Psychological Statistics

ANCOVA

Suppose you want to know whether or not studying technique has an impact on exam scores for a class of students. We randomly split the class into three groups. Each group uses a different studying technique for one month to prepare for an exam. However, we want to account for the current grade that the student already has in the class because it might affect the result of the experiment. Which statistical test will you use to compare the exam scores while controlling for another variable (i.e. grade)?

Welch's ANOVA

A researcher wants to compare the average exam scores between three different study groups: Group A, Group B, and Group C. The researcher collected exam scores from each group and performed preliminary statistical tests. The results of the Shapiro-Wilk test for normality and Levene's test for equality of variances are as follows: \n \n Shapiro-Wilk's Test for Normality: \n Group A: p-value = 0.125 \n Group B: p-value = 0.053 \n Group C: p-value = 0.072 \n \n Levene's test for equality of variances: \n p-value = 0.017 \n \n Based on these results, which statistical test is most appropriate for comparing the average exam scores among the three study groups?

Those subjects in the light classical music condition showed the highest task performance scores.

A study about the effect of background music on task performance was conducted. After the experiment, the data were analyzed and these are the results:



Based on the results, what can you conclude about this study?

Multiple Regression

A researcher wants to determine if spirituality, self-esteem, and self-efficacy can significantly are significant predictors of anxiety among freshmen college students. What statistical test should be utilized in this research problem?

z test

What statistical test should you use if you will compare scores of two groups that have a sample size of n ≥ 30, population mean and variance are known, and the data is approximately normally distributed?

There is a significant negative correlation between psychological well-being and work-related stress. It means that respondents with high level of psychological well-being are likely to have low stress level, or vice versa.

What can you say about the result of this correlation matrix?

t test for independent samples

A researcher wants to determine if there is a significant difference in the depression tendency between male and female high school students. Upon gathering the scores on a depression scale, it was discovered that both groups have equal variances, data follows a normal curve when analyze by a normality test, and there were no significant outliers. Which statistical test should be utilized?

Personality traits significantly predict job performance.

A researcher conducted a multiple regression analysis to examine the relationship between personality traits (extraversion, neuroticism, openness) and job performance (measured by supervisor ratings) in a sample of 200 employees. The researcher obtained a statistically significant F-value from the ANOVA table. Which of the following interpretations is most appropriate for the ANOVA results in this multiple regression analysis?

t test for dependent samples

Research has shown that losing even one night’s sleep can have a significant effect on performance of complex tasks such as problem solving (Linde & Bergstroem, 1992). To demonstrate this phenomenon, a sample of n =25 college students was given a problem-solving task at noon on one day and again at noon on the following day. The students were not permitted any sleep between the two tests. For each student, the difference between the first and second score was recorded. It was revealed that the distribution of difference scores is approximately normally distributed and there were no significant outliers in the data. What statistical test should be use?

t test for independent samples

Mariza is conducting a study that will determine the difference between high school and college students in terms of stress level. Upon gathering the scores of the participants using a stress scale, she found out that the data for the two groups were normally distributed, variances were homogeneous, and there were no significant outlier/s. Which statistical test should she utilize?

Mann-Whitney U Test

Numerous studies have found that males report higher self-esteem than females, especially adolescents (Kling, Hyde, Showers, & Buswell, 1999). A recent study found that males scored an average of 8 points higher than females on a standardized questionnaire measuring self-esteem. The researcher would like to know whether this is a significant difference. Which statistical test is appropriate to use if the data is non-normal, has an unequal variance, and there were significant outliers?

regression

What does the correlation coefficient (r) means

The result is significant at 0.05 level

 If the computed correlation coefficient has one asterisk after the magnitude (e.g. 0.99\*), what does it mean?

alpha

The statistical significance is represented by what symbol?

Two-Way ANOVA

Some people like to pour beer gently down the side of the glass to preserve bubbles. Others splash it down the center to release the bubbles into a foamy head and \n free the aromas. Champagne, however, is best when the bubbles remain concentrated in the wine. A group of French scientists recently verified the difference between the two pouring methods by measuring the number of bubbles in each glass of champagne poured two different ways and at three different temperatures (Liger-Belair, 2010). Based on the mentioned example, which do you think is the most appropriate statistical test to use in analyzing their data?

There is a statistically significant relationship between gender and preference for a specific genre of music.

A researcher is interested in examining whether there is a relationship between gender (male vs. female) and preference for a specific genre of music (rock, pop, hip-hop, country). The researcher collects data from a sample of 500 individuals and constructs a contingency table to analyze the relationship. The chi-square test of independence is conducted, and the resulting p-value is 0.001.

80%

What is the conventional statistical power when conducting a study?

One-Way ANOVA

There is some research indicating that college students who use Facebook while studying tend to have lower grades than non-users (Kirschner & Karpinski, 2010). A representative study surveys students to determine the amount of Facebook use during the time they are studying or doing homework. Based on the amount of time spent on Facebook, students are classified into three groups and their grade point averages are recorded. If the assumptions for normality, homogeneity of variance, and no significant outliers were met in this study, which statistical test is appropriate to analyze its data?

Two-way ANOVA

A researcher wants to investigate the effects of both a new medication (medication A, medication B) and dosage level (low, high) on participants' reaction times. The researcher randomly assigns participants to the medication groups and dosage levels. The data collected are continuous and meet the assumptions of normality and homogeneity of variances. Which of the following statements accurately describes the appropriate statistical treatment for this experimental study?

Chi-square Test for Independence

A researcher wants to determine if parenting style (authoritarian, authoritative, permissive) is significantly related to Grade Point Average (Excellent, Average, Poor). Which statistical test should be utilized?

Independent Samples t Test

A researcher wants to compare the average exam scores between two different teaching methods used in a university course. The researcher collected exam scores from two independent groups of students: Group A, who were taught using Method X, and Group B, who were taught using Method Y. Which statistical test is most appropriate for this research question, considering the following assumptions? \n \n Assumptions: \n \n 1. The exam scores are approximately normally distributed within each group. \n 2. The variances of the exam scores are equal in both groups. \n 3. The observations within each group are independent.

Directed Reading Activities significantly affect reading comprehension. Specifically, those who received the directed reading activities intervention showed higher reading comprehension scores than those who were not given any intervention.Directed Reading Activities significantly affect reading comprehension.

Specifically, those who received the directed reading activities intervention showed higher reading comprehension scores than those who were not given any intervention.

An experiment was conducted to determine if directed reading activities significantly affect reading comprehension. Two groups were included in this study (i.e., Group 1 - No Intervention, Group 2 - Directed Reading Activity Condition) and the reading comprehension were compared using independent samples t test. The following are the results:



What can we conclude with the results?

Interaction Effect

A research study was conducted to examine the impact of eating a high protein breakfast on adolescents' performance during a physical education physical fitness test. Half of the subjects received a high protein breakfast and half were given a low protein breakfast. All the adolescents, both male, and female were given a fitness test with high scores representing better performance. The combination of the effect of gender and eating high protein or low protein is an example of

Pearson's r

Research results indicate that physically attractive people are also perceived as being more intelligent. As a demonstration of this phenomenon, a researcher obtained a set of n = 40 photographs of male college students. The photographs were shown to a sample of female college students who used a 7-point scale to rate several characteristics, including intelligence and attractiveness, for the person in each photo. The average attractiveness rating and the average intelligence rating were computed for each photograph. The researcher plans to use the averages to determine whether there is relationship between perceived attractiveness and perceived intelligence. If the two variables follow a normal curve, the scatterplot shows linear correlation, and there were no significant outliers, which statistical test should be utilized?

Wilcoxon Signed-Rank Test

Research suggests that the antioxidants in foods such as blueberries can reduce and even reverse age-related declines in cognitive functioning (Joseph et al., 1999). To test this phenomenon, a researcher selects a sample of n = 25 adults aged 70 to 75 and administers a cognitive function test to each participant. The participants then drink a blueberry supplement every day for 4 months before they are tested again. The researcher compares the scores before treatment with the scores after treatment. If the difference scores were approximately normally distributed but there were significant outliers, which statistical test is the most appropriate to use?

t test for independent samples

Childhood participation in sports, cultural groups, and youth groups appear to be related to improved self-esteem for adolescents. In a representative study, a researcher compares scores on a standardized self-esteem questionnaire for a sample of n = 100 adolescents with a history of group participation and a separate sample of n = 100 who have no history of group participation. If the two populations met the assumption for normality, homogeneity of variances, and no significant outlier, what statistical test should be utilized?

Cramer's V

What is the appropriate effect size estimate for a study with a 3x4 contingency table?

Kruskal-Wallis H Test

Previous studies investigated the influence of background noise on classroom performance for children aged 10 to 12. In a similar study, students in one classroom worked on an arithmetic task with calming music in the background. Students in a second classroom heard aggressive, exciting music, and students in a third room had no music at all. The researchers measured the number of problems answered correctly for each student to determine whether the music conditions had any effect on performance. If the assumptions for normality and homogeneity of variance are met for this study, but there were significant outliers, what statistical test should be utilized?

Partial Correlation

Suppose a researcher wants to know how the stress people experience in married life is related to how long they have been married. However, the researcher realizes that part of what might make marital stress and marriage length go together is whether couples have children. Having children or not could make stress and length go together, because those married longer are more likely to have children, and having children may create marital stress. Thus, simply figuring the correlation between marital stress and marriage length would be misleading. The researcher wants to know what the relation between stress and marriage length would be if everyone had the same number of children. Or, to put it another way, the researcher wants somehow to subtract out the influence of number of children from the relation between marital stress and length. In this example, the researcher would use

Multicollinearity Assumption

In multiple regression analysis, which of the following assumptions is violated when there is a strong linear relationship between/among the predictor variables?

There is no relationship between personality type and preference for social interaction.

A psychologist is conducting a study to investigate the relationship between personality type (introvert vs. extrovert) and preference for social interaction (high vs. low). The psychologist collects data from a sample of 200 participants and constructs a contingency table to analyze the relationship. The chi-square test of independence is conducted, and the resulting p-value is 0.08. \n \n Based on this research example, which of the following interpretations is most appropriate?

Chi-square Test for Goodness of Fit

A researcher would like to determine whether infants, age 2 to 3 months, show any evidence of color preference. The babies are positioned in front of a screen on which a set of four colored patches is presented. The four colors are red, green, blue, and yellow. The researcher measures the amount of time each infant looks at each of the four colors during a 30 second test period. The color with the greatest time is identified as the preferred color for the child. Which statistical test is appropriate to use in determining the most preferred color among the subjects?

One Sample t Test

To examine the relationship between alcohol consumption and birth weight, a researcher selects a sample of n = 20 pregnant rats and mixes alcohol with their food for 2 weeks before the pups are born. One newborn pup is randomly selected from each subject’s litter and the average birth weight for the n = 20 pups is recorded. It is known that the average birth weight for regular rats (without exposure to alcohol) is 5.6 grams. What is the appropriate statistical test in this example?

Repeated Measures ANOVA

A recent study indicates that simply giving college students a pedometer can result in increased walking (Jackson & Howton, 2008). Students were given pedometers for a 12-week period and asked to record the average number of steps per day during weeks 1, 6, and 12. The objective of this study is to determine if there were significant differences in the average number of steps per day in the mentioned weeks. Which of the following statistical test is appropriate in analyzing the data of this study?

Chi-square Goodness of Fit Test

A researcher wants to determine if the distribution of political party affiliations in a specific region is consistent with the expected distribution based on a national survey. The researcher collects data from 500 participants in the region and wants to compare the observed frequencies with the expected frequencies for each political party. Which of the following statements accurately describes the appropriate statistical treatment for this study?

Highly stressed people are likely to be absent

 After correlating two sets of data (Stress Level and Absenteeism) using SPSS, a psychometrician obtained a correlation coefficient of 0.93\*. This means that

Paired t Test

A researcher is investigating the effectiveness of acupuncture treatment for chronic back pain. A sample of n = 20 participants is obtained from a pain clinic. Each individual rates the current level of pain and then begins a 6-week program of acupuncture treatment. At the end of the program, the pain level is rated again and the researcher records whether the pain has increased or decreased for each participant. Which statistical test should they use if there were no assumptions violated?

Mann-Whitney U Test

There is some evidence indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman, 2008). In a similar study, a researcher showed male college students photographs of women and asked the students to rate the attractiveness of each woman using a 7-point scale. One of the women was selected as the target. For one group of participants, the target was photographed with a large tattoo on her shoulder and for a second group, her photograph showed no tattoo. The researcher plans to compare the target’s ratings for the two groups to determine whether the tattoo had any effect on perceived attractiveness. If the two groups have a negatively skewed distribution and the variance is not homogeneous, which statistical test is appropriate to use?

Games-Howell

A significant difference was revealed after using Welch's ANOVA. If the groups have equal sample sizes, what post hoc test will you use to determine pairs that are significantly different?

There is no significant association between exercise frequency and self-reported stress levels.

A researcher is interested in examining the association between exercise frequency (low, moderate, high) and self-reported stress levels (low, medium, high) in a sample of 300 participants. The researcher calculates Kendall's Tau correlation coefficient and obtains a value of r = -0.25, p = 0.23. Based on this research example, which of the following interpretations is most appropriate?

Repeated Measures ANOVA

To examine the effect of sleep deprivation on motor skills performance, a sample of n = 10 participants was tested on a motor-skills task after 24 hours of sleep deprivation tested again after 36 hours, and tested once more after 48 hours. The dependent variable is the number of errors made on the motor skills task. Which statistical test is appropriate to use in this study?

Two-Way ANOVA

A researcher investigated different combinations of temperature and humidity to examine how heat affects performance. The researcher compared three temperature conditions (70º, 80º, and 90º) with a high humidity and a low humidity condition for each temperature. A separate group of participants was tested in each of the six different conditions. For each participant, the researcher recorded the number of errors on a problem-solving task. The researcher would like to know how different combinations of temperature and humidity influence performance. If the data acquired does not violate the assumptions for parametric testing, what statistical treatment should be utilized?

Simple Linear Regression

A researcher wants to determine if hopelessness can significantly predict depression tendency. Which statistical test should be utilized in this problem?

One-Way ANOVA

New research suggests that watching television, especially medical shows such as Grey’s Anatomy and House can result in more concern about personal health (Ye, 2010). Surveys administered to college students measure television viewing habits and health concerns such as fear of developing the diseases and disorders seen on television. Students are classified into three categories based on their television viewing patterns (little or none, moderate, and substantial) and health concerns are measured on a 10-point scale with 0 indicating “none.” The objective is to compare the health concerns among the groups. Assumptions were tested and it was revealed that the distribution of residuals is approximately normal, there were no significant outliers, and the variances are equal. What statistical test is appropriate to use?

Chi-square Test for Independence

A researcher is investigating the relationship between personality and birth order position. A sample of college students is classified into four birth-order categories (1st, 2nd, 3rd, 4th, or later) and classified as being either extroverted or introverted. Which statistical test is appropriate for this study?

Wilcoxon Signed-Rank Test

Ivan is conducting a research that will determine the effectiveness of hypnotherapy in treating anxiety disorders. He randomly selected 35 individuals who are diagnosed with anxiety disorders. Before the therapy, he gave the Beck Anxiety Inventory to assess their anxiety level. He then conducted the therapy to the 35 individuals and after that, he gave the Beck Anxiety Inventory again to assess their anxiety level. Upon analyzing the scores that he acquired from his subjects, he discovered that the data is approximately normally distributed, but there were significant outliers in the difference scores. What statistical test should be utilized to compare the scores of the participants before and after therapy?

Welch's t test

A researcher is comparing the effectiveness of two sets of instructions for assembling a child’s bike. A sample of eight fathers is obtained. Half of the fathers are given one set of instructions and the other half receives the second set. The researcher measures how much time is needed for each father to assemble the bike. The scores are the number of minutes needed by each participant. Upon checking the assumptions, it was revealed that the distribution for both groups was approximately normal, there were no significant outliers, but the variances are unequal. Which statistical test is appropriate for this study?