Submit a 1-page paper analyzing the relationship between study design and statistical analysis used in the case study. Explain why you think that the agen

1

© 2022 Walden University, LLC. Adapted from Plummer, S.-B., Makris, S., & Brocksen, S. M. (Eds.). (2014).

Sessions: Case histories. Laureate International Universities Publishing.

Tiffani

Tiffani is a 16-year-old heterosexual Caucasian female referred to Teens First after being arrested for prostitution. Teens First is a court-mandated teen counseling program for adolescent survivors of sexual exploitation and human trafficking. At Teens First, social workers provide a holistic range of services for their clients. Tiffani has been provided room and board in the residential treatment facility and will meet with a social worker to address her multiple needs and concerns. Tiffani has been arrested three times for prostitution in the last 2 years. Right before her most recent charge, a new state policy was enacted to protect youth 16 years and younger from prosecution and jail time for prostitution. The Safe Harbor for Exploited Children Act allows the state to define Tiffani as a sexually exploited youth and therefore not imprison her. She was mandated to services at the agency, unlike her prior arrests when she had been sent to detention. Tiffani had been living with a man named Donald since she was 14 years old. She had had limited contact with her family members and had not been attending school. She described Donald as her “husband” (although they were not married) and her only friend. During intake, it was noted that Tiffani had multiple bruises and burn marks on her legs and arms. She reported that Donald had slapped her and burned her with cigarettes when he felt she did not behave. Tiffani has been treated for several sexually transmitted infections (STIs) at local clinics and is currently on an antibiotic for a kidney infection. It appears that over the last 2 years, Tiffani has had neither outside support nor interactions with anyone beyond Donald and some other young women also being trafficked.

Childhood and Early Adolescence During social work sessions, Tiffani gave a rather in-depth description of her childhood. At first, Tiffani provided a family history that was filled with only happy memories. She remembered her life up to age 8 as filled with moments of joy. She remembered going to school, playing with her sister, and her mother and father getting along. As the social worker and Tiffani continued to meet, Tiffani shared what she remembered as a gradual but definitive change in the family dynamics around the time when she turned 8 years old. She remembered being awakened by music and laughter in the early hours of the morning. When she went downstairs to investigate, she saw her parents along with her uncle Nate passing a pipe back and forth between them. She remembered asking them what they were doing and her mother saying, “adult things,” and putting her back in bed.

2

© 2022 Walden University, LLC. Adapted from Plummer, S.-B., Makris, S., & Brocksen, S. M. (Eds.). (2014).

Sessions: Case histories. Laureate International Universities Publishing.

Tiffani remembered being woken up by noise several times after that and seeing her father and her uncle passing the pipe between them. Sometimes her mother was there, and sometimes she was not. Often when her mother was not there, Nate would see her and ask her to come over. Her father would ask her to show them the dance that she had learned at school. When Tiffani danced, her father and Nate would laugh and offer her pocket change. Sometimes they were joined by their friend Jimmy. For years, the music and noise downstairs continued, later accompanied by screams and shouting and sounds of people fighting. One morning, Shondra yelled at Robert to “get up and go to work.” Tiffani and Diana saw Robert come out of the bedroom and slap Shondra so hard she was knocked down. Robert then went back into the bedroom. Tiffani also noticed significant changes in her home’s appearance. The home, which was never fancy, was almost always neat and tidy. Tiffani noticed that dust would gather around the house, dishes would pile up in the sink, dirt would remain on the floor, and clothes would go for long periods of time without being washed. Tiffani remembered cleaning her own clothes and making meals for herself and her sister during this period. Sometimes Tiffani and her sister would come downstairs in the morning to find empty beer cans and liquor bottles on the kitchen table along with the pipe. Her parents would be in the bedroom, and Tiffani and her sister would leave the house and go to school by themselves. Tiffani was unclear if her parents were working or how the bills were paid. Often there was not enough food to feed everyone, and she would go to bed hungry. During one session, Tiffani described an incident of sexual abuse. One night she was awoken by her uncle Nate and his friend Jimmy in her room. Her parents were apparently out, and they were the only adults in the home. They asked her if she wanted to come downstairs and show them the new dances she learned at school. Once downstairs, Nate and Jimmy put some music on and started to dance. They asked Tiffani to start dancing with them, which she did. While they were dancing, Jimmy spilled some beer on her. Nate said she had to go to the bathroom to clean up. Nate, Jimmy, and Tiffani all went to the bathroom. Nate asked Tiffani to take her clothes off so she could get in the bath. Tiffani hesitated to do this, but Nate insisted it was okay since he and Jimmy were family. Tiffani eventually relented and began to wash up. Nate would tell her that she missed a spot and would scrub the area with his hands. After this incident, others occurred, with increasing levels of molestation each time. Tiffani felt very bad about this but had difficulty explaining why, even to herself. She was very afraid of everyone in her family except her sister, Diana. She was also afraid that Diana might be subjected to the same thing. The last time it happened, when Tiffani was 14, she pretended to be willing to dance for them, but when she got downstairs, she ran out the front door of the house. Tiffani ran down the block, intending to go to her school because it was one of the few places she felt safe. She said she was barefoot and in her pajamas, and it was very cold. About halfway to her school, a car stopped, and a man inside asked her where she was going. When Tiffani replied that she was going to school, the man said that it was the middle of

3

© 2022 Walden University, LLC. Adapted from Plummer, S.-B., Makris, S., & Brocksen, S. M. (Eds.). (2014).

Sessions: Case histories. Laureate International Universities Publishing.

the night. Tiffani did not want to tell him the whole story, so she told him that there was trouble at home and she just wanted to go to school early.

Donald

The man introduced himself as Donald and asked her why she did not go to her boyfriend’s house. When Tiffani said she did not have a boyfriend, Donald replied that if she had a boyfriend, she would have somebody to take care of her and keep her safe when these things happened. He then offered to be her boyfriend. Tiffani did not say anything, but when Donald said he’d give her a ride, she agreed and got in the car. Donald took Tiffani to his apartment, explaining that the school would be closed for hours. When they got to his apartment, Donald fed Tiffani and gave her beer, explaining that it would help keep her warm. Tiffani did not like the taste of the beer, but at Donald’s insistence, she drank it. When Tiffani was drunk, Donald began kissing her, and they had sex. Tiffani knew about sex from school and some of her girlfriends, but she had never had it with anyone before. She was grateful to Donald because he had helped her get away from Nate and Jimmy. Donald had also told her that he loved her and they would be together forever. Tiffani was afraid that if she did not have sex, Donald would not let her stay—and she had nowhere else to go. For the next 3 days, Donald brought her food and beer and had sex with her several more times. Donald told Tiffani that she was not allowed to do anything without his permission. This included watching TV, going to the bathroom, taking a shower, and eating and drinking. Donald bought Tiffani a dress, explaining to her that she was going to “find a date” and get men to pay her to have sex with her. When Tiffani said she did not want to do that, Donald hit her several times. Donald explained that if she didn’t do it, he would get her sister, Diana, and make her do it instead. Out of fear for her sister, Tiffani relented and did what Donald told her to do. Tiffani and the social worker talked often about her continued desire to be reunited with Donald. They discussed what Donald represented for Tiffani and why he was such an important part of her life. She often described him as the person who “saved” her and felt she owed much to him. She vividly remembered the fear she felt the nights Nate and Jimmy touched her, and she was convinced they would have raped her that last night if she hadn’t left.

© 2022 Walden University, LLC Page 1 of 5

A Short Course in Statistics This information was prepared to call your attention to some basic concepts underlying statistical procedures and to illustrate what types of research questions can be addressed by different statistical tests. You may not fully understand these tests without further study. However, you are strongly encouraged to note distinctions related to the type of measurement used in gathering data and the choice of statistical tests. Feel free to post questions in the “Contact the Instructor” section of the course.

Statistical Symbols

µ mu (population mean) α alpha (degree of error acceptable for incorrectly rejecting the null hypothesis, probability that results are unlikely to occur by chance) ≠ (not equal) ≥ (greater than or equal to) ≤ less than or equal to) ᴦ (sample correlation) ρ rho (population correlation) t r (t score) z (standard score based on standard deviation) χ2 Chi-square (statistical test for variables that are not interval or ratio scale [i.e., nominal or ordinal]) p (probability that results are due to chance)

Descriptives

Descriptives are statistical tests that summarize a data set. They include calculations of measures of central tendency (mean, median, and mode) and dispersion (e.g., standard deviation and range).

Note: The measures of central tendency depend on the measurement level of the variable (nominal, ordinal, interval, or ratio). If you do not recall the definitions for these levels of measurement, see https://www.questionpro.com/blog/nominal-ordinal-interval- ratio/

You can only calculate a mean and standard deviation for interval or ratio scale variables.

For nominal or ordinal variables, you can examine the frequency of responses. For example, you can calculate the percentage of participants who are male and female; or the percentage of survey respondents who are in favor, against, or undecided.

Often nominal data is recorded with numbers, e.g., male=1, female=2. Sometimes people are tempted to calculate a mean using these coding numbers. But that would be

© 2022 Walden University, LLC Page 2 of 5

meaningless. Many questionnaires (even course evaluations) use a Likert scale to represent attitudes along a continuum (e.g., Strongly like … Strongly dislike). These too are often assigned a number for data entry, e.g., 1–5. Suppose that most of the responses were in the middle of a scale (3 on a scale of 1–5). A researcher could observe that the mode is 3, but it would not be reasonable to say that the average (mean) is 3 unless there were exact differences between 1 and 2, 2 and 3, etc. The numbers on a scale such as this are ordered from low to high or high to low, but there is no way to say that there is a quantifiably equal difference between each of the choices. In other words, the responses are ordered but not necessarily equal. Strongly agree is not five times as large as strongly disagree. (See the textbook for differences between ordinal and interval scale measures.)

Inferential Statistics

Statistical tests for analysis of differences or relationships are inferential, allowing a researcher to infer relationships between variables.

All statistical tests have what are called assumptions. These are essentially rules that indicate that the analysis is appropriate for the type of data. Two key types of assumptions relate to whether the samples are random and the measurement levels.

Other assumptions have to do with whether the variables are normally distributed. The determination of statistical significance is based on the assumption of the normal distribution. A full course in statistics would be needed to explain this fully. The key point for our purposes is that some statistical procedures require a normal distribution and others do not.

Understanding Statistical Significance

Regardless of what statistical test you use to test hypotheses, you will be looking to see whether the results are statistically significant. The statistic p is the probability that the results of a study would occur simply by chance. Essentially, a p that is less than or equal to a predetermined (α) alpha level (commonly .05) means that we can reject a null hypothesis. A null hypothesis always states that there is no difference or no relationship between the groups or variables. When we reject the null hypothesis, we conclude (but don’t prove) that there is a difference or a relationship. This is what we generally want to know.

Parametric Tests

Parametric tests are tests that require variables to be measured at interval or ratio scale and for the variables to be normally distributed.

© 2022 Walden University, LLC Page 3 of 5

These tests compare the means between groups, which is why they require the data to be at an interval or ratio scale. They make use of the standard deviation to determine whether the results are likely to occur or very unlikely in a normal distribution. If they are very unlikely to occur, then they are considered statistically significant. This means that the results are unlikely to occur simply by chance.

The T-Test Common uses:

• To compare mean from a sample group to a known mean from a population

• To compare the mean between two samples o The research question for a t-test comparing the mean scores between

two samples is: Is there a difference in scores between group 1 and group 2? The hypotheses tested would be: H0: µgroup1 = µgroup2

H1: µgroup1 ≠ µgroup2

• To compare pre- and post-test scores for one sample o The research question for a t-test comparing the mean scores for a

sample with pre and posttests is: Is there a difference in scores between time 1 and time 2? The hypotheses tested would be : H0: µpre = µpost

H1: µpre ≠ µpost

Example of the form for reporting results: The results of the test were not statistically significant, t (57) = .282, p = .779, thus the null hypothesis is not rejected. There is not a difference in between pre and post scores for participants in terms of a measure of knowledge (for example).

An explanation: The t is a value calculated using means and standard deviations and a relationship to a normal distribution. If you calculated the t using a formula, you would compare the obtained t to a table of t values that is based on one less than the number of participants (n-1). n-1 represents the degrees of freedom. The obtained t must be greater than a critical value of t in order to be significant. For example, if statistical analysis software calculated that p = .779, this result is much greater than .05, the usual alpha-level which most researchers use to establish significance. In order for the t-test to be significant, it would need to have a p ≤ .05.

ANOVA (Analysis of Variance) Common uses: Similar to the t-test. However, it can be used when there are more than two groups.

The hypotheses would be H0: µgroup1 = µgroup2 = µgroup3 = µgroup4

H1: The means are not all equal (some may be equal)

© 2022 Walden University, LLC Page 4 of 5

Correlation Common use: to examine whether two variables are related, that is, they vary together. The calculation of a correlation coefficient (r or rho) is based on means and standard deviations. This requires that both (or all) variables are measured at an interval or ratio level.

The coefficient can range from -1 to +1. An r of 1 is a perfect correlation. A + means that as one variable increases, so does the other. A – means that as one variable increases, the other decreases.

The research question for correlation is: “Is there a relationship between variable 1 and one or more other variables?”

The hypotheses for a Pearson correlation:

H0: ρ = 0 (there is no correlation) H1: ρ ≠ 0 (there is a real correlation)

Nonparametric Tests

Nonparametric tests are tests that do not require variables to be measured at interval or ratio scale and do not require the variables to be normally distributed.

Chi-Square Common uses: Chi-square tests of independence and measures of association and agreement for nominal and ordinal data.

The research question for a chi-square test for independence is: Is there a relationship between the independent variable and a dependent variable?

The hypotheses are:

H0 (The null hypothesis) There is no difference in the proportions in each category of one variable between the groups (defined as categories of another variable).

Or:

The frequency distribution for variable 2 has the same proportions for both categories of variable 1.

H1 (The alternative hypothesis) There is a difference in the proportions in each category of one variable between the groups (defined as categories of another variable).

The calculations are based on comparing the observed frequency in each category to what would be expected if the proportions were equal. (If the proportions between observed and expected frequencies are equal, then there is no difference.)

© 2022 Walden University, LLC Page 5 of 5

Other Nonparametric Tests Spearman rho: A correlation test for rank ordered (ordinal scale) variables.