Psych 308 - Psychological Statistics Exam 1
Which of the following is a true compare/contrast between descriptive and inferential statistics?
Descriptive statistics describe the sample; inferential statistics make inferences about the population.
What type of phenomena is number of siblings?
Discrete
Which type of phenomena have magnitude (i.e., involve more or less of a phenomena)?
Discrete; continuous
One frequently evaluated aspect of sexual risk-taking among teens is the number of sexual partners they have had. How would you classify the sexual partners variable in terms of the nature of phenomena and the scale of measurement?
Discrete; ratio
Discrete variables
Variables that are recorded in discrete amounts, such as counting the number of times you've done something. This can be done in discrete increments (1, 2, 3, 4 etc.)
Continuous variables
Variables that have no set increments, but are recorded on a continuum instead. An example of this can be height (5'1, 5'2, 5'3, etc.) There isn't a limit to how precise you can be on height
Suppose you have three demographic variables: gender, education, and income. Gender is coded as 0=male, 1=female. Education is coded as 1=high school diploma, 2=associates degree, 3=bachelors, 4=masters, 5=doctorate. Income is coded in dollars. Please (a-c) explain which measure(s) of central tendency can be used to describe each and why, (d) explain for which variable(s) you cannot report indexes of variability and why, (e) explain for which variable(s) you can report indexes of variability and why. When discussing the "why" for each answer, speak in terms of scales of measurement
a - Gender is a nominal variable, and as a result, can only use the mode as a measure of central tendency. This allows you to be able to determine which gender is most frequent b - Education is used on a scale of 1-5, with each level depicting some sort of increase, due to the fact that they represent degrees in education. This means that education is an ordinal variable and can use mean, median, as well as mode within the data set. Mode would allow you to see which education is the most frequent, and the mean can tell you the average amount of education. The median will be able to tell you where the middle degree is, which can help determine skewness. However, it can only be used if the data set is an odd number or if the two middle numbers are the same. c - Income is coded in specific numbers, which is a dollar amount. This means that the scale of measurement used would be ratio, which means that you are able to use mean, median and mode for this variable. It would be best to use the mean for this in order to determine the average income for the sample, and the mode to determine which income is most frequent. The median can also be used to help determine the middle of the data set. d - We would not be able to report indexes of variability for the gender variable, because it is nominal, as well as the fact that it only has two categories within the variable. e - We are able to report indexes of variability for both the education and income variables due to the fact that they are ordinal and ratio, respectively. They use numerical scales, which can help us apply the data to help report indexes of variability.
Please (a-c) define the three scales of measurement (nominal, ordinal, ratio) and give an example of each, (d) describe how ordinal and ratio are different from nominal, and (e) describe how ratio is different from ordinal.
a - Nominal: This scale of measurement doesn't have any ranking to it. The numbers used are more for categorizing rather than determining whether something has more or less value than another variable. An example of this could be eye color. You could assign blue eyes to the number 1 and brown eyes to the number 2, but that doesn't mean that one has more value than the other. b - Ordinal: This scale of measurement sets numbers on a scale of less or more, but not in a precise way. Each number on the scale means that there is an increase or decrease in amount, but it isn't clear how much of a difference there is between the two. An example of this could be the answer to the phrase "I am good with technology" (1-Strongly Agree, 2-Agree, 3-Neutral, 4-Disagree, 5-Strongly Disagree.) Each category shows an increase of agreeableness, but doesn't specify the amount more that the person agrees with the statement. c - Ratio: This scale of measurement does have set increments to the scale. Each number means less or more of something, and it also shows the precise difference in amount of each number on the scale. This means that you are able to do math on the thing, because number 2 is double the amount of number 1. An example of this could be how many cats you own (1, 2, 3, 4, etc.) You can't own half a cat, so this means that each level has an equal amount of increase. d - Nominal categorizes things by assigning a number. This means that there is no increase in value between number 1 and 2. In both ordinal and ratio, there is an increase in value between the two categories. The numbers in ordinal and ratio mean that there is less or more of something, where nominal just organizes them into categories with no numerical value placed on them. e - With ordinal, the increase in number/value is not specific. It shows some sort of increase, but isn't clear on exactly how much of an increase there was. Ratio is different because it uses a scale with set increments, where the increase between 1-2 and 2-3 are equal. This means you area able to determine just how much of an increase there was.
This study explored individual, family, and peer predictors of involvement and psychological investment in fights among Samoan youth. Participants were 310 adolescents ages 13 through 19 living in Samoa, who completed a paper-pencil survey at school. MANCOVAs compared those involved in fights with those not, and those more invested in fighting with those less invested. In terms of individual predictors, for both of the independent variables, groups differed on school engagement, religiosity, proactive aggression, reactive aggression, moral disengagement, and social dominance but not self-regulation, empathy, or moral identity. Groups also differed on all peer variables: proactive aggression, reactive aggression, fight investment, and fight involvement. For involvement, groups differed on maternal and paternal psychological control and disrespect, but not parental monitoring. For investment, there were no differences on family variables. Path models found proactive aggression and peer fight involvement predictive of involvement, and proactive aggression, moral disengagement, peer investment, and maternal psychological control predictive of investment. Stevens, D. L., & Hardy, S. A. (2013)
a - Population: The population in this study are Samoan youth. Sample: The sample in this study is 310 adolescents living in Samoa who were between the ages of 13 and 19. b - Constant: Everyone in the study were people who were living in Samoa during the time of the study. Variable: One variable would be religiosity of the students in the study. c - The study design would be correlational d - The study was Cross-sectional, because it was a one time survey, and it was also a real world setting, because the participants took the survey at school and it was based on their own lives. e - The study was conducted through a survey.
Mean (there are two ways of defining the mean—one that is a common definition and one dealing with deviations, please use both)
1 - The mean is the average number of the scores in the data set. (Add all the scores together and divide them by the amount of sample size) 2 - The mean is also the point around which the deviations balance. If you add all the deviations from the mean together, they will equal zero.
About what percent of scores are beyond three standard deviations from the mean of a normal distribution (both directions combined)?
1%
What was the mean on premarital?
1.58
What are the most siblings anyone had?
13
What is the average amount of time spent on scriptures per day?
13.51 minutes
What percentage of BYU Student Study participants thought that premarital sex is "always wrong"?
64%
The IQ has a mean of 100 with a standard deviation of 15 in the population. If I randomly call a phone number in the U.S., and have the person who answers take the IQ, what are the chances they will scores between 85 and 115?
68%
Based on the data reported in the table below, at what percentile would you say someone would be who has dated 5 people?
79th
What is the most siblings people could have before being considered a statistical outlier in the distribution?
8
What scale of measurement was used for region?
Nominal
What is the key difference between nominal and ordinal scales of measurement?
Nominal does not have magnitude, ordinal does.
How would you describe the distribution shown above?
Normal
What scale of measurement was used for premarital?
Ordinal
Which type(s) of variable(s) can be displayed using histograms?
Ordinal and Ratio
Which scale(s) of measurement can be used to operationalize a continuous variable (i.e., to turn it into data)?
Ordinal and ratio
What is the shape of the distribution for scriptures (based on the skewness score)?
Positively skewed
What scale of measurement is most ideal from a statistical standpoint?
Ratio
What scale of measurement was used for scriptures?
Ratio
What scale of measurement was used for siblings?
Ratio
What is the key difference between ordinal and ratio scales of measurement?
Ratio variables are more precise than ordinal variables.
What three pieces of information correspond to any given point on a distribution?
Raw scores, z-scores, and percentages
What's the research setting?
Real world
What is one of the major pros of correlational research design?
Real-world validity
Which of the following was NOT a variable in this study?
Religiousness
What scores in a distribution would typically be considered outliers?
Scores beyond 3 standard deviations from the mean.
What are the three characteristics of distributions?
Shape, central tendencies, and variability
How many outliers were there on siblings (i.e., how many people would need their scores Winsorized)?
17
In the graph above, about how many teens were 15?
200
What is the median for siblings?
3
What is the mode for siblings?
3
What is the mean for siblings?
3.6
What percentage of BYU Student Study participants were from Utah - this is the variable utah (rounded; since this item was only asked of students from the USA, refer to the numbers in the Valid column not the Percent column)?
33%
How many teens would be considered outliers?
45
What's the sample in this study?
475 U.S. teens
Which of the following is a difference between a population and a sample?
A population is all the people you are interested in, while the sample is all the people you have data on.
Population
A population is who the study is about.
Sample
A sample is a small amount of people from within the population that you can then perform the study on.
Which of the following is an inferential statistic?
ANOVA
What is one of the major pros of experimental research design?
Ability to infer causality
What is the relationship between methods and statistics? Note: to "infer causality" means to claim cause-effect.
Ability to infer causality depends largely on how you got the data, not on how you analyze it.
What's the population in this study?
All teens
What does the following formula tell us: Σ(X-M)^2/N?
Average squared deviation from the mean
Why is the standard deviation more interpretable than variance?
Because standard deviation is in the original units of the variable.
What type of phenomena is region of the country?
Categorical
Hundreds of studies have examined parenting using the parenting styles model, initially outlined by Dianna Baumrind. The four parenting styles are authoritative, authoritarian, permissive, and neglectful. Suppose you did such a study, assessed parenting, and then assigned each family to one of these four parenting styles. How would you classify the parenting styles variable in terms of the nature of the phenomena and the scale of measurement?
Categorical; nominal
Which of the following is true regarding statistics?
Competence with statistics is a broadly applicable and highly marketable skill which is trending upward.
Which of the following best distinguishes constants and variables?
Constants are things that are the same across people; variables are things that vary across people.
What type of phenomena is attitudes about premarital sex?
Continuous
What type of phenomena is time spent on scripture study?
Continuous
BYU professors and graduate students conducted a longitudinal study of links between time spent using social media and mental health (Coyne, Rogers, Zurcher, Stockdale, & Booth, 2020). Participants responded to a single social media use item, "How much time do you spend on social networking sites, like Facebook, on a typical day?," using a Likert scale from 1 (none) to 9 (more than 8 hours). How would you classify the social media use variable in terms of the nature of the phenomena and the scale of measurement?
Continuous; ordinal
What's the basic design for this study?
Correlational
Which of the following was a constant rather than a variable in this study?
Country
What's the difference between cross-sectional and longitudinal design?
Cross-sectional designs involves a single time point, while longitudinal designs involve multiple time points.
The z-score formula divides every deviation from the mean by the standard deviation of the scores. What is the purpose of dividing by standard deviation?
Dividing by the standard deviation changes the standard deviation to 1.
Which of the following variables is the most likely to be positively skewed?
Drug use
Which of the following characteristics will likely lead to negative skewness?
High social desirability and/or low difficulty
Which of the following best describes the shape of distribution shown above?
Highly positively skewed
Which of the following is the correct sequence involved in the scientific method?
Hypothesis formation>Research design>Data collection>Data analysis>Draw conclusions
The IQ has a mean of 100 with a standard deviation of 15 in the population. Let's say I randomly select 200 people from the population and have them take the IQ. Which of the following would be true?
If I randomly pick out one person from the sample, I have a 50% chance of getting someone with a score lower than 100
Please write a results paragraph for the descriptive statistics shown above, using APA style reporting. Please report (a) the range of scores or minimum/maximum, (b) means, and (c) standard deviations. Also, (d) note any potential problems with the data, such as skewness, outliers, or missing data. Then (e) add any comments about what we learn about the phenomena from these descriptives.
In this study, 3370 religious youth were asked to report how often their church caused them to think of important things as well as how often their church was boring or disengaging by using a (a) 1-4 (R=3) scale with 1 meaning usually, 2 meaning sometimes, 3 meaning rarely and 4 meaning never. In the first question, it was shown that 62% of youth answered 1, with those who answered the question with 2 were in the 90th percentile. On average the youth answered between a 1 and a 2 (b) (M=1.5). It is also important to note the standard deviation from the mean was at a .76 (c) (SD=.76). (d) Despite these results, there are also some potential issues with the data. However, out of the 3370 youth who were in the sample, 1162 of them did not submit their surveys. This can cause discrepancies within the data due to the fact that there were not as many scores to use as data. This survey also presented a slight positive skewness (Skewness=1.56). (e) This data shows that a majority of religious youth find themselves interested and engaged in their church, with only 3.31% of teens reporting that their church never caused them to think about important things. The results for the second question were quite different from the first. We asked the youth how often their church was boring or disengaging, while still using the (a) 1-4 scale (R=3). As opposed to the first question, only 14% of teens reported that their church was usually disengaging (1), with those who answered 2 being in the 51st percentile. For this question, the average answer was between a 2 and a 3 (b) (M=2.6) with the standard deviation from the mean at a 1.0 (c) (SD=1.0). The results for this question showed pretty normal results with little to no skewness (Skewness=.04) and similar scores on each scale. (d) There were also similar issues with this question as there were with the previous question. Out of the 3370 youth in the sample, 1154 of them did not submit their answers. This could potentially change the results due to a smaller sample size. As mentioned before, these results were quite different from the first question in the survey. (d) With a pretty even spread of results, it tells us that many teens find their church to be at the very least somew
Please write up the descriptive statistics for region, premarital, and scriptures using APA style. Please note (a) the mode for nominal variables and (b) mean and (c) standard deviation for ordinal and ratio. Please (d) comment on distribution shape and any other issues of note. Lastly, (e) point out any trends that seem interesting or surprising.
In this survey, we asked students in what region of the US they were raised. (a) Out of the 884 students that participated, 628 (71%) stated that they grew up in the west part of the US. In addition to that, we also asked the students whether they were raised in Utah or not. The answers to this question showed that, out of the 888 students that answered, 597 (67%) said that they did not grow up in Utah, meaning that only 291 students (33%) grew up in Utah. (d) It should be noted that the distribution for region was slightly negatively skewed, showing that more students came from the western part of the US than the eastern and midwestern part. Something that could also be an issue to note is the fact that the states were grouped together. While this helps us determine what region people are from, it also covers a large amount of area, and it would be possible to get more accurate data by asking which state each student is from. (e) Something that I found interesting was the increased number of students living in the western and southern parts of the United States. Since this survey was of BYU students, it would make sense that the closer you grew up to BYU, the more likely you would be to attend the university. Premarital: We also asked students their opinion on premarital sex, using a 1-4 scale. (a) Out of the 944 students that answered the survey, 608 (64%) answered that premarital sex was always wrong. (b) On average, students said that premarital sex was either always wrong or almost always wrong (M=1.58). (c) In addition to this, the standard deviation for this survey was .89 (SD=.89). (d) The distribution of the data for this survey was slightly positive as well, with a skewness of 1.38 (skewness=1.38). This shows that most of the students in the survey viewed premarital sex as something that is wrong or looked down on. (e) In all honesty, I was surprised at the amount of people who answered "almost always wrong" and "never wrong" on the survey. Because of BYU's affiliation with the Church of Jesus Christ of Latter Day Saints, I would think that almost all the students would have a negative view on premarital sex. And while that was the case for the most part, around 17% of students answered either a 3 o
Which of the following is true of the z-distribution?
It has a mean of 0 and standard deviation of 1
Which of the following gives us a larger standard deviation?
Larger distances between scores and the mean
Which of the following increases sampling error?
Larger population standard deviation
What's the study duration?
Longitudinal
Suppose I have a dataset of the IQ scores for 10,000 people (M = 100, SD = 15). If I wanted to shrink the scale of this variable to be more like other variables in my dataset, I might divide each score by 10. If I were to do that transformation, what would you guess my new sample mean and standard deviation would be?
M = 10, SD = 1.5
Which of the following symbols are sample statistics?
M, SD
Which measure(s) of central tendencies are sensitive to outliers?
Mean
Which descriptive statistics are typically reported in psychology journal articles?
Mean and standard deviation
Which of the following is measure of central tendency?
Median
Which measure(s) of central tendency are appropriate for nominal variables?
Mode
What is the shape of the distribution for premarital (based on the skewness score)?
Moderately positively skewed
Participants in the NSYR dataset were asked "How often, if at all, do you think about or plan for your future?" Responses were on a 5-point Likert scale from 1 "Never" to 5 "Very often". Based on the content of the item, the response scale, and the descriptive statistics (M = 4.15, SD = .96), what might you anticipate the shape of the distribution to be?
Negatively skewed
Variable
Something that is different for the participants in the population or the sample.
What does this formula calculate: √(Σ(X-M)^2/N)?
Standard deviation
Z-scores are in what units?
Standard deviations
The z-score formula divides every deviation from the mean by the standard deviation of the scores. What is the purpose of subtracting the mean from each score?
Subtracting the mean changes the mean to 0.
What does the following formula tell us: Σ(X-M)^2?
Sum of squared deviations from the mean
What's the data collection strategy for this study?
Survey
Standard deviation
The average deviation from the mean. (After square rooting the variance
Variance
The average squared deviation from the mean.
The ACT has a population mean of 18 and standard deviation of 6. If a person has a z-score of -.5, which of the following is true for them?
They are a half standard deviations below the mean.
The ACT has a population mean of 18 and standard deviation of 6. If a person has a z-score of 2, which of the following is true for them?
They have an ACT score of 30
Please (a) pick a variable you are interested in studying; (b) identify the type of phenomena it is—categorical, discrete, or continuous, and justify your answer; (c) identify and describe measurement approach you would use; (d) identifying the scale of measurement you would use—nominal, ordinal, or ratio, and justify your answer; (e) describe the way you would gather data—the methodology.
a - Something I am interested in studying is the amount of people who have different animal allergies, such as none, cat, dog, horse and bird. b - This type of phenomena would be categorical, because there isn't a numerical value between the different variables. c - I would gather my data using a survey format. Because this study is based on something that is already occurring in peoples lives, I would need to use a survey to determine the types of animal allergies people have. d - I would use the nominal scale of measurement because the categories wouldn't show in increase of value, there isn't less or more of something. It depicts the different categories, not an increased number. e - My study would be correlational, because it wouldn't have any sort of manipulation. I would also use a Cross-sectional study, because I wouldn't need to study the same group of people over a period of time in order to determine what kinds of animal allergies they have. I would also be using a real world setting, due to the fact that I would be observing the participants instead of manipulative a variable.
See the following formula: √(Σ(X-M)^2/N) . Please (a) give the name and symbol for this formula, (b) if we remove the square root, then what is the name and symbol for the formula, (c) what is the name and symbol for the numerator in the formula--the top of the formula, (d) what is the name and symbol for the denominator--the bottom of the formula, (e) describe how values generated by this formula are interpreted—i.e., what do the numbers mean?
a - The formula shown above is used for Standard Deviation (SD), which can also be reported as σ, or "sigma." b - The name of the formula used without the square root would be the variance (SD^2). The variance can also be depicted as σ^2, or "sigma squared." c - The numerator in the formula is called the Sum of Squares (SS), which is also represented as the formula Σ(X-M)^2. d - The denominator, N, is known as the sample size in the data set. In other words, it is the number of values within the data. e - The standard deviation is used to help determine the average deviation from the mean. In other words, it shows us how far away, on average, a data point would be away from the mean while using the original units in the data set. It can tell us how far away a point is from the mean, by saying that is it "one standard deviation away from the mean." It can also help us determine any outliers, because outliers are generally 3 standard deviations away from the mean.
Which of the following is a descriptive statistic?
mean
In order to estimate the average hours of sleep per night for teens throughout the U.S., you compute the mean hours of sleep for 500 teens. All U.S. teens are the _____, the 500 teens are the _______, the average sleep throughout the U.S. is the ______, and the mean hours sleep for the 500 teens is the _______.
population, sample, population parameter, sample statistic
Which of the following is ideal in a good sample?
representative of the population
Which of the following is an index of variability?
standard deviation
Descriptive statistics
stats that are calculated using a sample data in order to describe the sample
Inferential statistics
stats that are calculated using a sample data in order to make inferences about the population as a whole