Chapter 6: Comparing Two Means Section 6.1: Comparing Two Groups Quantitative Response

Transcription

1 Stat 300: Intro to Probability & Statistics Textbook: Introduction to Statistical Investigations Name: American River College Chapter 6: Comparing Two Means Section 6.1: Comparing Two Groups Quantitative Response REVIEW: Exploratory Data Analysis or EDA Guidelines Shape (Graph) What does the data distribution look like? o Possible Shapes - Symmetric (mound shape), Skewed Left, Skewed Right, Uniform, Bimodal. o Graphs to Consider Dotplot, Histogram, Boxplot Center What is a typical or representative value? o Different ways to measure the center Mean, Median, Mode, Midrange o Which measure (mean, median, mode) is the best way to represent a typical value? Spread or Variability How far does the data spread from the center? o Different ways to measure the spread Standard Deviation, Range, Inner Quartile Range (IQR) o Is the data consistent? Are the data close together? Outliers Are there any unusual observations that deviate from the overall pattern on the distribution? NEW: In this section, you will use an Exploratory Data Analysis to compare two groups of data. Example 1: Old Faithful - Part 3 In Chapter P, we used the Old Faithful data set to conduct our first EDA in order to analyze how long a tourist would have to wait to see an eruption of the Old Faithful Geyser in Yellowstone National Park in In this analysis, you will compare the time in between eruptions of Old Faithful in 1978 to time in between eruptions of Old Faithful in Questions to consider: Were the waiting times between eruptions similar or different in the two years? Were the times between eruptions more consistent in 1978 or 2003, or were they similar? Were tourists more likely to wait longer in 1978 or 2003 to see an eruption of Old Faithful? Data Set: For this exploration, you will need to access the data set labeled: Old Faithful Part 3: 1978 v 2003 in the StatCrunch group for this course. This data set contains the time between eruptions collected between 6 am and midnight August 1 8, 1978 and August 1-8, (a) What are the observation units in this study? (b) Identify and classify the two variables in your data table.

2 Stat 300 Text: Intro. to Statistical Investigations Section 6.1 Page 2 of 6 (c) Looking at your data table, where are the observational units located? Where are the variables located? [Hint: The answers to these questions are the rows or columns of the data table.] EDA - Comparing time between eruptions of Old Faithful. In StatCrunch, you will carry out your analysis on the time variable, but you need to make use of the GROUP BY: year feature. (d) SHAPE: Use StatCrunch, to make a dotplot to compare the time between eruptions in 1978 and Directions in StatCrunch Graph > Dotplot Select Column: time Group by: o Choose YEAR Click Compute! Your graph should look like this: (e) ANALYZE/COMPARE THE SHAPES: Compare the shapes of the two distributions. Describe one aspect of the shape that was apparent in 1978, but not in (f) CENTER: Use StatCrunch to calculate the different measures of center of the distributions. (Use appropriate notation.) In which year (1978 or 2003) did tourists generally have to wait a shorter amount of time for the next eruption? (g) VARIABILITY: Looking at the dotplots, which distribution has more variability? How do you know? Explain your answer and how you can see variability in the dotplot.

3 Stat 300 Text: Intro. to Statistical Investigations Section 6.1 Page 3 of 6 (h) VARABILITY: Use StatCrunch to calculate the standard deviation for the times between eruptions in 1978 and in (Use appropriate notation.) In which year (1978 or 2003) was the waiting time until the next eruption more consistent? Explain how the standard deviation of the distribution is related to the consistency or variability in the distribution. (g) OUTLIERS: Use StatCrunch to create two boxplots for the time between eruptions of Old Faithful in 1978 versus Have StatCrunch mark the outliers using fences. Are there any outliers in the distribution? StatCrunch Directions: Graph > Boxplot o Under Column - Click: time. o Under Group by - Click: year Under Other Options: o Click: Use fences to identify outliers o Click: Draw boxes horizontally. Click Compute! Your graph should look like this: (h) ANALYZE THE BOXPLOT: Compare the two distributions by analyzing their boxplots. Which distribution has a smaller IQR? Explain how can you tell by looking at the boxplot? If a distribution has a smaller IQR, does that mean that the distribution has more variability or more consistency than the other distribution? How do you know? Explain. Consider the statement: The quickest 75% of times in 1978 were below the longest 75% of times in Explain how this is evident by looking at the boxplots. (i) Based on the distributions of times between eruptions, in which year would you have preferred to be a tourist waiting for the next eruption of Old Faithful? Can you think of one way in which 1978 would have been preferable and a different way in which 2003 would have been preferable?

4 Stat 300 Text: Intro. to Statistical Investigations Section 6.1 Page 4 of 6 Example 2: Nutritional Data for Fast Food Restaurants 2017 For this example you need to access the data set named: Nutritional Data for Fast Food Restaurants 2017 in the StatCrunch group. (a) What are the observational units in this data table? How many observation units are there in the table? [Hint: Should you look at the rows or columns for the observation units in a data table?] (b) How many variables are in this data table? [Hint: Should you look at the rows or columns for the observation units in a data table?] Which variables are categorical? Which variables are quantitative? Exploratory Data Analysis: Comparing Calorie Content at Fast Food Restaurants Use the following two variables in the data table to conduct an EDA: Fast Food Restaurant Calories (c) Classify each of the following the variables as categorical or quantitative Variable 1 - Fast Food Restaurant Variable 2 - Calories (d) SHAPE: Use StatCrunch to create the comparative dotplots, histograms, and boxplots, for the calorie content GROUPED BY fast food restaurant. For this set of data, which set of graphs do you think is the most useful to compare the distributions of calorie content at the various fast food restaurants in the table? Why? Circle one: Dotplots Histograms Boxplots Identify the shape that best describes each calorie content distribution by fast food restaurant. List each restaurant under the work that best describes the distribution. (One has been done for you.) Skewed Right Skewed Left Symmetric/Normal - Sonic

5 Stat 300 Text: Intro. to Statistical Investigations Section 6.1 Page 5 of 6 The shape of the calorie content distribution for sample items from Sonic is skewed right. Describe what this means IN CONTEXT. (Do not write: There is a tail on the right side. This question is asking you to describe WHY it is skewed right. THINK about what is causing the skew. THINK about why it is not symmetric.) (e) CENTER: Do all of the fast food restaurants generally have the same calorie content for a typical item? Explain how your answer. (f) CENTER: Group the restaurants together that do have similar calorie content for a typical item. How can you tell this by looking at the comparative boxplot graph? (g) VARABILITY: Which fast food restaurants have the highest variability across the calorie contents of items in the data table? Which fast food restaurants are more consistent across the calorie contents of items in the data table? Explain your answer. Describe how you can tell which calorie content distributions are have high variability or high consistency by looking at the boxplots. (h) ANALYZE IT! If you were on a diet while on a road trip, what would be the best fast food restaurant(s) to eat at in order to have to a larger variety of items to choose from with a lower calorie content? Explain how your made your decision. (i) In this example, you have compared the calorie content of items at different fast food restaurants. Describe at least one problem with our analysis and suggest what variables should compare in order to improve our analysis.

6 Stat 300 Text: Intro. to Statistical Investigations Section 6.1 Page 6 of 6 Exploratory Data Analysis: Comparing Calorie Content at Fast Food Restaurants Now, use the following two variables in the data table to conduct an EDA: Type Calories (j) Classify each of the following the variables as categorical or quantitative Variable 1 - Type Variable 2 - Calories (k) Which Type of items in the data table have the largest variability in calorie content? Describe how you reached your conclusion. (l) Which Type of items in the data table have the largest consistency in calorie content? Describe how you reached your conclusion. (m) Identify the TWO TYPES of items in the data table that fit this description: 100% of the calorie contents from items TYPE A are less than 100 % of the calorie contents from items in TYPE B. Type A: Type B: Describe how you reached your conclusion. (n) Follow the directions below to create a Means Plot in StatCrunch Directions in StatCrunch Graph > Means Plot Select Column: Calories Group by: o Choose Type Click Compute! à Can you tell what the Means Plot graphic displays? Hover over each item to see a summary of each plot. THINK about the topics that we have discussed throughout this course.