• Course Overview
• Statistical review (continued)
• Brief history of testing
• Norms and sampling

• E-411-PRMA Course Website
• Cohen, R. J., Swerdlik, M. E., & Sturman, E. D. (2013). Psychological testing and assessment: An introduction to tests and measurement. New York, NY: McGraw-Hill
• Website readings on item response theory and generalizability theory
• Will be using R in class and on assignments
• http://kennslubanki.hi.is/tolfraedi

• Thoughts?
• What was I measuring?
• Pros/cons of the tests?
• Will return to this test throughout the course

• What is measurement?
• Assignment of numerical values based on a set of rules
• What is a test?
• Instrument used to measure

• Scales - Nominal, ordinal, interval, and ratio
• An item measuring ...
• Temperature (in Celsius)
• Temperature (in Kelvin)
• Speed
• Gender
• Happiness

• What is a probability distribution
• Assigns a probability, likeliness of occurence, of a score of all possible scores
• May be parametric or non-parametric
• Normal
• What skew might you expect these outcomes to look like?
• Reaction time in a psychological experiment
• Number of children in a family
• Scores on an easy test
• Height in Reykjavík
• Platykurtic, mesokurtic, and leptokurtic
• Plot your data, rely less on statistics!

• GRE exam: Mean = 500, SD = 100, and 1000 participants
• Jarl gets a 650 on the GRE, about how many students scored below him?
• 330 students score below Þöll, what was her score?

        pnorm(650, mean = 500, sd = 100) * 1000
        # 933.1928
        qnorm(330/1000, mean = 500, sd = 150)
        # 456.0087

• 330 students score below Þöll, what percentile is she in?
• Percentiles represent a reasonably simple and intuitive way to classify scores relative to other test takers

        # Assign X the values of 5, 3, 1 and Y the values of 6, 0, and 0
        x <- c(5, 3, 1)
        y <- c(6, 0, 0)
        # Calculate the correlation
        cor(x , y)
        # 0.8660254

• Pretend we are interested in predicting height given someones weight
• We might consider a linear regression model

• There is a relationship between the estimated slope and the correlation between two variables in a SLR

• What is r if b is 0.287249, the SD of weight is 15.49869 and the SD of height is 4.472136?
• Does that parallel what you thought based on the plot?
• What would b become if r = 0.4?

• 2200 BCE, Chinese believed to use testing for determining who would get governmental jobs
• Greek and Romans categorized individuals based on personality type ("blood" or "phlegm")
• Francis Galton's classification based on "natural gift" (i.e. eugenics)
• Contributed to development of questionnaries, rating scales, and self-report inventories
• Wilhelm Wundt's laboratory and his focus on "standardization"
• James Cattell's mental tests
• Charles Spearman - reliability and factor analysis

• 1905, Binet and Simon publish a test measuring intelligence in mental retarded school children in Paris
• 1939, Wechsler publishes a test to measure intelligence in adults (would become WAIS)
• Group intelligence test administered by the US military during WWI and WWII
• WWI personality tests used to screen recruits

• Psychological traits and states exist
• Psychological traits and states can be measured
• Behavior on tests predicts non-test behavior
• Measurement error is part of the process
• Test can be fair
• Test can benefit society

• Individuals scores are relative only to some reference group
• This group should represent the entire pool of test takers for the tested construct
• Collectively, this group is known as a normative sample and data from them are the norms
• Understanding the normative sample is very important

• Simple random sample
• Stratified random sample
• Cluster random sample
• Purposive sample
• Convenience sample

• Developmental Norms
• Age Norms
• A 6 year old performs at the level of a 10 year old
• This is on this material only though!
• Grade Norms
• School year typically 10 months in the US (and Iceland?)
• A 4th grader is performing at the level of a 5th grader in third month
• This is on this material only though!
• National Norms, national representative
• Anchor norms enable two tests to be compared
• In USA, students could take SAT or ACT for admission to college

• Fixed reference group scores are used as the basis for calculation of future administrations of the test
• SAT does this through using anchor items and equating
• Criterion-referenced, evaluate a score with reference to a set criteria or standard NOT other test takers

• How would you score the grades in a class room?
• What do you think is the fairest way?

• Please read the chapter on reliability (chapter 5)
• Please watch the RStudio videos