Ch2 - Stats for Testing

Question 1

Measurement

Answer 1

the use of certain devices/rules for assigning numbers to objects/events

Question 2

Variables + types

Answer 2

anything that varies
• Visible/invisible
• Discrete (errors in counting)/continuous (measurement errors)
• Dichotomous / Polytomous (discrete variables assuming + than 2 values)

Question 3

Nominal scales type of data

Answer 3

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

Question 4

Ordinal scales properties

Answer 4

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

Question 5

Interval scales properties

Answer 5

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

Question 6

Ratio scales properties

Answer 6

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

Question 7

Problem with ratio IQs

Answer 7

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

Question 8

2 types of stats

Answer 8

• Descriptive: maths dedicated to organize / summarize / etc data
  
  • Inferential: used to estimate pop values based on sample values

Question 9

Statistics def

Answer 9

relate to sample data

Question 10

Parameter def

Answer 10

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

Question 11

Frequency distributions

Answer 11

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

Question 12

Graphs (+ best types for discrete vs continuous data)

Answer 12

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

Question 13

• Measures of central tendency

Answer 13

○ 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)

Question 14

Range

Answer 14

distance between the 2 extreme points

Question 15

Semi-interquartile range

Answer 15

1/2 of the interquartile range (IQR) - the middle 50% of a distribution

Question 16

IQR

Answer 16

distance between the points that demarcate the tops of the first and third quarters of a distribution

Question 17

Variance

Answer 17

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

Question 18

Sum of squares

Answer 18

represents total amount of variability in a score distribution

Question 19

Standard deviation

Answer 19

square root of the variance - represents the average variability in a set of scores

Question 20

Properties of the Normal Curve Model

Answer 20

• Its limits extend to +/- infinity
  
  • Is unimodal
  • Mean = median = mode = center

Question 21

Standard Normal Distribution

Answer 21

Normal Curve with a mean of 0 and a standard deviation of 1

Question 22

Uses of the Normal Curve

desctiptive/inferential

Answer 22

• 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

Question 23

Sampling distribution

Answer 23

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

Question 24

Standard Error

Answer 24

the standard deviation of the sampling distribution

Question 25

Z distribution

Answer 25

the standard normal distribution

○ Smaller samples: Student’s t-distribution

Question 26

Standard error of the mean

Answer 26

(SEm) -> s / √n
• S = standard deviation of the sample
• N = number of cases in the sample
Applying this to the mean 1x gives us a 68% confidence interval around the mean
To have larger confidence we need to apply it 2x (95% CI)

We can establish ranges within which the pop parameters are likely to be found
Assuming that
• The sample mean is the best estimate of the pop mean
• The st error of the mean = the st dev of the hypothetical sampling distribution of means, assumed to be normal

Question 27

Nonnormal distributions

Answer 27

Proportions under the curve no longer apply
• May all have the same frequencies
• May have +1 mode

Question 28

Kurtosis

Answer 28

• Kurtosis: stems from Greek for “convexity” - flatness of peakedness of a distribution
○ Platykurtic: more dispersion, more extended tails
○ Leptokurtic: least dispersion, not much extended tails
○ Mesokurtic: normal distribution

Question 29

Skewness

Answer 29

lack of symmetry

	○ Normal distribution - Sk  = 0
	○ Negatively skewed: Sk <0
            ○ Positively skewed: Sk >0

Question 30

Univariate vs bivariate stats

Answer 30

Univariate statistics: measures of a single variable
Bivariate or multivariate: at least 2 sets of measurements on the same groups of people or matched pairs for 2 sets of individuals

Question 31

Coefficients of determination (in correlations)

Answer 31

• Coefficients of determination: tell us how much the variance in Y can be explained by the variance in X (obtained by squaring the correlation coefficient)

Question 32

Regression towards the mean

Answer 32

extreme scores on one variable are associated with scores closer in the mean in another

Question 33

Regression line

Answer 33

slope represents the strength/magnitude of the relationship between 2 variables
○ Greater slope = greater relationship between the variables
○ Allowed us to predict a variable of Y based on a variable of X known to be related

Question 34

Conditions for using Pearson’s r

Answer 34

• The pairs of observations are independent of one another
  
  • The variables to be correlated are continuous and measured on interval or ratio scales
  • The relationship between the variables is linear, that is, it approximates a straight-line pattern

Question 35

Heteroscedasticity

Answer 35

the dispersion in the scatterplot is not uniform throughout the range of values

Question 36

Homoscedasticity

Answer 36

uniform dispersion though the range

Question 37

Spearman’s rho (rs)

Answer 37

correlation for ordinal variables

Question 38

Eta (n)

Answer 38

correlation for curvilinear relationships

Question 39

Point biserial correlation (rpb)

Answer 39

when one variable is dichotomous

Dichotomous variables: often in true/false answer tests

Question 40

Phi or fourfold coefficient

Answer 40

when both variables are dichotomous

Question 41

Multiple correlation coefficient (R)

Answer 41

when a single dependent v is correlated with 2+ predictors