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Evaluate the effectiveness of a national organization's advertising campaign to reduce smoking by analyzing the number of cigarettes smoked before and after exposure to the campaign. Results indicate that the campaign did not reduce smoking significantly.
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Practice • As part of a program to reducing smoking, a national organization ran an advertising campaign to convince people to quit or reduce their smoking. To evaluate the effectiveness of their campaign, they had 15 subjects record the average number of cigarettes smoked per day in the week before and the week after exposure to the advertisement. Determine if the advertisements reduced their smoking (Alpha = .05).
Practice • Dependent t-test • t = .45 • Do not reject Ho • The advertising campaign did not reduce smoking
Practice • You wonder if there has been a significant change (.05) in grading practices over the years. • In 1985 the grade distribution for the school was:
Practice • Grades in 1985 • A: 14% • B: 26% • C: 31% • D: 19% • F: 10%
Step 1: State the Hypothesis • H0: The data do fit the model • i.e., Grades last semester are distributed the same way as they were in 1985. • H1: The data do not fit the model • i.e., Grades last semester are not distributed the same way as they were in 1985.
Step 2: Find 2 critical • df = number of categories - 1
Step 2: Find 2 critical • df = number of categories - 1 • df = 5 - 1 = 4 • = .05 • 2 critical = 9.49
Step 5: Calculate 2 O = observed frequency E = expected frequency
2 6.67
Step 6: Decision • Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0
2 = 6.67 2 crit = 9.49 Step 6: Decision • Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0
Step 7: Put answer into words • H0: The data do fit the model • Grades last semester are distributed the same way (.05) as they were in 1985.
The Three Goals of this Course • 1) Teach a new way of thinking • 2) Self-confidence in statistics • 3) Teach “factoids”
r = tobs = (X - ) / Sx r =
What you have learned! • Introduced to statistics and learned key words • Scales of measurement • Populations vs. Samples
What you have learned! • Learned how to organize scores of one variable using: • frequency distributions • graphs • measures of central tendency
What you have learned! • Learned about the variability of distributions • range • standard deviation • variance
What you have learned! • Learned about combination statistics • z-scores • effect sizes • box plots
What you have learned! • Learned about examining the relation between two continous variables • correlation (expresses relationship) • regression (predicts)
What you have learned! • Learned about probabilities
What you have learned! • Learned about the sampling distribution • central limit theorem • determine probabilities of sample means • confidence intervals
What you have learned! • Learned about hypothesis testing • using a t-test for to see if the mean of a single sample came from a population value
What you have learned! • Extended hypothesis testing to two samples • using a t-test for to see if two means are different from each other • independent • dependent
What you have learned! • Extended hypothesis testing to three or more samples • using an ANOVA to determine if three or means are different from each other
What you have learned! • Extended ANOVA to two or more IVs • Factorial ANOVA • Interaction
What you have learned! • Learned how to examine nominal variables • Chi-Square test of independence • Chi-Square test of goodness of fit
Next Step • Nothing new to learn! • Just need to learn how to put it all together
Four Step When Solving a Problem • 1) Read the problem • 2) Decide what statistical test to use • 3) Perform that procedure • 4) Write an interpretation of the results
Four Step When Solving a Problem • 1) Read the problem • 2) Decide what statistical test to use • 3) Perform that procedure • 4) Write an interpretation of the results
Four Step When Solving a Problem • 1) Read the problem • 2) Decide what statistical test to use • 3) Perform that procedure • 4) Write an interpretation of the results
How do you know when to use what? • If you are given a word problem, would you know which statistic you should use?
Example • An investigator wants to predict a male adult’s height from his length at birth. He obtains records of both measures from a sample of males.
Possible Answers a. Independent t-test k. Regression b. Dependent t-test l. Standard Deviation c. One-Sample t-test m. Z-score d. Goodness of fit Chi-Square n. Mode e. Independence Chi-Square n o. Mean f. Confidence Interval p. Median g. Correlation (Pearson r) q. Bar Graph h. Scatter Plot r. Range • Line Graph s. ANOVA j. Frequency Polygon t. Factorial ANOVA
Example • An investigator wants to predict a male adult’s height from his length at birth. He obtains records of both measures from a sample of males. • Use regression
Decision Tree • First Question: • Descriptive vs. Inferential • Perhaps most difficult part • Descriptive - a number or figure that summarizes a set of data • Inferential - use a sample to conclude something about a population • hint: these use confidence intervals or probabilities!
Decision Tree: Descriptive • One or Two Variables
Decision Tree: Descriptive: Two Variables • Graph, Relationship, or Prediction • Graph - visual display • Relationship – Quantify the relation between two continuous variables (CORRELATION) • Prediction – Predict a score on one variable from a score on a second variable (REGRESSION)
Decision Tree: Descriptive: Two Variables: Graph • Scatterplot vs. Line graph • Scatterlot • Linegraph • Both are used to show the relationship between two variables (it is usually subjective which one is used)
