COMM550/Midterm

From Driscollwiki

1 Descriptive stats
2 Testing hypotheses
- 2.1 Increasing power
- 2.2 Poong's fantastic example:
3 t-test
- 3.1 Degrees of freedom (d.f.)
- 3.2 Computing t-test
4 ANOVA
5 F table
6 The logic of statistics
7 Research & experimental design
8 APA style (citations, bias, formatting)
9 Control for extraneous variance
10 Threats to validity
11 Partitioning of variance
12 Scales
13 One-tailed v. Two-tailed tests

Descriptive stats

Testing hypotheses

$p$ -value: the probability that we will obtain the observed outcome when the null is assumed as true, which we cannot determine before the analysis

Decrease by half for one-tailed test

alpha: criterion we set to decide whether or not to reject the null before the analysis.

$0.5$ is the conventional alpha
Equal to the probability of Type I error

If the $p$ -value obtained is smaller than the alpha, then we can reject the null hypothesis.

beta: is typically hard to calculate

Set prior to the analysis
Equal to the probability of a Type II error

power: is the probability that we correctly reject the false null hypothesis

1-beta

Increasing power

http://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/statpower/statpower_28.html

Increase sample size
Increase alpha level
Use a one-tailed test (if appropriate)
Select reliable measures for the study
Develop a strong research design
Use all information available to identify an appropriate population and recruit

participants for the study

Poong's fantastic example:

Here's an example for better understanding of "power" and "alpha." hopefully.

I got a result from a public opinion poll: 50% of people support Obama with 95% of confidence level and +/- 3% points. This means that the proportion of population who support Obama would be between 47% and 53% with a prob of 95%. and that the true proportion would be NOT within the interval with a prob of 5% (Type I error).

Because I don't want the type I error, I reset the alpha level as .0000...00000001%. Then, the result would be changed like this: 50% of people support Obama with 99.9999...9999999% of confidence level and +/- 49% points (hypothetically). This means that the true proportion of population who support Obama would be between 1% and 99% with a prob of 99.999...99%. This statement is, in fact, meaningless (or "powerless"), even though the chance to be wrong is almost zero. Power is the degree to which the stat analysis provides meaningful results.

$t$ -test

Most important to reproduce formula from Chap 7.1

Degrees of freedom ( $d . f .$ )

$d . f . = (n 1 + n 2 - 2)$

Sum of samples in each group minus number of groups

Computing t-test

$M_{1} \neq M_{2}$

$t$ -test: $\frac{M_{1} - M_{2}}{\sigma_{diff}}$

$M_{1} \neq M_{2} \neq M_{3} \neq M_{4}$

$\frac{Variance_{Among}}{Variance_{Within}}$

ANOVA

One-way ANOVA

One IV
Two (or more) groups/conditions

Degrees of freedom ( $d . f .$ )

$d f b + d f w = d f t o t a l$

$(k - 1) + (N - K) = (N - 1)$

$k$ : number of groups, conditions
$N$ : total number of subjects under observation

$F$

$F=\frac{\mbox{Variance among groups}}{\mbox{Variance within groups}}$

$F=\frac{\frac{SS_{among}}{df_{among}}}{\frac{SS_{within}}{df_{within}}}$

$F=\frac{MS_{among}}{MS_{within}}$

Two-way ANOVA

Factorial ANOVA

Two or more IVs
Two or more groups, conditions, levels

Degrees of freedom ( $d . f .$ )

$S S b e t w e e n = S S first IV + S S second IV + ... + S S last IV$

SS_{first IV} = SS_{main effect of first IV} = (a − 1)
- $a$ : the number of levels in first IV
SS_{second IV} = SS_{main effect of second IV} = (b − 1)
- $b$ : the number of levels in second IV
$S S interaction effect between first and second IV = (a - 1)(b - 1)$
$S S error = S S within = N - a b$
$S S total = N - 1$

$df_{\mbox{first IV}}+df_{\mbox{second IV}}+df_{\mbox{interaction}}+df_{\mbox{error/within}}=df_{\mbox{total}} \Rightarrow (a-1) + (b-1) + ((a-1)(b-1)) + (N-ab) = N-1$

F

Compare against $F$ based on your alpha (0.01 or 0.05), using $d f among,within$

$t$

Compare against $t$ tabke, in order to find your $p$ using $d f$

Partitioning of Variance

(For both single- and multi-factor ANOVA)

$S S t o t a l = S S between/among + S S w i t h i n$

$S S t o t a l$ : distances of the individual scores from the grand mean
$S S between/among$ : distances of the sub-group means from grand mean
$S S w i t h i n$ : distances of the individual scores from their sub-group means

See pp368-372 of Hayes

F table

Williams, Chp 9

TODO locate calculations

The logic of statistics

$\frac{\mbox{Systematic variance}}{\mbox{Error variance}}$

Error is always within

Why is stats a ratio?

Hypothesis testing

Working toward rejecting the null hypothesis

Cannot prove your research hypothesis

Mantras

Minimize error variance
Control for extraneous variance
Maximize systemic variance

Research & experimental design

Types of experiments

Types of design

Experimental design

X = IV (manipulated)

(X) = IV (not manipulated)

~X = manipulable, not manipulated

Y = DV

R = random

m = matched

Defective design

Two groups, no control

$X_{a}\ Y_{a}$
$X_{b}\ Y_{b}$

See: FBR Chp 19

Sampling

APA style (citations, bias, formatting)

Control for extraneous variance

IV is constant
Randomization [best!]
Matching participants.

Note: Can also statistically control (like with ANCOVA) or work the IV into the design (as with a factorial design).

Threats to validity

Internal - regarding conduct of the experiment (people, materials)
- History
- Instrumentation
- Maturation
- Measurement
- Statistical regression towards the mean
  - Sample begins to lose its breadth
- Attrition
- Selection
- Interaction
External (FBR p477) - generalizability
- Reactive or interaction effects in testing
- Selection bias, Interaction of selection and IV
- Effect of being observed, Reactive effects of experimental arrangements
- Effect of previous trials on later trials
Construct

Partitioning of variance

Scales

Gutman scale

Each element in the scale builds on the previous

Would you,

Permit Armenians to enter the country
Grant Armenians residents citizenship
Hire an Armenian to work in your home
Marry an Armenian

Semantic scale

Pairs of opposites

Good . _ . _ . _ . bad
Strong . _ . _ . _ . weak
Hot . _ . _ . _ . cold

Likert scale (TODO check spelling)

Strongly disagree
Disagree
Neutral (Neither disagree nor agree)
Agree
Strongly Agree

One-tailed v. Two-tailed tests

http://www.ats.ucla.edu/stat/mult_pkg/faq/general/tail_tests.htm

COMM550/Midterm

From Driscollwiki

Contents

Descriptive stats

Testing hypotheses

Increasing power

Poong's fantastic example:

t-test

Degrees of freedom (d.f.)

Computing t-test

ANOVA

One-way ANOVA

Degrees of freedom (d.f.)

F

Two-way ANOVA

Factorial ANOVA

Degrees of freedom (d.f.)

F

t

Partitioning of Variance

F table

The logic of statistics

Why is stats a ratio?

Hypothesis testing

Mantras

Research & experimental design

Types of experiments

Types of design

Experimental design

Defective design

Sampling

APA style (citations, bias, formatting)

Control for extraneous variance

Threats to validity

Partitioning of variance

Scales

Gutman scale

Semantic scale

Likert scale (TODO check spelling)

One-tailed v. Two-tailed tests

Views

Personal tools

Navigation

Search

Toolbox

$t$ -test

Degrees of freedom ( $d . f .$ )

Degrees of freedom ( $d . f .$ )

$F$

Degrees of freedom ( $d . f .$ )

$t$