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]]>Topics:

**Introduction to Estimation **link:intro estimation

- Learning Objectives

- Define statistic
- Define parameter
- Define point estimate
- Define interval estimate
- Define margin of error

**Degrees of Freedom **link:Degrees of Freedom

- Learning Objectives

- Define degrees of freedom
- Estimate the variance from a sample of 1 if the population mean is known
- State why deviations from the sample mean are not independent
- State the general formula for degrees of freedom in terms of the number of values and the number of estimated parameters
- Calculate s
^{2}

**Characteristics of Estimators **link:characteristics

- Learning Objectives

- Define bias
- Define sampling variability
- Define expected value
- Define relative efficiency

**Introduction to Confidence Intervals **link:intro confidence Interval

- Learning Objectives

- Define confidence interval
- State why a confidence interval is not the probability the interval contains the parameter

**t Distribution **link:t distribution

- Learning Objectives

- State the difference between the shape of the t distribution and the normal distribution
- State how the difference between the shape of the t distribution and normal distribution is affected by the degrees of freedom
- Use a t table to find the value of t to use in a confidence interval
- Use the t calculator to find the value of t to use in a confidence interval

**Confidence Interval for the Mean **link:Confidence interval for the mean

- Learning Objectives

- Use the inverse normal distribution calculator to find the value of z to use for a confidence interval
- Compute a confidence interval on the mean when σ is known
- Determine whether to use a t distribution or a normal distribution
- Compute a confidence interval on the mean when σ is estimated

**Difference between Means **link:Difference Between Means

- Learning Objectives

- State the assumptions for computing a confidence interval on the difference between means
- Compute a confidence interval on the difference between means
- Format data for computer analysis

**Correlation **link:pearson correlation

- Learning Objectives

- State why the z’ transformation is necessary
- Compute the standard error of z’
- Compute a confidence interval on ρ

**Proportion **link:ci for proportion

- Learning Objectives

- Estimate the population proportion from sample proportions
- Apply the correction for continuity
- Compute a confidence interval

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**Introduction to Sampling Distributions **link:Introduction to Sampling Distributions

- Learning Objectives

- Define inferential statistics
- Graph a probability distribution for the mean of a discrete variable
- Describe a sampling distribution in terms of “all possible outcomes”
- Describe a sampling distribution in terms of repeated sampling
- Describe the role of sampling distributions in inferential statistics
- Define the standard error of the mean

**Sampling Distribution of the Mean **link:Sampling Distribution of the Mean

- Learning Objectives

- State the mean and variance of the sampling distribution of the mean
- Compute the standard error of the mean
- State the central limit theorem

**Sampling Distribution of Difference Between Means **link:Sampling Distribution difference between means

- Learning Objectives

- State the mean and variance of the sampling distribution of the difference between means
- Compute the standard error of the difference between means
- Compute the probability of a difference between means being above a specified value

**Sampling Distribution of Pearson’s r **link:sampling distribution of r

- Learning Objectives

- State how the shape of the sampling distribution of r deviates from normality
- Transform r to z’
- Compute the standard error of z’
- Calculate the probability of obtaining an r above a specified value

**Sampling Distribution of p **link:Sampling Distribution of p

- Learning Objectives

- Compute the mean and standard deviation of the sampling distribution of p
- State the relationship between the sampling distribution of p and the normal distribution

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]]>Topics:

**Introduction to Normal Distributions **link:Introduction to Normal

- Learning Objectives

- Describe the shape of normal distributions
- State 7 features of normal distributions

**History of the Normal Distribution **link:History Normal

- Learning Objectives

- Name the person who discovered the normal distribution and state the problem he applied it to
- State the relationship between the normal and binomial distributions
- State who related the normal distribution to errors
- Describe briefly the central limit theorem
- State who was the first to prove the central limit theorem

**Areas Under Normal Distributions **link:Areas of Normal Distrubution

- Learning Objectives

- State the proportion of a normal distribution within 1 standard deviation of the mean
- State the proportion of a normal distribution that is more than 1.96 standard deviations from the mean
- Use the normal calculator to calculate an area for a given X”
- Use the normal calculator to calculate X for a given area

**Standard Normal Distribution **link:Standard Normal Distribution

- Learning Objectives

- State the mean and standard deviation of the standard normal distribution
- Use a Z table
- Use the normal calculator
- Transform raw data to Z scores

**Normal Approximation to the Binomial **link:Normal Approximation to Binomial

- Learning Objectives

- State the relationship between the normal distribution and the binomial distribution
- Use the normal distribution to approximate the binomial distribution
- State when the approximation is adequate

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]]>Topics:

Note: All topics below are summarized by the following note outline: Research Design

**Measurement **

- Learning Objectives

- Define reliability
- Describe reliability in terms of true scores and error
- Compute reliability from the true score and error variance
- Define the standard error of measurement and state why it is valuable
- State the effect of test length on reliability
- Distinguish between reliability and validity
- Define three types of validity
- State the how reliability determines the upper limit to validity

**Basics of Data Collection**

- Learning Objectives

- Describe how a variable such as height should be recorded
- Choose a good response scale for a questionnaire

**Sampling Bias**

- Learning Objectives

- Recognize sampling bias
- Distinguish among self-selection bias, undercoverage bias, and survivorship bias

**Experimental Designs**

- Learning Objectives

- Distinguish between between-subject and within-subject designs
- State the advantages of within-subject designs
- Define “multi-factor design” and “factorial design”
- Identify the levels of a variable in an experimental design
- Describe when counterbalancing is used

**Causation**

- Learning Objectives

- Explain how experimentation allows causal inferences
- Explain the role of unmeasured variables
- Explain the “third-variable” problem
- Explain how causation can be inferred in non-experimental designs

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]]>Topics:

**Remarks on the Concept of “Probability” **link:Probability Intro

- Learning Objectives

- Define symmetrical outcomes
- Distinguish between frequentist and subjective approaches
- Determine whether the frequentist or subjective approach is better suited for a given situation

**Basic Concepts **link:Basic Concepts

- Learning Objectives

- Compute probability in a situation where there are equally-likely outcomes
- Apply concepts to cards and dice
- Compute the probability of two independent events both occurring
- Compute the probability of either of two independent events occurring
- Do problems that involve conditional probabilities
- Compute the probability that in a room of N people, at least two share a birthday

**Permutations and Combinations **link:Permutations and Combinations

- Learning Objectives

- Calculate the probability of two independent events occurring
- Define permutations and combinations
- List all permutations and combinations
- Apply formulas for permutations and combination
- Describe the gambler’s fallacy

**Binomial Distribution **link:Binomial Distribution

- Learning Objectives

- Define binomial outcomes
- Compute the probability of getting X successes in N trials
- Compute cumulative binomial probabilities
- Find the mean and standard deviation of a binomial distribution

**Poisson Distribution **link:Poisson

- Learning Objectives

- Use the Poisson distribution to calculate the probabilities of various numbers of “successes” based on the mean number of successes

**Multinomial Distribution **link:Multinomial

- Learning Objectives

- Define multinomial outcomes
- Compute probabilities using the multinomial distribution

**Hypergeometric Distribution **link:Hypergeometric

- Learning Objectives

- Use the hypergeometric distribution to calculate probabilities when sampling without replacement

**Base Rates **link:Base Rates

- Learning Objectives

- Compute the probability of a condition from hits, false alarms, and base rates using a tree diagram
- Compute the probability of a condition from hits, false alarms, and base rates using Bayes’ Theorem

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]]>Topics:

**Introduction to Bivariate Data **link:Intro Bivariate

- Learning Objectives

- Define “bivariate data”
- Define “scatter plot”
- Distinguish between a linear and a nonlinear relationship
- Identify positive and negative associations from a scatter plot

**Values of the Pearson Correlation **link:Values of the Pearson

- Learning Objectives

- Describe what Pearson’s correlation measures
- Give the symbols for Pearson’s correlation in the sample and in the population
- State the possible range for Pearson’s correlation
- Identify a perfect linear relationship

**Properties of Pearson’s r **link:Properties of r

- Learning Objectives

- State the range of values for Pearson’s correlation
- State the values that represent perfect linear relationships
- State the relationship between the correlation of Y with X and the correlation of X with Y
- State the effect of linear transformations on Pearson’s correlation

**Computing Pearson’s r **link:Computing Pearson’s r

- Learning Objectives

- Define X and x
- State why Σxy = 0 when there is no relationship
- Calculate r

**Variance Sum Law II **link:Variance Sum Law II

- Learning Objectives

- State the variance sum law when X and Y are not assumed to be independent
- Compute the variance of the sum of two variables if the variance of each and their correlation is known
- Compute the variance of the difference between two variables if the variance of each and their correlation is known

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**What is Central Tendency? **link:What is Central Tendency

- Learning Objectives

- Identify situations in which knowing the center of a distribution would be valuable
- Give three different ways the center of a distribution can be defined
- Describe how the balance is different for symmetric distributions than it is for asymmetric distributions.

**Measures of Central Tendency **link:Measures of Central Tendency

- Learning Objectives

- Compute mean
- Compute median
- Compute mode

**Median and Mean **link:Median and Mean

- Learning Objectives

- State when the mean and median are the same
- State whether it is the mean or median that minimizes the mean absolute deviation
- State whether it is the mean or median that minimizes the mean squared deviation
- State whether it is the mean or median that is the balance point on a balance scale

**Additional Measures of Central Tendency **link:Additional Measures

- Learning Objectives

- Compute the trimean
- Compute the geometric mean directly
- Compute the geometric mean using logs
- Use the geometric to compute annual portfolio returns
- Compute a trimmed mean

**Comparing Measures of Central Tendency **link:Comparing Measures

- Learning Objectives

- Understand how the difference between the mean and median is affected by skew
- State how the measures differ in symmetric distributions
- State which measure(s) should be used to describe the center of a skewed distribution

**Measures of Variability **link:Variability

- Learning Objectives

- Determine the relative variability of two distributions
- Compute the range
- Compute the inter-quartile range
- Compute the variance in the population
- Estimate the variance from a sample
- Compute the standard deviation from the variance

**Shapes of Distributions **link:shapes

- Learning Objectives

- Compute skew using two different formulas
- Compute kurtosis

**Effects of Linear Transformations **link:Effects of Linear Transformations

- Learning Objectives

- Define a linear transformation
- Compute the mean of a transformed variable
- Compute the variance of a transformed variable

**Variance Sum Law I **link:Variance Sum Law

- Learning Objectives

- Compute the variance of the sum of two uncorrelated variables
- Compute the variance of the difference between two uncorrelated variables

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Topics:

**Beginning Graphing and Qualitative and Quantitative Variables **link:Intro to graphs

- Learning Objectives

- Create a frequency table
- Determine when pie charts are valuable and when they are not
- Create and interpret bar charts
- Identify common graphical mistakes

**Stem and Leaf Displays **link:stem and leaf

- Learning Objectives

- Create and interpret basic stem and leaf displays
- Create and interpret back-to-back stem and leaf displays
- Judge whether a stem and leaf display is appropriate for a given data set

**Histograms **link:Histograms

- Learning Objectives

- Create a grouped frequency distribution
- Create a histogram based on a grouped frequency distribution
- Determine an appropriate bin width

**Frequency Polygons **link:Frequency Polygons

- Learning Objectives

- Create and interpret frequency polygons
- Create and interpret cumulative frequency polygons
- Create and interpret overlaid frequency polygons

**Box Plots **link:Box Plots

- Learning Objectives

- Define basic terms including hinges, H-spread, step, adjacent value, outside value, and far out value
- Create a box plot
- Create parallel box plots
- Determine whether a box plot is appropriate for a given data set

**Bar Charts **link:Bar Charts

- Learning Objectives

- Create and interpret bar charts
- Judge whether a bar chart or another graph such as a box plot would be more appropriate

**Line Graphs **link:Line Graphs

Learning Objectives

- Create and interpret line graphs
- Judge whether a line graph would be appropriate for a given data set

**Dot Plots **link:Dot Plots

Learning Objectives

- Create and interpret dot plots
- Judge whether a dot plot would be appropriate for a given data set

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**What are Statistics?** link: What are statistics?

- Learning Objectives

- Describe the range of applications of statistics
- Identify situations in which statistics can be misleading
- Define “statistics”

**Importance of Statistics** link: Importance of statistics

- Learning Objectives

- Give examples of statistics
- Give examples of how statistics can lend credibility to an argument

**Descriptive Statistics** link: Descriptive Statistics

- Learning Objectives

- Define “descriptive statistics”
- Distinguish between descriptive statistics and inferential statistics

**Inferential Statistics **link: Inferential Statistics

- Learning Objectives

- Distinguish between a sample and a population
- Define inferential statistics
- Identify biased samples
- Distinguish between simple random sampling and stratified sampling
- Distinguish between random sampling and random assignment

**Variables **link: Variables

- Learning Objectives

- Define and distinguish between independent and dependent variables
- Define and distinguish between qualitative and quantitative variables
- Define and distinguish between discrete and continuous variables

**Percentiles** link:Percentiles

- Learning Objectives

- Define percentiles
- Use three formulas for computing percentiles

**Levels of measurement **link:Levels of measurement

- Learning Objectives

- Define and distinguish among nominal, ordinal, interval, and ration scales
- Identify a scale type
- Discuss the type of scale used in psychological measurement
- Give examples of errors that can be made by failing to understand the proper use of measurement scales

**Distributions **link: Distributions

- Learning Objectives

- Define “distribution”
- Interpret a frequency distribution
- Distinguish between a frequency distribution and a probability distribution
- Construct a grouped frequency distribution for a continuous variable
- Identify the skew of a distribution
- Identify bimodal, leptokkurtic, and platykurtic distributions

**Summation Notation** link:Summation Notation

- Learning Objectives

- Use summation notation to express the sum of all numbers
- Use summation notation to express the sum of a subset of numbers
- Use summation notation to express the sum of squares

**Logarithms** link: http://algebranotes.info/logarithmic-functions-2/

- Learning Objectives

- Compute logs using different bases
- Convert between bases
- State the relationship between logs and proportional change

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