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Learning Objectives: (1) To learn how to enter data into SPSS; (2) To learn how to obtain frequency distribution tables and histograms and how to interpret them; (3) To learn how to obtain descriptive statistics and how to interpret them; (4) To use frequency distributions and descriptive statistics to make decisions about data; and (5) To compare different distributions.
Scenario: Dr. Torres teaches two sections of Stat 95 at SJSU. After grading the first exam, he wants to compare the two sections to see which one performed better on the exam. Use the data below to help Dr. Torres compare the two sections. The data represent percentages on the exam.
Section 1Section 262687376698297636199909185938085778271787377526466775558767384897681697270786570
Summary of Tasks:
Compute the mean, median, mode, minimum, maximum, range, and standard deviation for each group.
Create a histogram for each distribution.
Answer the following questions using the data and graphs.
Questions (Be sure to use complete sentences):
Describe the center of each distribution.
What are the mean, median, and mode for each distribution?
Look at the frequency distribution table. What is the most frequently occurring score in each distribution? What percent of students in each section received this score?
Name the measure of central tendency that divides the top 50% from the bottom 50% of scores.
Based on these measures of central tendency, which Section performed better? Explain your answer.
Describe the variability in each distribution.
What is the minimum and maximum score in each distribution?
What is the range for each distribution? What does this measure tell us about the dispersion of scores in each distribution?
What is the standard deviation for each distribution? What does this measure tell us about the dispersion of scores in each distribution?
Which Section displays more variability? Explain your answer.
Describe the shape of each distribution
Based on the three measures of central tendency, are the distributions approximately normal or are they skewed? Explain your answer.
Based on the histograms, do the distributions appear approximately normal or skewed? Explain your answer. Does this answer agree with your answer to the previous question?
Generate a box-plot, and identify the scores at each quartile for section 1 and Section 2.
I would like you to generate by hand a stem-and-leaf plot for Section 1.
EXCEL Central Limit Theorem exercise.
Learning Objectives: (1) To learn how to enter data into Excel; (2) To learn how to generate a rectangular distribution of random numbers from 0-10. (3) To simulate collecting sample means from a distribution of random numbers (4) to simulate generating a distribution of sample means from a rectangular distribution of random numbers. and (5) To compare different distributions.
Open an Excel Worksheet.
Pick a cell and type in the cell the following formula: =RAND()*10. Be sure to include the equal sign. This formula will generate random numbers between 0-10
Move the cursor over the cell. You will notice the arrow changes to a cross, then if you place the cross over over the bottom right corner of the cell, the cross becomes a cross-hair (looks like a plus sign). When your cursor is in cross-hair mode, Left Click and drag the cell. This will replicate the contents of the cell, and generate more random numbers between 0-10.
Scroll down, until you have generated 90 random numbers between 0-10
Generate sample means with sample size of 3.
Return cursor to top of column of random generated numbers, Select cell one column over (ie., select an empty cell right next to the column you generated).
Select Auto Sum(Average. A selection box will appear of the numbers Excel is guessing you want to average. Drag the selection box to include 3 random generated numbers. This generates a sample mean, sample size = 3.
Repeat the step above for the second set of three numbers.
Replicate the sample means for all 90 scores. You will Select six cells (a first sample mean, followed by two empty cells, followed by the second sample mean, followed by two empty cells. Total of six cells). Place cursor over lower right corner of selected cells, cursor turns to cross-hair mode. Drag to end of adjacent column.
We assume that taking the average of randomly generated numbers simulates random selection.
Print a histogram in SPSS of the random numbers and print a histogram of the Distribution of the Sample Means. DO NOT PRINT OUT ALL THE NUMBERS, JUST THE FREQUENCY DISTRIBUTIONS.
Describe the shapes of the frequency distribution of variables and the frequency distribution of sample means. What is the difference between the two shapes, and how does the Central Limit Theorem explain that difference?
REPEAT TWICE. You will have a total of six graphs (three of the variable distributions, and three of the sample mean distributions)
You will notice that every command on excel refreshes the randomly generated numbers, and along with it the new sample means. You do not need to repeat the scrolling, just refresh the list of randomly generated numbers and copy and paste the values into SPSS.
To save paper, try to get all the graphs on the same page, you can usually do this by shrinking the graph or using the Snipping Tool, make an image copy of the graph and then shrink the image copy.
For each of the three randomly generated lists of numbers and their sample means, pick two variables (raw scores) from above AND below the mean (four total), give me their Z-score, and the probability associated with the z-score. Pick ONLY two sample means and provide the z-statistics of the sample mean.
I WOULD LIKE ONE POSITIVE AND ONE NEGATIVE Z-STATISTIC this means you need to know the mean of the sample means.
SHOW THE STEPS AND THE WORK. Show the calculations for the z-scores and z-statistics.
Lady Tasting Tea Chapter 1
What problems did Fisher have to tackle in the designing the experiment that could determine if the Lady could distinguish between milk-then-tea and tea-then-milk cups of tea?
In examining the fertility index and rainfall records at Rothamsted, what two main errors did he conclude about the indexes and how did he express results about the rainfall?
What did Fisher conclude scientists needed to start with to do an experiment, and what would a useful experiment do?
Cancelled Class Exercises: Critical Reasoning
An elementary school teacher is interested in the relation between sugar consumption and activity level in preschool children. The teacher gives 30 preschool children from the Preppy Preschool Playland either 0 milligrams, 20 milligrams, or 50 milligrams of sucrose (i.e., sugar) in a breakfast drink. He then observes their behavior for 30 minutes during their morning outdoor play period and codes their activity level. Identify each of the following for this study:
a. The population
b. The sample
c. The independent variable
d. The levels of the independent variable
e. The dependent variable
Schacter and Gross (1968) gathered data from a group of 60 male students for about one hour in the afternoon. At the end of this period of time, a clock on the wall was correct (5:30 PM) for 20 participants, slow (5:00 PM) for 20 others, and fast (6:00 PM) for 20 more. The actual time for all groups was 5:30, the usual dinnertime for these students. While participants filled out a final questionnaire, the experimenters provided Wheat Thins for the students to eat. The weight of the crackers each student consumed was measured. The means were: 5:00 group 20grams; 5:30 group 30 grams; 6:00 group 40 grams. Identify each of the following for this study:
a. The population
b. The sample
c. The independent variable
d. The levels of the independent variable
e. The dependent variable
f. The descriptive statistic
g. Any inferences warranted by this study
Identify at least one confounding variable that undermines the conclusion drawn in the following fictional study description: Prof. Martin was interested in which of two popular statistics textbooks (Statistics: It Will Change Your Life and Statistics: Bigger, Better, Stronger) was better for students. Prof. Martin compared the two texts by assigning one text to a section of statistics taught by Prof. Miller at 10:00 AM on MWF and the other text to a section of statistics taught by Prof. Mervin from 7-10 PM on Wednesday evenings. At the end of the term, all students took the same comprehensive test. Students who were assigned Statistics: Bigger, Better, Stronger performed better on the test than did students who were assigned Statistics: It Will Change Your Life. Prof. Martin therefore concluded that the former textbook was the better one.
The following figure appeared on the Statistics Canada Web site. Evaluate the figure. What aspects of the figure should be changed so it more clearly depicts the data?
Figure: Absenteeism Rates Up
What is meant by a representative sample? Why is it important to obtain a representative sample?
What is the difference between a Type I and a Type II error? Which kind of error is more likely to be published and why? Give an example of each, and describe a situation that makes these kinds of errors dangerous.
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