WGU C784-STATISTICS MOD 5 |57 QUESTIONS AND ANSWERS

When one variable causes change in another, we call the first variable the ___________________ variable*. The affected variable is called the _______________ variable*. When one variable causes change in another, we call the first variable the explanatory variable*. The affected variable is called the response variable*. In a randomized experiment, the researcher manipulates values of the explanatory variable and measures the resulting changes in the response variable. The different values of the explanatory variable are called treatments. An experimental unit is a single object or individual to be measured. A two-way table, also known as a two-way frequency table or contingency table, is used to show the relationship between two ______________________variables ( C→C ); the rows show the categories of one variable, and the columns show the categories of the other variable. categorical variables ( C→C ) ______________________. These represent the total number of instances that fall in both the corresponding row and header. The data in the green cells show _______________________________. These are equal to the sum of the number of individuals in the corresponding row or column. The cells in yellow show joint frequencies*. These represent the total number of instances that fall in both the corresponding row and header. For example, data in the "Male" row and "With Autism" column counts the number of males with autism. The data in the green cells show marginal frequencies*. These are equal to the sum of the number of individuals in the corresponding row or column. For example, data in the "Totals" column and "Female" row shows the total number of females in the study. It may be helpful to remember that marginal frequencies appear in the margins of the table. The bottom, right cell (in both the "Totals" column and the "Totals" row) measures the total number of individuals in the study. The relationship between two variables that are both quantitative can be displayed in a __________________________. scatterplot; As we've seen earlier, every point on a coordinate plane can be represented by an ordered pair*, ( x , y ). Here, the x -value is typically the _________________variable's value for a piece of data, and the y -value is the corresponding value for the ________________________variable. A simple way to remember this fact is that the term "explanatory" has an " x " in it. explanatory variable; response variable Side-by-side box plots are a good choice for two-variable data where the explanatory variable is ____________ data and the response variable is ____________ data. Categorical Quantitative Which variable, explanatory or response, is displayed on the x -axis on side-by-side boxplots? Side-by-side boxplots can be horizontal or vertical, so either variable (explanatory or response) can be displayed on the x -axis. A scatterplot is a good choice to display two-variable data that are both __________ variables. Quantitative The relationship between the x -variable and the y -variable is called _____________. Correlation What determines the location of a dot on a scatterplot? A dot is placed on a scatterplot according to its x - and y -value. When analyzing a possible relationship for two-variable data, if both variables are categorical, what is the most appropriate choice to display the data? a) Side-by-side boxplots b) Scatterplot c) Bar chart d) Two-way frequency table e) Histogram Answer: D A two-way frequency table is the most appropriate way to graphically display a possible relationship for two-variable data, when both variables are categorical. A hospital hires an independent consulting firm to perform a study about patients with high blood pressure, and the medicine they are being prescribed. The study is examining the relationship between a patient's starting blood pressure when they entered the treatment program and the dosage of blood pressure medicine they are prescribed during their treatment. For this study: What is the explanatory variable? Is the explanatory variable categorical or quantitative? What is the response variable The explanatory variable is patient's starting blood pressure. The explanatory variable is a quantitative variable. The response variable is the dosage of blood pressure medicine they are prescribed. The response variable is also a quantitative variable. As both the explanatory and response variables are quantitative (Q→Q) , a scatterplot would be an appropriate graphical display. When working with two-variable data, if the explanatory variable is categorical and the response variable is quantitative, what is the most appropriate choice to display the data? a) Side-by-side boxplots b) Scatterplot c) Bar chart d) Two-way frequency table e) Histogram Answer: A When working with two-variable data, if one variable is categorical and the other is quantitative, a side-by-side boxplot is the most appropriate way to display the data. 13. When working with two-variable data, if both variables are quantitative, what is the most appropriate choice to display the data? a) Side-by-side boxplots b) Scatterplot c) Bar chart d) Two-way frequency table e) Histogram Answer: B When working with two-variable data, if both variables are quantitative, a scatterplot is the most appropriate choice to display the data. In a two-way table, what does the sum of the joint frequencies in one row equal? a) The quantitative variable b) A marginal frequency c) The correlation coefficient d) The number of individuals in the placebo group Correct. The correct answer is b. In a two-way table, the sum of the joint frequencies in one row equals a marginal frequency. If both variables are categorical, a ________- _________ ____________ ______________ is used to display the data. two-way frequency table There are several ways we can analyze the data presented in this table. If we calculate the percentage that each cell is of the total, the results are called relative frequencies. When the relative frequencies are calculated from the row total or the column total, they are called __________________ _____________________. conditional percentages. Each row is a different gender. If we are trying to see if gender influences the choice of exercise program, then gender is the explanatory variable. In this case, we are calculating the relative frequency by rows; that is, we are calculating the relative frequency by gender. To determine relative frequency for women, we divide the data in the top row by the total number of women. To determine the relative frequency for men, we divide the data in the second row by the total number of men. The pe conditional row percentages. Each column is a different exercise program. If we are trying to determine how each exercise program is appealing to different genders, then the exercise program becomes the explanatory variable. In this case, the explanatory variable is in the columns, so we will be calculating the relative frequency by columns, that is, we are calculating the relative frequency by exercise program. To determine relative frequency for each cell, we divide the data by the corresponding column's total number of i conditional column percentages Calculating Overall Percentages 5 Box Plot Summary If the explanatory variable is categorical and the response variable is quantitative, we can use descriptive statistics, namely the ___________________________ for the quantitative variable, and compare the statistics for each of the categories five-number summary, for the majority of the data points, there is a linear relationship indicating a positive correlation, meaning: When two quantitative variables move in the same direction; meaning that as one variable (response variable ) increases, the other variable (explanatory variable) increases. If the relationship is linear, the strength of the correlation (linear relationship) can be measured using a statistic called the correlation coefficient*. A correlation coefficient is a number that falls somewhere from −1 to 1 . A measure of the linear relationship between two attributes. The numerical value demonstrates how closely the attributes vary together. Correlation coefficients near -1 and +1 have strong linear correlation, while a correlation coefficient near 0 has weak (or no) linear correlation. A correlation coefficient at or near −1 represents a strong ____________________________________. A correlation coefficient at or near 1 represents a strong _____________________________. negative linear correlation ie. When two variables move in opposite directions, in a linear fashion: as the explanatory variable increases the response variable decreases. positive linear correlation ie. When two variables move in the same direction, in a linear fashion; the explanatory variable increases the response variable increases. To solve for the variation in data you take the ____________________ between the maximum and minimum. To solve for the variation in data you take the difference between the maximum and minimum. For the treatment group this is equal to 2.24−(−1.19)=3.43; for the placebo group this is equal to 0.78−(−2.29)=3.07. 3.07 is less than 3.43, Therefore the placebo group has less variation in its data. A scatterplot is useful for which type of data? a. Both variables are categorical. b. One variable is categorical, one variable is quantitative. c. Both variables are quantitative. d. One variable is discrete, one variable is continuous. c. Both variables are quantitative. True or False? A scatterplot always shows the explanatory variable on the horizontal, or x-axis. a. True b. False a. True on the X axis (hint- X for explanatory) 1. A hospital is studying the effectiveness of two different heartburn treatments (Treatment A and Treatment B) administered daily for a week. The results are measured after one week of treatment, by placing a patient into one of two groups: heartburn subsided OR heartburn remained. Which numerical measure could be used to analyze the data? a. Correlation coefficient b. Five-number summary c. Median d. Conditional percentages Correct. The answer is d. Both variables are categorical (C→C) so we will use a two-way table. Therefore, our numerical measure will be conditional percentages.