Question 1

Describe each of the three techniques researchers use when deciding whether a relationship exists between two variables.

Accepted Answer

The three techniques researchers use when deciding whether a relationship exists between two variables are correlation analysis, experimental research, and observational research.

1. Correlation analysis: This technique involves examining the statistical relationship between two variables. Researchers use correlation coefficients, such as Pearson's r or Spearman's rho, to determine the strength and direction of the relationship between the variables. A positive correlation indicates that as one variable increases, the other variable also increases, while a negative correlation indicates that as one variable increases, the other variable decreases. However, correlation does not imply causation, so researchers must be cautious when interpreting these results.

2. Experimental research: In experimental research, researchers manipulate one variable (the independent variable) to observe the effect on another variable (the dependent variable). By controlling for other factors, researchers can determine whether changes in the independent variable cause changes in the dependent variable. This technique allows researchers to establish a cause-and-effect relationship between the variables.

3. Observational research: Observational research involves observing and recording the natural behavior of individuals or groups without intervening or manipulating any variables. Researchers can use techniques such as surveys, interviews, or naturalistic observation to gather data on the relationship between two variables. While observational research does not establish causation, it can provide valuable insights into the association between variables in real-world settings.

Overall, these three techniques provide researchers with different approaches to examining the relationship between variables, allowing them to draw more robust conclusions about the nature of the relationship.

Question 2

What are five measures of association that are useful when interpreting bivariate statistics? Describe each one and also specify which level of data each one is applicable to.

Accepted Answer

1. Pearson's correlation coefficient: This measure assesses the strength and direction of the linear relationship between two continuous variables. It ranges from -1 to 1, with 1 indicating a perfect positive relationship, -1 indicating a perfect negative relationship, and 0 indicating no relationship. This measure is applicable to interval or ratio level data.

2. Spearman's rank correlation: This measure assesses the strength and direction of the monotonic relationship between two variables, regardless of whether the relationship is linear. It is based on the ranks of the data rather than the actual values. This measure is applicable to ordinal or interval level data.

3. Point-biserial correlation: This measure assesses the relationship between a continuous variable and a dichotomous variable. It is essentially a special case of Pearson's correlation coefficient, where one of the variables is dichotomous. This measure is applicable to interval or ratio level data for the continuous variable and nominal level data for the dichotomous variable.

4. Phi coefficient: This measure assesses the relationship between two dichotomous variables. It is similar to Pearson's correlation coefficient, but is specifically designed for nominal level data. It ranges from -1 to 1, with 1 indicating a perfect positive relationship, -1 indicating a perfect negative relationship, and 0 indicating no relationship.

5. Cramer's V: This measure assesses the strength of association between two nominal variables. It is an extension of the phi coefficient, allowing for the comparison of larger contingency tables. It ranges from 0 to 1, with 1 indicating a perfect association and 0 indicating no association.

Each of these measures provides valuable insights into the relationship between variables, and the choice of measure depends on the nature of the variables being analyzed and their level of measurement.

Question 3

Is a Type I or Type II error more likely if a 0.05 level is used? Explain.

Accepted Answer

The likelihood of committing a Type I or Type II error depends on the significance level (alpha) chosen for a statistical test, as well as the effect size, sample size, and the true state of the population being tested.

A Type I error, also known as a false positive, occurs when the null hypothesis is true, but we incorrectly reject it. This means we are seeing an effect or difference when there is none. A Type II error, also known as a false negative, occurs when the null hypothesis is false, but we fail to reject it, meaning we are not seeing an effect or difference when there is one.

When a 0.05 level (alpha = 0.05) is used, it means that there is a 5% chance of committing a Type I error if the null hypothesis is true. This is because the 0.05 level is the threshold for statistical significance; if the p-value obtained from the test is less than 0.05, we reject the null hypothesis.

Whether a Type I or Type II error is more likely cannot be determined solely by the alpha level. However, setting a lower alpha level (such as 0.01) would reduce the likelihood of committing a Type I error but increase the likelihood of a Type II error, assuming all other factors are constant. Conversely, setting a higher alpha level (such as 0.10) would increase the likelihood of committing a Type I error but decrease the likelihood of a Type II error.

The probability of committing a Type II error is denoted by beta (β), and the power of the test (1 - β) is the probability of correctly rejecting a false null hypothesis. To reduce the likelihood of a Type II error, researchers can increase the sample size, which increases the power of the test, or choose a larger effect size as the threshold for detecting a difference.

In summary, using a 0.05 level means that there is a 5% chance of committing a Type I error if the null hypothesis is true. Whether a Type I or Type II error is more likely also depends on other factors such as sample size, effect size, and the true state of the population. A balance between the risks of Type I and Type II errors must be considered when designing experiments and choosing significance levels.

Question 4

Describe four ways a researcher can display information about univariate statistics.

Accepted Answer

The answer of Describe four ways a researcher can display...

Question 5

Why is knowing the variability or dispersion of a variable as important as knowing its central tendency? How is variation measured?

Accepted Answer

The answer of Why is knowing the variability or dispersion...

Question 6

Describe,as simply as possible,what is meant by the statement "It is statistically significant at the 0.05 level."

Accepted Answer

The answer of Describe,as simply as possible,what is meant by...

Question 7

A "codebook" is
A)only used in existing statistics research.
B)a document that tells the researcher where variables are located in the data file and what numbers go with what variable attributes.
C)the set of instructions that tell interviewers or experimenters how to treat respondents or subjects.
D)an unnecessary part of data analysis since computers were invented.
E)a sheet of paper with a grid of 80 columns corresponding to data card columns,with rows representing an individual card.

Accepted Answer

A codebook is a document that provides information about the variables in a dataset, including their location in the data file and the attributes associated with each variable. It is a crucial tool for researchers who need to understand the contents of a dataset and analyze the data effectively. While codebooks are commonly used in statistics research, they can be helpful in many other fields that rely on data analysis, including social sciences, healthcare, and business.

Question 8

You discover that the years of marriage before a divorce for nine whites and nine nonwhites are as follows:Whites 12,1,8,9,10,17,3,6,6 Non-Whites 1,9,15,18,11,13,14,7,3
 
Which statement about this data is true?
A)There is no difference in the range for the two groups.
B)The median years of marriage prior to divorce is three years longer for whites than nonwhites.
C)The mean years of marriage prior to divorce are the same for both groups.
D)On average,nonwhites stay married longer prior to divorce than whites.
E)The mode for the two groups is the same.

Accepted Answer

To compare the average years of marriage prior to divorce, we need to find the mean for both groups. For whites, the mean is (12+1+8+9+10+17+3+6+6)/9 = 8.33 years. For non-whites, the mean is (1+9+15+18+11+13+14+7+3)/9 = 11.11 years. Therefore, on average, non-whites stay married longer prior to divorce than whites.

Question 9

Explain how a researcher codes,enters,and cleans data so that it can be used for statistical analysis.What procedures are involved in each of these steps?

Accepted Answer

The answer of Explain how a researcher codes,enters,and cleans data...

Question 10

Calculate the mode for the following six shoe sizes: 9,10,10,8,12,11.
A)8
B)8.5
C)9
D)9.5
E)10

Accepted Answer

The mode is the value that appears most frequently in a set of data. In this case, the shoe size that appears most frequently is 10, so the mode is 10. Therefore, the best choice is E.

Question 11

An elementary school teacher has three classes.She finds the following mean and standard deviations for student IQ scores. 
She knows she is most effective when the students all have similar IQ levels.Which class is she likely to be most effective with?
A)Class #1
B)Class #2
C)Class #3
D)Classes #1 and #2 equally
E)Classes #1 and #3 equally

Accepted Answer

Class #2 has the smallest standard deviation, which indicates that the IQ scores are more tightly clustered around the mean. This suggests that the students in Class #2 have more similar IQ levels, and therefore the teacher is likely to be more effective in this class.

Question 12

Discuss the concepts of control variables and trivariate tables.What are three limitations of trivariate tables?

Accepted Answer

The answer of Discuss the concepts of control variables and...

Question 13

A researcher wants to express the middle of a distribution of numbers whereby half the cases are higher and half the cases are lower than the middle value.What statistical measure should the researcher use?
A)Mean
B)Median
C)Mode
D)Standard deviation
E)Correlation

Accepted Answer

The median is the best choice for expressing the middle of a distribution of numbers where half the cases are higher and half the cases are lower than the middle value. Unlike the mean, the median is not affected by extreme values or outliers.

Question 14

Calculate the mean for the following six shoe sizes: 9,10,10,8,12,11.
A)8
B)8.5
C)9
D)9.5
E)10

Accepted Answer

The mean is calculated by adding all the numbers together and then dividing by the number of values. (9+10+10+8+12+11) / 6 = 60 / 6 = 10.

Question 15

Calculate the median for the following six shoe sizes: 9,10,10,8,12,11.
A)8
B)8.5
C)9
D)9.5
E)10

Accepted Answer

The median is the middle value of a set of numbers when assorted in numerical order. In this case, the numbers can be assorted as 8,9,10,10,11,12. The middle value is 10, so the median is 10.

Question 16

What are two ways in which statistical relationships can be described? Provide an example for each one.

Accepted Answer

The answer of What are two ways in which statistical...

Question 17

Which neighbourhood(s)has an income distribution resembling a normal curve?
A)Glenbrook
B)Meadowbrook
C)Elmbrook
D)Glenbrook and Elmbrook
E)Meadowbrook and Elmbrook

Accepted Answer

The answer of Which neighbourhood(s)has an income distribution resembling a...

Question 18

Which neighbourhood(s)has an income distribution resembling a skewed curve?
A)Glenbrook
B)Meadowbrook
C)Elmbrook
D)Glenbrook and Elmbrook
E)Meadowbrook and Elmbrook

Accepted Answer

Both Glenbrook and Elmbrook have a higher concentration of higher-income households, resulting in a skewed income distribution. Meadowbrook, on the other hand, has a more even distribution of income levels.

Question 19

Which neighbourhood(s)has the greatest differences in family income?
A)Glenbrook
B)Meadowbrook
C)Elmbrook
D)Glenbrook and Elmbrook
E)Meadowbrook and Elmbrook

Accepted Answer

The answer of Which neighbourhood(s)has the greatest differences in family...

Question 20

Describe each of the three measures of central tendency.What are the main differences between them? How are they affected by a normal versus a skewed distribution of data?

Accepted Answer

The answer of Describe each of the three measures of...

Quiz 11: Analysis of Quantitative Data

Describe each of the three techniques researchers use when deciding whether a relationship exists between two variables.

What are five measures of association that are useful when interpreting bivariate statistics? Describe each one and also specify which level of data each one is applicable to.

Is a Type I or Type II error more likely if a 0.05 level is used? Explain.

Describe four ways a researcher can display information about univariate statistics.

Why is knowing the variability or dispersion of a variable as important as knowing its central tendency? How is variation measured?

Describe,as simply as possible,what is meant by the statement "It is statistically significant at the 0.05 level."

A "codebook" is

You discover that the years of marriage before a divorce for nine whites and nine nonwhites are as follows:Whites 12,1,8,9,10,17,3,6,6 Non-Whites 1,9,15,18,11,13,14,7,3 Which statement about this data is true?

Explain how a researcher codes,enters,and cleans data so that it can be used for statistical analysis.What procedures are involved in each of these steps?

Calculate the mode for the following six shoe sizes: 9,10,10,8,12,11.

An elementary school teacher has three classes.She finds the following mean and standard deviations for student IQ scores. She knows she is most effective when the students all have similar IQ levels.Which class is she likely to be most effective with?

Discuss the concepts of control variables and trivariate tables.What are three limitations of trivariate tables?

A researcher wants to express the middle of a distribution of numbers whereby half the cases are higher and half the cases are lower than the middle value.What statistical measure should the researcher use?

Calculate the mean for the following six shoe sizes: 9,10,10,8,12,11.

Calculate the median for the following six shoe sizes: 9,10,10,8,12,11.

What are two ways in which statistical relationships can be described? Provide an example for each one.

Which neighbourhood(s) has an income distribution resembling a normal curve?

Which neighbourhood(s) has an income distribution resembling a skewed curve?

Which neighbourhood(s) has the greatest differences in family income?

Describe each of the three measures of central tendency.What are the main differences between them? How are they affected by a normal versus a skewed distribution of data?