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 problem1) Read the problem

• 2) Decide what statistical test to use

• 3) Perform that procedure3) Perform that procedure

• 4) Write an interpretation of the results4) Write an interpretation of the results

Four Step When Solving a Problem

• 1) Read the problem

• 2) Decide what statistical test to use2) 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. Regressionb. Dependent t-test l. Standard

Deviationc. One-Sample t-test m. Z-scored. Goodness of fit Chi-Square n. Modee. Independence Chi-Square n o. Meanf. Confidence Interval p. Mediang. Correlation (Pearson r) q. Bar Graphh. Scatter Plot r. Rangei. Line Graph s. ANOVAj. 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

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Happiness Score

Neu

roti

cism

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Line Graph

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Happiness Score

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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

Mean Median Mode

Nominal NO NO OK

Ordinal NO OK OK

Interval OK OK OK

Ratio OK OK OK

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

02468

101214161820

8 11 14 17 20 23 26 29 32 35 38

Neuroticism Score

Fre

quen

cy

Histogram

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Neuroticism Score

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Bar Graph

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Biology History Math Psychology Sociology

Major

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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.)

Cookbook

• Due Wednesday!

• Can be graded on the day of the final

• Grading (out of 20 points)– 5 points for complete table of contents– 10 points for no major sections missing

Cookbook

• Major sections:– 4 major topics (e.g., ANOVA, one-sample t-test,

regression, etc.) will be randomly selected for each student

– Must be able to find each section using the table of contents

– For each major topic a student is missing 10 points will be deducted