Exam 2 - Chapter 12 + 13 (Statistics)

Question 1

Descriptive stats: Mean, Standard Deviation, Frequency Distributions

Answer 1

Mean: The average score in a data set. Sum all scores then divide by number of scores.

Standard Deviation: The average deviation from the mean (square root of variance)

Frequency Distributions: A list of scores from lowest to highest that shows how often individuals got each score.

Question 2

Scales of measurement

Answer 2

The levels of a Variable can be described by:

1. Nominal - Categories have no numerical difference
2. Ordinal - Categories without equal intervals that can be put in numerical order
3. Interval - Categories with equal intervals, can be ordered, and no true zero
4. Ratio - Categories with equal intervals, can be ordered, but with a true zero

Question 3

What is: p-value

Answer 3

The probability of getting results as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true.

Question 4

Interpreting P-Value

Answer 4

P-value is interpreted in relation to α (Alpha), if p-value is less than α, we fail to reject the null (there is a statistically significant difference).

High p-value: Data is likely under the Null (there was no effect)

Low p-value: Data is unlikely under the Null (there WAS an effect)

Question 5

What is: α (Alpha)

Answer 5

Alpha Sets the threshold that determines the cut-off to reject the null

• p-value is interpreted through α (Alpha)

Standard Alpha: 0.05

Question 6

(ANOVA) Analysis of Variance:

aka: F-Test

Answer 6

ANOVA (F-test) is used to determine statistical significance when comparing more than two groups (ie: 3+ levels of one IV, or more than 1 IV).

• Larger F-value = more likely to reject the Null.
• Calculate F-value for each effect: Main effect 1, main effect 2, + interaction.
• “Post hoc” test: IF the interaction is significant, calculate F-value for simple effects

Question 7

What is a T-Test

Answer 7

T-test: Used to determine statistically significant differences of two groups

Question 8

The ratio for t-test and F-test

Answer 8

T-Test Ratio: T-value is a ratio of two aspects of the data: the difference between the group means & variability within the groups.

F-Test Ratio: F-stat is a ratio of two types of variance: systematic variance & error variance

• Systematic Variance (Between-group Variance): deviation of the group means from the grand mean (mean score of all individuals)
• Error Variance: Error Variance (Within-group Variance): individual variance from respective group mean.

Larger F-ratio = likelihood of significant results

Question 9

Effect Size

Answer 9

Tells us about the magnitude (strength) of an effect.

• Mean differences = Simple & NOT useful bc they depend on contexts.

Question 10

Standardized Effect Size Measures: Cohen’s d:

Answer 10

Standardization allows comparison across studies.

Cohen’s d: The difference between groups means measured by how many standard deviations apart they are.

• Stable measurement ⇒ bc mostly unaffected by sample size (useful for interpreting results)
• Can go over 1.00 (unlike r), and typically reported without a sign

Scale:

• Small = 0.2
• Medium = 0.5
• Large = 0.8

Small Cohen’s d ⇒ lots of overlap (small difference between populations)

A Large Cohen’s d ⇒ small overlap (big difference between populations)

Question 11

Null Hypothesis Significance Testing (NHST)

Answer 11

Goal: of NHST is to determine if the results of a study are likely true or if they just happened by chance.

Null Hypothesis (H0): There is no difference between population distributions.

Research Hypothesis (H1): There IS a difference between population distributions.

Question 12

NHST Steps/Process:

Answer 12

1. Establish a distribution of all possible differences if the Null hypothesis is true.
2. Choose a cutoff value that determines how far the value of the mean difference needs to be from ZERO to reject the Null hypothesis (Threshold set by Alpha)
3. Run a study, collect data
   Calculate Test Statistic (t-test, z-test, etc) and p-value
4. Calculate Test Statistic (t-test, z-test, etc) and p-value
5. Decide to reject or fail to reject the null (Determine if p-value is lower than α (Alpha), if p < α, reject the null).

Question 12

Type I and Type II errors

Answer 12

Type I Error: Incorrect decision to reject the null hypothesis (when it is true).

• False Positive → determined by the α (Alpha) level
• Lower α (Alpha) = smaller chance of Type I error

Type II Error: Incorrect decision to accept the null hypothesis when it is false.

• False Negative → determined by 3 things: α (Alpha) level, Sample size, Effect size.