Ch2 - Stats for Testing Flashcards
Measurement
the use of certain devices/rules for assigning numbers to objects/events
Variables + types
anything that varies
• Visible/invisible
• Discrete (errors in counting)/continuous (measurement errors)
• Dichotomous / Polytomous (discrete variables assuming + than 2 values)
Nominal scales type of data
Categorical data: data related to variables such as gender, color, that derive from assigning people, objects or events in categories/classes
• The only property of the numbers given to define the categories is identity
• We can only count the frequencies within each category
Ordinal scales properties
Added property of rank order: the elements in a set can be lined up in a series arranged on the basis of a single variable (ex: birth order)
• Rank orders carry no information regarding the distance between positions
In psych, rank-ordered tests are reported as percentile rank scores (PR)
• Ordinal numbers from 1 to 100, rank indicates the % of individuals in a group who fall at or below a given level of performance
○ Ex: 70 - level of performance that equals or exceeds 70% of the group
Ordinal data can be manipulated like nominal data, but also with Spearman’s rho correlation coefficient
Interval scales properties
Difference between any 2 consecutive numbers is the same that the numbers represent
• Ex: if 2 days are 12 days apart, they are exactly 3 times as far apart as 2 days that are 4 days apart
○ *some months are longer than others so it does not apply to months
• There is no agreed upon starting point for the calendar, so no absolute 0 - can’t be interpreted as ratios
Ratio scales properties
Numbers achieve additivity: they can be added, substracted, multiplied, divided and the result will be a meaningful ratio
• Have a true/absolute 0 - represents NONE of what is measured
• Ex: an object of 16pounds is 2x as heavy as an 8pound object, and 0pounds indicates weightlessness
Problem with ratio IQs
Ratio IQs were obtained by:
• (Mental Age (result on S-B test) / Child’s chronological age) x 100 = ratio IQ
• Idea: average children would have an IQ of 100 (since their mental age would equal their actual age)
• BUT: did not work with adolescents/adults bc their development is less uniform / less intense
○ Mental age = ordinal-level measurement
○ Chronological age = ratio scale
○ Dividing the 2 cant lead to a meaningful number
2 types of stats
- Descriptive: maths dedicated to organize / summarize / etc data
- Inferential: used to estimate pop values based on sample values
Statistics def
relate to sample data
Parameter def
relate to population data
○ Mathematically exact numbers (or constants) that are not usually attainable unless a population is so fixed and circumscribed that all of its members can be accounted for
Frequency distributions
frequency with which each scores occurs in a distribution
• Can also include percentile rank scores (Cumulative Percent Column)
• Grouped frequency distributions: when the ranges are too large
Graphs (+ best types for discrete vs continuous data)
Frequency tables can be made into graphs for even easier reading
• Discrete/categorical data: pie charts or bar graphs
• Continuous/metric data: histograms/frequency polygons
• Measures of central tendency
○ Mode: + frequent value in a distribution (bimodal/multimodal = more than one variable with the same value)
○ Median: value that divides a distribution that has been arranged in order of magnitude into 2 halves
○ Mean: arithmetic average (u for pop and M for sample)
Range
distance between the 2 extreme points
Semi-interquartile range
1/2 of the interquartile range (IQR) - the middle 50% of a distribution
IQR
distance between the points that demarcate the tops of the first and third quarters of a distribution
Variance
sum of squared differences between each values and the mean of that distribution, divided by n (AKA Average sum of squares SS) - represents average variability in distribution
Sum of squares
represents total amount of variability in a score distribution
Standard deviation
square root of the variance - represents the average variability in a set of scores
Properties of the Normal Curve Model
- Its limits extend to +/- infinity
- Is unimodal
- Mean = median = mode = center
Standard Normal Distribution
Normal Curve with a mean of 0 and a standard deviation of 1
Uses of the Normal Curve
desctiptive/inferential
• Descriptive Uses ○ Normalizing scores: transforming them so that they have the same meaning, in terms of their position, as if they were coming from a normal distribution • Inferential Uses ○ Estimating population parameters ○ Testing hypotheses about differences
Sampling distribution
hypothetical distributions of values made on the assumption that an infinite number of samples of a given size could be drawn from a population - if this were done, the resulting distributions of statistics (sampling distributions) would be normal
Standard Error
the standard deviation of the sampling distribution
