychologist engages in role playing with the parents, modeling their correct behavior, etc. During this phase of discussing the program with the parents, a baseline period occurs for two weeks where the parents take the child to K-Mart every day and record the duration and severity of the child's tantrums. The intervention is implemented and the parents take the child to K-Mart every day. The intervention lasts for two weeks and the parents record the duration and severity of the child's tantrums.
This is a single-subjects, A-B research study. Use both graphic and statistical methods. Graphing can be completed through Excel. Statistically, the data can be analyzed using five techniques: (1) ordinary least squares regression (i.e., point-biserial correlation coefficient), (2) the reliable change index (C), (3) Cohen's d coefficient, (4) percentage mean baseline change (MBC), and (5) the percentage of non-overlapping distributions (PND).
A teacher wants to increase the number of times a third grader, George, completes his homework. He is a well-behaved and popular boy, but he does not complete his homework regularly. The teacher meets with the parents and develops an intervention. George's parents agree to get him a desk. The parents also agree to work with George at a set time each night for one hour to help George complete his assignments. A baseline period occurs for one month where the teacher counts the number of times the George completes his homework. Afterward, the intervention is implemented and it lasts for one month. At the end of the month, there has been little improvement. The teacher meets again with the parents and finds out that they did not work with George every night. After threatening to call the Division of Youth and Family services (as well as the use of other more positive techniques, the teacher is able to resolve the conflict. The new program is implemented. This time, in addition to greater adherence by the parents, George is also offered a token by the teacher each time he completes his homework. He can turn-in the tokens at the school store for rewards. The program is implemented for one month and the teacher counts the number of times George completes his assignments.
This is a single-subjects, A-B-C research study. Use both graphic and statistical methods. Graphing can be completed through Excel. Statistically, the data can be analyzed using five techniques: (1) ordinary least squares regression (i.e., point-biserial correlation coefficient), (2) the reliable change index (C), (3) Cohen's d coefficient, (4) percentage mean baseline change (MBC), and (5) the percentage of non-overlapping distributions (PND).
A market researcher has the hypothesis that people with high incomes are more likely to watch the 11:00 p.m. news that the 6:00 p.m. news. A random sample of 80 participants is selected. The participants are divided equally into two groups according to whether they earn $60,000 per year (the high income group) and less than $20,000 per year (the low income group). Of the high-income participants, the researcher finds a frequency of 30 who report a preference for watching the 11:00 p.m. news. And, among the low income participants, the researcher finds a frequency of 15 who report a preference for watching the 11:00 p.m. news. The independent variable is income. The dependent variable is on the nominal scale and it is the binary answer to whether the participant prefers the early or late news program.
Use a 2 x 2 Chi-Square: two rows for the independent variable of income (high vs. low) and two columns for the dependent variable of which they prefer, the 6:00 p.m. news or the 11:00 p.m. news.
Among Republicans, a researcher hypothesizes that there is a dependable relationship between party loyalty and the number of hours per week spent working for their candidate. A 20-item "Party Loyalty Questionnaire" is designed. It is given to 60 Republicans. The questionnaire yields a single, composite score. Its internal consistency reliability is high (alpha coefficient = .90). Scores from the questionnaire are then compared with the average number of hours per week being volunteered to the candidate. The dependent variable is party loyalty which is on the interval scale of measurement.
Use the Pearson correlation coefficient.
It has been traditional for the man rather than the woman to receive the check when a couple dines out. A researcher wondered whether this would still be true if the woman was clearly in charge, asking for the wine list, and so on. A large random sample of restaurants was selected. One couple was used in all restaurants, but in half the man assumed the traditional in-charge role, and in the other half the woman was in charge. The data were in the form of the number of times the check was presented to each member of the couple. The independent variable (man or woman in charge) was clearly manipulated. The dependent variable was whether the man or the woman received the check. The dependent variable is on the nominal scale.
Use chi square, in this instance a 2 x 2 chi square, with the independent variable (who is in charge) in the rows and the dependent variable (who gets the check) in the columns. Post hoc testing is not necessary because the analysis is a 2 x 2 chi square. Had this been a test of association, the chi square could have been followed up with either the phi coefficient or the tetrachoric coefficient. Remember from the lecture on meta-analysis that any inferential statistic can be turned into a correlation coefficient.
A political analyst attempted to find out whether the political slant of a newspaper affects the voting preference of its readers. In a large eastern city, a random sample of homes was selected where Newspaper L (Liberal) was delivered. Also a random sample of homes receiving Newspaper C (Conservative) was selected. The voting preference of each head of household was obtained and categorized as Republican, Democrat, or Other. This is post-facto research. The subjects themselves chose which newspaper independent variable) to have delivered. The dependent variable is on the nominal level of measurement. The measures are in the form of how many persons subscribe to which newspaper and how many persons vote in which category. Frequency of occurrence within mutually exclusive categories defines the nominal case.
Use chi square, in this instance a 2 x 3 chi square, with the independent variable (political slant - liberal or conservative) in the rows and the dependent variable (Republican, Democrat, Other) in the columns. A significant overall effect would require post hoc testing in the form of follow-up a 2 x 2 chi square analyses. The follow-up analysis would need to be apportioned using the Bonferroni Correction.
A researcher decides to develop an assessment system to assist clinician in the diagnosis of attention deficit/hyperactivity disorder (ADHD) among college students. It's called the College ADHD Response Evaluation (CARE) and it consists of two questionnaires: a student response inventory (SRI) and a parent response inventory (PRI). The researcher wishes to investigate the validity of the DSM-IV based inattentiveness scale of the SRI. The researcher administers the self-report instrument to 50 college students with ADHD and 50 normal controls. Participants were classified on the test according to whether they had high scores (i.e., a T score > 65, i.e., a score 1.5 SDs above the M) or not (T score < 65). Testing was completed at the time students entered the University of Delaware. Four years later, results from the test were compared to the dependent variable of whether the Academic Services Center at the University eventually classified participants as to whether ADHD was present, or not. The dependent variable was on the nominal scale of measurement.
Use diagnostic utility/efficiency statistics, including: sensitivity, specificity, positive and the odds ratio.
Some researchers, such as Michael Eysenck (son of the famous English psychologist, Hans Eysenck), have concluded that there are cognitive biases among people with anxiety disorders. In order to test part of this theory, researchers made the prediction that anxious individuals will have more memories of defeat than of victory. A group of senior college varsity football players was selected and given a test of trait anxiety (N = 200). Based on the test scores, two groups were formed: high anxiety (n = 40) and low anxiety (n = 40). The football players in these two groups were then asked to recall the most vivid memories of their high school football careers. Responses were coded by the researchers according to whether the memory recalled a triumph or defeat.
Use the Chi-Square; specifically, a 2 x 2 Chi square: two rows for the independent variable of anxiety (high vs. low) and two columns for the dependent variable of which they recalled a victory or defeat.
A market researcher, working for a manufacturer of hair coloring for men, wished to establish whether men without grey hair enjoyed life more. A large random sample of males aged 40 and older was selected and categorized as to hair color — grey hair present vs. grey hair absent. Each participant was then asked to answer yes or no to the question, "On balance, would you say you are enjoying life?" The independent variable is hair color. The dependent variable is on the nominal scale and it is the binary answer to whether the participant is enjoying life.
Use the Chi-Square; specifically, a 2 x 2 Chi square: two rows for the independent variable of hair color and two columns for the dependent variable of enjoying life.
Acid rain is considered by some environmentalists to be the nation's most serious environmental problem. It is formed by the combination of water vapor in clouds with nitrogen oxide and sulfuric dioxide emissions from the burning of coal, oil, and natural gas. The acidity of rain in southern, central, and northern Florida consistently ranges from 4.5 to 5 on the pH scale, a decidedly acid condition. To determine the effects of acid rain on the acidity of soils in a natural ecosystem, engineers at the University of Florida's institute of Food and Agricultural Sciences irrigated eight experimental plots each in southern, central, and northern Florida. The resulting pH tests were skewed and converted to ranks. The researchers wanted to determine whether irrigation reduced pH levels more in one region than in the other two.
Use the Kruskal-Wallis (K-W) test. If the K-W analysis is significant, post hoc testing will be apportioned through the application of three (3 (3-1)/2) Mann-Whitney U tests. The familywise error rate will be corrected using the Bonferroni correction.
A manufacturer of household appliances is considering one of three chains of department stores to be the exclusive sales merchandiser for its products in a particular region of the United states. Before choosing one chain, the manufacturer wants to make a comparison of the product exposure that might be expected for the three chains. Eight locations are selected where all three chains have stores. On a specific day, 30 random shoppers entering the store are asked to rank the quality of the store on a scale of 1 to 6, with higher scores indicating greater satisfaction. The question the manufacturer has is whether any one of the three stores has higher customer satisfaction.
Use the Kruskal-Wallis (K-W) test. If the K-W analysis is significant, post hoc testing will be apportioned through the application of three (3 (3-1)/2) Mann-Whitney U-tests. The familywise error rate will be corrected using the Bonferroni correction.
A researcher for an electronics corporation wants to establish whether, other things being equal, the tonal quality of a stereo system is judged to be better as the size of the speaker is increased. A random sample of participants was selected and asked to listen to the same CD played on "different sound systems." Actually, the amplifier, the size and quality of the speaker, and so on remained the same. Only the size of the speaker enclosure was allowed to vary. Three enclosure sizes were used—small, medium, and large. The subjects were asked to rank-order their preferences, from 3 (best) to 1 (worst). The order in which the participants were presented with the various speaker sizes was counterbalanced, so that some participants had the large speaker first, others the small speaker first, and so on. The dependent variable (judgment of tonal quality) is in ordinal form, that is, the participants rank order the three speakers.
Use the Kruskal-Wallis statistic to compare the ranks (1, 2, and 3) of each participant under the three listening conditions. If the overall analysis is significant, post hoc testing will be completed using a series of Mann-Whitney U tests. The family wise error rate will be adjusted using the Bonferroni correction.
A researcher assumes there will be a difference in the amount of TV viewing by the principal wage earners in high and low socioeconomically placed families. A random sample of families is selected and coded according to three classes of socioeconomic status: less than high school, high school graduate, and 13 years of education or more. The person with the highest level of education in each household was then contacted and asked for the average number of hours of TV viewing per day in their home. Specifically, they were asked whether, on average, members in their family typically watched: (1) less than ½ hour of TV per day, (2) ½ hour to 1 hour, (3) 1-2 hours, (4) 2-3 hours, (5) 3-4 hours, (6) more than 4 hours. The dependent variable (number of hours of TV viewing per day) is considered to be on the ordinal scale.
Use the Kruskal-Wallis statistic. If the overall analysis is significant, post hoc testing will be completed using a series of Mann-Whitney U tests. The family wise error rate will be adjusted using the Bonferroni correction.
A researcher was interested in establishing whether attendance in a preschool program affects the social maturity level of children. A random sample of 60 kindergarten children was selected and watched closely by trained observers for one full week. The children were on the basis of perceived social maturity using Likert scaling (5 = strongly agree that the child was socially mature down to 1 = strongly disagree that the child was socially mature). The children were then divided into two groups on the basis of whether or not they had previously attended a day-care center. This is post-facto research; each child's parents, not the researcher, decided whether the child would attend a day-care center. The independent variable (whether the child attended the day-care center) and the dependent variable of social maturity was on the ordinal scale of measurement.
Use the Mann-Whitney U test which compares the ranks of two independent groups.
Some researchers suspect that because of academic and other frustrations, adolescents with learning disabilities (LD) have more symptoms of depression and even possibly higher levels of suicidal ideation than would non-LD adolescents. Two groups of 16-year-old students, one labeled LD and the other non-LD (50 male adolescents in each group), were selected on the basis of a certain school district's records. All students were then given the Reynolds Suicide Ideational Questionnaire (SIQ-JR). Scores from the SIQ-JR are in interval form, but the sample means are much higher than the sample median and the standard deviation is large, relative to the mean, the distributions are significantly skewed to the right. With severe skews of this sort, reported as z = +2.40 and z = +2.45, respectively, the interval data were converted to ordinal.
Use the Mann-Whitney U test which compares the ranks of two independent groups. The Mann-Whitney was used because the interval data were converted to ranks.
A researcher wished to test the hypothesis that taller men are more likely than shorter men to be judged as leaders. A random sample of 30-year-old men was selected. They were measured for height and placed into two groups: short (5' 8" and less vs. 5' 9" and more). The men were then brought before a panel of personnel managers and rank-ordered on the basis of perceived leadership qualities, with the rankings ranging from a low of 1 to a high of 5. Each subject was assigned the median rank of the panel's decisions. The independent variable (height) was not manipulated. The dependent variable of leadership qualities was on the ordinal scale.
Use the Mann-Whitney U test.
A researcher wants to test the hypothesis that students are more likely to show verbal aggressiveness (assertively challenge the professor, etc.) in small classes than they are in large classes. Random samples of 10 large classes at the University of Delaware (UD) (i.e., 50 students or more) and 10 small classes at UD (less than 25 students) are selected. A three-judge panel visits each classroom and ranks the aggressiveness of each scale using the percentage of aggressiveness observed. The percentages are ranked data.
Use the Mann-Whitney U-test.
A team of chemists has isolated an insecticide that will increase the pulse of the corn earworm. The goal is to control these crop-damaging insects by inducing fatal heart attacks. Two corn fields were randomly selected. One field was sprayed with the new insecticide and the other acted as the control. The percentage of damage was recorded for each field. Percentages, like percentiles, are ordinal units.
Use the Mann-Whitney U-test.
A political analyst wishes to establish whether a difference in income exists between registered Republicans and registered Democrats. Random samples are selected of 25 Republicans and 25 Democrats, and the annual income for each participant is obtained. Because the income distribution in the population is known to be skewed, the interval scores are converted to ordinal ranks.
Use the Mann-Whitney test.
A researcher is interested in whether, among elementary school children, there is linkage between being taller and being able to run faster. To test this hypothesis, a random sample of 10 year olds obtained. Each child is measured for height (in inches) and timed in the 100 yard dash (in seconds). The dependent variable is time which is on the interval scale of measurement.
Use the Pearson correlation coefficient.
A researcher wanted to test the hypothesis that racial prejudice is a function of personal authoritarianism. A random sample of college students was selected and measured on the F scale of the MMPI, an index of personal rigidity and authoritarianism and its measured in T-score units which are interval. All participants were then given the A-S (for Anti-Semitic) scale, a measure of prejudice toward Jews. The A-S scale is the dependent variable and it also is measured in T-score units.
Use the Pearson correlation coefficient.
An investigator studying the relationship between anxiety and school achievement selects a random sample of 15 fifth-grade students, all aged 10 years. Each student is given an anxiety test (the scores are interval and high scores signify anxiety), and then these measures are paired with the students' scores on an academic achievement test. Data from the achievement test are measured on the interval scale.
Use the Pearson correlation coefficient.
A group of 12 third-graders is randomly selected and given a standardized arithmetic test. A trained observer watches the children for a period of one week and then rank-orders them in terms of the amount of introversion each child displays. The dependent variable is the amount of introversions and the researcher wishes to discover whether there is a co-occurrence between arithmetic achievement and introversion.
Use the Spearman's rho coefficient to calculate the correlation. Rho is used instead of the Pearson r because introversion is rank ordered.
Some psychologists believe that language skills are controlled by one brain hemisphere and musical skills by the other. To test this, a researcher is studying whether musical ability correlates inversely with reading ability among six year-old children. A random sample of six year-olds is selected and given a reading comprehension test which is evaluated on the interval scale of measurement. Each child is also evaluated by a musicologist (for pitch, rhythm, etc.) and then rank ordered on music ability. The dependent variable is music ability.
Use the Spearman's rho coefficient to calculate the correlation. Rho is used instead of the Pearson r because music ability is rank ordered.
A researcher working for a large corporation wished to test the hypothesis that the company's toothpaste, containing fluoride, reduces dental caries. A random sample of 18-year-olds was selected, and all participants were rated on the quality of their teeth: 3 points if no caries were present, 2 points if one carie was present, and 0 points if there were more than one carie. A dentist then filled the cavities for all participants having them. For the next three years, all participants received free monthly supplies of the fluoride toothpaste. Finally, at age 21, the participants were again rated on the quality of their teeth. The researcher then compared the number of persons with caries found in the first dental checkup with the number of persons with caries found at age 21. This is experimental research, repeated-measures design (in this case, before-after). The independent variable (toothpaste) is manipulated (rather than being assigned on the basis of whether the participants, on their own, were using it). The dependent variable is on the ordinal scale of measurement.
Use the Wilcoxon Signed Rank test.
A researcher wishes to discover whether the intake of orange juice affects the potassium (K) level in the bloodstream. A group of 30 elderly patients is randomly selected from those in a large nursing home, where the previous diet has been controlled. K levels are obtained for each subject and are on the interval scale of measurement. Then each participant is given a pint of orange juice. Two hours later, K levels are again measured.
Use the dependent samples t-test (a.ka. paired-samples t-test).
An investigator is interested in discovering whether a role-reversal procedure will influence men's attitudes toward women. Two samples of married men matched on IQ on the theory that a man's level of intelligence may be a factor in his willingness to change to a more enlightened attitude. were randomly and independently selected. The men in Group A were then instructed to reverse roles with their wives for the next two week-ends (he doing her work and she doing his). The men in group B were told nothing. Two weeks later men in both groups were given a test measuring their attitudes toward women's roles in our society (scores were on the interval scale and low scores indicating a traditional attitude and high scores a more enlightened attitude).
Use the dependent samples t-test (paired t-test) because the participants were matched on IQ.
A researcher is interested in whether systematic desensitization (SD) can be used to reduce anger among violent offenders. A random sample of 100 inmates was selected from a prison population of inmates who had all been convicted of violent felonies. Each participant was tested on a standardized anger provocation scale measured on the interval level. High scores reflect higher levels of anger. At the end of six weeks of SD training, the participants were all tested again.
Use the dependent samples t-test (paired t-test).
A study was conducted to determine the effects of practice and fatigue on muscle strength. A random sample of 20 recruits on their first day at the police training academy was selected and asked to do as many push ups as possible, which is on the interval level. After five weeks of training and exercise, the recruits were asked to do as many push ups as they could.
Use the dependent-samples t-test (paired-samples t-test).
A group of freshman football players in high school were told they had to bulk up in order to have any chance of playing on the varsity the following year. The group was randomly assigned into two groups, and for three months the young men were subjected to a strict weight training program. Group I, however, was also given a daily food supplement (without steroids) alleged to increase muscle mass, while Group II was given an identical appearing placebo. The dependent variable was weight gain in pounds which is on the interval scale of measurement.
Use the independent samples t-test (unpaired t-test).
A researcher believes increasing illumination increases speed of productivity among piecework employees. Two groups are randomly selected from among the piecework employees at the Hawthorne Electric Company. Each participant is given 100 transistors to solder to the connecting relays. The time taken (in hours, which is interval data) is recorded for each participant to complete the task. Group A works under the normal plant lighting conditions, while group B works under conditions where the illumination is increased by 50%.
Use the independent samples t-test (unpaired t-test).
A researcher is interested in whether coaching can have any effect on math SAT scores. A group of 100 high school seniors was randomly selected from a large metropolitan school district. The group was then randomly divided into two subgroups. One group was given three months of daily coaching in those math skills deemed important to the SAT, while the other group spent the same amount of time each day watching reruns of the TV show "Happy Days." At the end of the three-month period, all students took the SAT and their math scores were compared. his is experimental methodology, the independent variable being based on whether the students received the coaching. The dependent variable is math SAT scores which come in at least interval form.
Use the independent samples t-test (unpaired t-test).
A study was designed to test whether presenting one side or both sides of an argument is more effective in changing attitudes. Perhaps presenting just the pro side would be more effective because an audience might not be fully aware of the anti side. Or perhaps to appear impartial and to avoid having members of the audience go over to the anti side and therefore tune out the pro message, it would be more effective to at least present some of the anti arguments. A large random sample was selected, and the participants were randomly assigned to one of two conditions. Group A heard only the pro side of the issue, whereas Group B heard the entire pro side plus a few minutes of anti arguments. Both presentations were made by the same person. A questionnaire, tapping attitudes toward the issue, was then filled out by each participant. This is experimental research. The independent variable (one-sided versus two-sided presentations) was manipulated by the researcher. As no matching occurred and no attitude testing was done prior to the presentation, this was a between-subjects (after-only) design. The questionnaire was scored as interval data, and the assumption of a normal distribution was made.
Use the independent samples t-test (unpaired t-test).
A researcher wanted to find out whether IQ is a function of family size. IQ was measured on the interval scale. The speculation was that among families with fewer children, each child receives more parental attention and intellectual stimulation and should therefore have a higher IQ than would a child reared in a larger family. A large random sample of two-child families was selected as well as a similar sample of six-child families. The IQs of all children were measured, and the two sample groups were compared. The independent variable (family size) was a subject variable and was not manipulated. (Natural forces or their own decision, not the decision of the experimenter, determined which families had small or large numbers of children.) Thus, even if significance is established, the causal factor remains in the realm of speculation. Could it be, instead, that lower-IQ parents have more children? IQ scores are considered to be interval measures, and the underlying distribution to be fairly normal.
Use the independent-samples t-test. If the score for each child is to be used separately, use the equation for unequal values of N (there are three times as many IQ scores in the six-child families). If the children's IQ scores are to be averaged within each family, then equal values of N can be maintained.
A researcher wished to test the hypothesis that older men sleep less than younger men do. Random samples of 30-year-old men, 50-year-old men, and 70-year-old men were selected. Each subject was brought to a sleep laboratory and measured as to how many hours of sleep per night occurred. It also has been established that heavier people have more problems sleeping than thinner people and the researcher wanted to control this confound to valid interpretation. The independent variable (age) was a subject variable and it was not manipulated. The dependent variable was the number of hours of sleep and it was on the interval scale.
Use the one-way ANCOVA with weight employed as the covariate. Given that three groups took part in the investigation, if the overall analysis is significant, post hoc tests will be necessary and they will need to be completed using the Bryant-Paulson procedure.
An investigator wished to test the hypothesis that reading speed is a function of how extensively a student reads. A random sample of high school seniors was selected in September, and the subjects were asked how many books they had read during the summer. The subjects were then categorized in the following groups: group 1, no books read; group 2, one to three books; group 3, four to six books; and group 4, more than six books. Reading speed tests were then administered, the scores being in the form of words per minute. The participants were assigned to groups on the basis of how many books they themselves had chosen to read. The dependent variable was on the interval scale of measurement. The dependent variable (reading speed in words per minute) provides at least interval data. The distribution is close enough to normality to use interval tests.
Use the one-way ANOVA, the F ratio. If F is significant, proceed with Tukey's HSD or Games-Howell adjustment if there is a violation of the homogeneity assumption.
A researcher wished to find out whether the perception of a person's height depends on that person's perceived status. A random sample of army inductees was selected and equally divided into four groups. An actor gave a short address to each group separately, extolling the joys of army life. For the first group, the actor was dressed as a private; for the second, as a sergeant; for the third, as a captain; and, finally, for the fourth group, as a colonel. The inductees were asked to fill out a questionnaire evaluating the speech. Among the questions was one asking for an estimate of the lecturer's height. This is experimental research, between-subjects (after-only) design. The independent variable (perceived status) was manipulated by having the same actor wear different uniforms. The dependent variable (estimated height) provided at least interval data in this study. In addition, when the analysis was conducted, there was a violation of the homogeneity of variance assumption.
Use the one-way ANOVA. If the overall analysis is significant, post hoc testing must be completed using the Games-Howell's modification because there was a violation of the homogeneity of variance assumption.
A researcher wishes to discover whether the intake of orange juice affects the potassium level in the bloodstream. A group of 60 elderly patients is selected from those in a large nursing home, whether the previous diet has been controlled. Potassium blood levels are measured for each participant. Then each participant is given a pint of orange juice. Two hours later, potassium levels are again measured. This is experimental research, repeated-measures design (in this case, before-after). The independent variable (orange juice) is manipulated (rather than being assigned on the basis of whether the participants, on their own, were using it). The dependent variable is on the interval scale of measurement.
Use the paired t-test.
A researcher wished to test the hypothesis that special phonics training affects the reading ability of children with learning disabilities (LD). Two groups of children with LD were randomly selected and matched person-for-person on the basis of Full Scale IQs (FSIQs) from the WISC. Within each pair matched on FSIQs, one child was assigned to the experimental group and one to the control group. Both groups were administered a curriculum-based measure (CBM) of reading at the beginning of the study. The experimental group underwent six weeks of phonics training, whereas the control group did not. At the end of the six-week period, both groups were administered the CBM reading measure. Likewise, six months after the end of the study, both groups were administered the CBM reading measure. This is experimental research, between-subjects design. The independent variable was placement in the experimental- or control-treatment groups. The dependent variable (CBM reading measure) provided at least interval data in this study.
Use the repeated measures way ANOVA. If the overall analysis is significant, post hoc testing is not necessary because there are only two groups.
A longitudinal research study is conducted wherein the investigator wishes to establish that fluoride reduces dental caries. A large random sample of 100 six year-olds is selected. The group is given toothpaste containing fluoride. The participants are then evaluated at age 6, 8, 10, 12, 14, 16, and 18 years of age. At each age, the total number of dental caries is counted. The dependent variable (number or caries at each age) provides normally distributed data, which are at least interval. The fluoride toothpaste is introduced at age immediately after the age 10 assessment.
Use the time series analysis which is nothing more than a repeated measures ANOVA run on one group. If the overall analysis is significant, post hoc testing will need to be completed using dependent-samples (paired) t-tests. Post hoc tests will need to be adjusted using the Bonferroni correction.
A researcher wishes to test the subliminal perception hypothesis. A random sample of 100 college freshman is selected. They watch a movie once every two days for a period of two weeks. Each time they are offered fee popcorn and Coca-Cola during the middle of the movie. Thus, there are 14 sessions in all. After the third session, and during the showing of the fourth film onward, the participants are exposed to two messages flashed on the screen every five seconds, each lasting only 1/3,000 of a second (a point far below the human visual threshold). The alternating messages are "Hungry? Each popcorn" and "Thirsty? Have a Coke". Popcorn and Coca Cola consumption are measured after each movie. Both variables are on the interval scale of measurement.
Use the time series analysis which is nothing more than a repeated measures ANOVA run on one group. If the overall analysis is significant, post hoc testing will need to be completed using dependent-samples (paired) t-tests. Post hoc tests will need to be adjusted using the Bonferroni correction.
A researcher wishes to determine whether the implementation of a time-out procedure increases on-task time. A fourth grade teacher is having difficulty keeping students in her classroom on-task. There are 20 students in the classroom. The researcher helps the teacher learn correct usage of time-out methodology. Prior to implementation of the time-out procedure, the researcher observes children in the classroom on three occasions. Group time sampling is used across 15 minute periods with each minute divided into three 10-second intervals for observing and three 10-second intervals for recording. Data therefore are on the interval scale of measurement. The class then undergoes four weeks of time-out training. At the end of the four-week period, the researcher observes the children in the class for another three occasions using group time sampling. This is experimental research, repeated-measures design. The independent variable (time-out procedure) is manipulated. The dependent variable is the amount of on-task behavior which is measured on the interval scale of measurement.
Use the time series analysis which is nothing more than a repeated measures ANOVA run on one group. If the overall analysis is significant, post hoc testing will need to be completed using dependent-samples (paired) t-tests. Post hoc tests will need to be adjusted using the Bonferroni correction. The hypothesis is that on-task time will increase between time intervals 3 (last pretest measure) versus time intervals 4, 5, and 6.
A cultural anthropologist became interested in discovering whether differences in the age of menarche (the age when young women have their first menstrual cycle) are a function of climate. Two groups of young women were selected - one from a northern climate (Norway) and one from a southern climate (Italy). The participants were matched according to both height and weight, and their age at menarche were compared. The researcher is testing the hypothesis of difference—that age at menarche differs as a function of climate. The groups are correlated, having been matched on both height and weight.
Wilcoxon Signed Rank test
