PsychStats Exam 2 (Weeks 5-8, Inferential Statistics)

Point Estimate

a value (mean, SD, etc) calculated from sample data to serve as the best guess or approximation for an unknown population parameter

Confidence Intervals

margin of error; express a range of possible values for the population mean

constructed by finding the sample mean and building an interval around it

Effect Size

A broad umbrella term for any quantitative measure that shows the magnitude of a difference between groups or the strength of a relationship between variables

effect of IV on DV

Cohen’s D

a specific standardized measure of effect size

Difference between means divided by SD (signal : noise ratio)

Measures of Cohen’s D

<0.2 = =very small

0.2 - 0.49 = small

0.5 - 0.79 = medium

0.8 and above = large

Why are broad d cutoffs probably not very useful?

effect size interpretation depends on the area of research

ex. 0.60 could be gigantic for one field and minuscule for another

What counts as descriptive statistics?

central tendency (mean, median, mode)

variability/dispersion (range, IQ range, SD)

95% CI

Effect Size, Cohen’s D

Descriptive Statistics

summarize the sample (and allow inferences about the underlying population)

Inferential Statistics

characterize how extreme/odd the study results are if nothing actually happened (no effect of IV on DV)

What counts as inferential statistics?

t score, p score

Null Hypothesis Significance Testing Process

1. define the null hypothesis and alternative hypothesis

2. define the threshold for significance

3. perform the inferential statistical test

4. make a decision about the null hypothesis

T-Test

an inferential statistical test used to determine whether the difference between the means of two groups is statistically significant or happened purely by random chance

The more different the sample means are, the [] likely it is they were drawn from populations with the same mean

less

P-Value

What is the probability of getting 2 sample means that are at least this different, if they were actually drawn from populations with the same mean?

Measures of P Value

p < 0.5 = reject the null (statistically significant)

p > or = 0.5 = fail to reject the null (the conditions are similar)

Descriptive vs. Inferential Understanding Check

How to calculate the difference between groups in raw scores?

subtract the means from each other

Between-Groups (Independent Samples T Test)

nominal/ordinal IV, scale DV

comparing 2 samples (different participants in each

Within-Groups (Paired-Samples T Test)

Nominal/Ordinal IV, scale DV

comparing 2 samples (same participants in each)

One Sample T Test

recruit participants —> manipulate something —> measure DV

Fill in the blanks:

t(_) = (_), p = (_)

df, t value, p value

How do you find the p-value from the t-score?

1. Take the difference between the two means

2. Convert it to a t statistic

3. Locate it within a t distribution that represents the null hypothesis

4. Calculate p value of getting that t (or more extreme)

Alpha Cutoff

the threshold used to decide whether a research result is statistically significant or just a product of random choice (AKA, the 0.05 in p values)

What are the features in this graph?

open dots = individual data points

closed dot = group average

capital I around the closed dot = 95% CI

Type 1 Error

false alarm (concluding there’s a difference but there really isn’t)

rejecting the null when you should not have

Type 2 Error

miss (concluding that there isn’t a difference but there really is)

failing to reject the null when you should have rejected it

How do you calculate a t-statistic?

t = (M1 - M2) / pooled sample variability

Pooled Sample Variability

= SE Difference (in diagnostics of JASP)

Degrees of Freedom (DF)

the label for which t distribution we’re using

Sampling Distribution

the distribution that represents the null hypothesis (a distribution of endlessly sampled mean differences, if the null were true)

When should you use this t distribution graph?

1 IV with 2 levels, scale DV

2 levels = two groups being observed

DF for Paired Samples T test

df = N - 1

DF for Independent-Samples T Test

df = (Ngroup1 - 1) + (Ngroup2 - 1)

T distributions are very (_) at small sample sizes.

conservative

in a t distribution with small sample sizes, we need a LOT of evidence to reject the null

One-Way ANOVA

Analysis of Variance (F test)

One IV, more than 2 conditions

When to use T test or F Test?

T for two, F for few!

What’s the problem of comparing a bunch (over two) conditions to each other (like doing a bunch of t tests?)

type 1 error/false alarm rate becomes unacceptably high

How does ANOVA help control false alarm rates?

by just running one test (as opposed to multiple) and making our comparisons more conservative (by adjusting p-values for multiple testing and making it harder to reject the null)

Omnibus ANOVA

an overall ANOVA test first to determine if the results are significant enough to look at each comparison (is there any effect of the IV on the DV?)

Post-Hoc/Pairwise Testing

individual comparisons after the omnibus ANOVA

(“after the fact”)

What if the omnibus ANOVA is significant?

move to post-hoc testing

What if the omnibus ANOVA isn’t significant?

stop there and say infer all conditions are similar on the DV