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 Subject Before After 1 45 43 2 16 20 3 17 4 33 30 5 25 6 19 7 34 8 28 9 26 23 10 40 41 11 12 36 13 15 14 32

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%

Grades last semester

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 3: Create the data table

Step 4: Calculate the Expected Frequencies

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

Step 6: Decision Thus, if 2 > than 2critical 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”

Mean But here is the formula == so what you did was 70 + 80+ 80+ 90 = 320 320 / 4 = 80

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

CRN: 33496.0

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)

Scatter Plot Then you locate the each midpoints frequency point

Line Graph Then you locate the each midpoints frequency point

Decision Tree: Descriptive: One Variable Central Tendency, Variability, Z-Score, Graph Central Tendency – one score that represents an entire group of scores Variability – indicates the spread of scores Z-Score – converts a score so that is conveys the sore’s relationship to the mean and SD of the other scores. Graph – Visual display

Decision Tree: Descriptive: One Variable: Central Tendency Mean, Median, Mode

Decision Tree: Descriptive: One Variable: Central Tendency Mean, Median, Mode

Decision Tree: Descriptive: One Variable: Variability Variance, Standard Deviation, Range/IQR Variance Standard Deviation Uses all of the scores to compute a measure of variability Range/IQR Only uses two scores to compute a measure of variability In general, variance and standard deviation are better to use a measures of variability

Decision Tree: Descriptive: One Variable: Graph Frequency Polygon, Histogram, Bar Graph Frequency Polygon Histogram Interchangeable graphs – both show frequency of continuous variables Bar Graph Displays the frequencies of a qualitative (nominal) variable

Frequency Polygon Then you locate the each midpoints frequency point

Histogram

Bar Graph

Decision Tree: Inferential: Frequency Counts vs. Means w/ One IV vs. Means w/ Two or more IVs Frequency Counts – data is in the form of qualitative (nominal) data Means w/ one IV – data can be computed into means (i.e., it is interval or ratio) and there is only one IV Means w/ two or more IVs – data can be computed into means (i.e., it is interval or ratio) and there are two or more IVs Confidence Interval - with some degree of certainly (usually 95%) you establish a range around a mean

Decision Tree: Inferential: Frequency Counts Goodness of Fit vs. Test of Independence Goodness of Fit – Used to determine if there is a good fit between a qualitative theoretical distribution and the qualitative data. Test of Independence – Tests to determine if two qualitative variables are independent – that there is no relationship.

Decision Tree: Inferential: Means with two or more IVs Factorial ANOVA

Decision Tree: Inferential: Means with one IV One Sample, Two Samples, Three or more One Sample – Used to determine if a single sample is different, >, or < than some value (usually a known population mean; ONE-SAMPLE t-TEST) Two Samples – Used to determine if two samples are different, >, or < than each other Two or more – Used to determine if three or more samples are different than each other (ANOVA).

Decision Tree: Inferential: Means with one IV: Two Samples Independent vs. Dependent Independent – there is no logical reason to pair a specific score in one sample with a specific score in the other sample Paired Samples – there is a logical reason to pair specific scores (e.g., repeated measures, matched pairs, natural pairs, etc.)

Final Exam Test = 1 hour and 45 minutes 1:30 class is Mon, Dec 14 2:30-4:15 3:00 class is Tues, Dec 15 2:30-4:15 *Note about testing students

Cookbook Due: Final exam Early grade: Wednesday!