Chapter 14 Confidence Intervals

Pg (440-447 only)

Confidence intervals look like 78% (+ - 3%). The interval is 75% to 81%.

Non-parametric tests

Chi-square test of independence (two variables or groupings). The differences between groups are tested. You test the Ho and either reject or fail to reject Ho. No association between groups is called independence.





(SPSS, Analyze, Descriptive Statistics, Cross-tab, Statistics, Chi-square)








Chi-square test of goodness of fit (one variable or group). The differences between the group and your expectations (chance) are tested. You test the same way as the test of independence. Expectations of Ho are equal proporation across all choices (chance).



(SPSS, Analyze, Nonparametric Tests, Chi-square)







Chi-square test of significance of a proportion (compare 2 frequencies only like "yes" and "no"). Small case of goodness of fit test.

Chi-square homework set in blackboard.

Non-parametric tests (Chapter 13)

Chapter 13 (Pages 407-416, 431-432 only)

Parametric techniques when we have scaled data (interval or ratio) such as r, z, t, F.

Non-parametric techniques when we have non-scaled data (ranked or categorical) such as Chi-square or phi coefficient.

Chi-square test of independence (conditional probability):
This is the test of two variables (groups) that shows they are independent of each other.

Chi-square test of goodness-of-fit:
Compare proportions.

ANOVA and exam 2

Repeated measures output. If you get significance then do Post Hoc, which is a paired samples t-test with corrected p-value for multiple t-test. Bonforoni correction: 0.05 divided by the number of comparisons.






Between Groups:





Important output for Between Groups ANOVA. It follows the BG WG formulas.



Study guide in blackboard for exam 2.



Studying in this exam (7 kinds):

1-way ANOVA (2 kinds) - (1-way = 1 independent variable)

1. Between Groups (SPSS: Analyze, Compare Means, One-way ANOVA)

2. Repeated measures (SPSS: Analyze, General Linear Model, Repeated Measures)

T-test (3 kinds)

1. Single sample (SPSS: Analyze, Compare Means, One sample t-test)

2. Between Groups (SPSS: Analyze, Compare Means, Independent samples t-test)

3. Repeated measures (SPSS: Analyze, Compare Means, Paired-samples t-test)

Pearson r

Simple linear regression

ANOVA - Chapter 12

Don't read pg 368-373.

Things beyond this class:

1. Factorial ANOVA designs
2. Dunns procedure

Announced that even though the course schedule has the 1st draft of full report due, the draft is now due Apr 5.

ANOVA accounts for the variation within groups (WG) and between groups (BG).

Optimal case is low variation within groups (WG) and large variation between groups (BG) because it is said that you have controlled extraneous variables and are measuring what you want to measure.

Total Variance (TV) = BG + WG

F statistic = BG/WG

A significant F statistic does not tell you which means are significantly different from which means. It only tells you that at least one mean is significantly different from another.

T-test and ANOVA

T-tests are designed for smaller samples.

Three ways to compare means of two groups (sample vs. population, sample vs. sample, pre vs. post)

pg 308-320 is not on the test. Scan it, but don't do z-test practice problems.

pg 339 #3 question (make sure you understand how to answer this.)

Data enter one column for age and one column for status (married or bachelor).



ANOVA

Chapter 12

T-test only accomodates comparing 2 means. ANOVA is used to compare more than 2 means. Multiple t-tests inflates the alpha level, so we use ANOVA, since a extreme sample would show up multiple times in the pairings. Sample 1 vs. Sample 2, Sample 1 vs. Sample 3, etc. If sample 1 is an outlier, each pairing might give you a type 1 error.

ANOVA is the workhorse of statistics...any research question you have, many would conform it to how to run an ANOVA. That is a little backwards, but it has been like that in the past.

We will study between-groups and repeated-measure ANOVAs.

ANOVA (analysis of variance)

When to use ANOVA:
1. More than two means compared
2. The group means should vary widely from grand mean (mean of means)
3. The groups' raw data does not vary widely. (Close clustering of scores)

Total variance = Variance + error or Between-groups variance + within-groups variance

Between-groups variance is the good stuff. (treatment + error)
Within-groups variance is the bad stuff (variance due to error only since each member of the group is exposed to the same treatment).

F statistic = BG/WG or (treatment + error)/error

F = 1 (means treatment had no effect)

Chapter 11

Analyze data from experiments, quasi-experiments, and comparing groups

T-test (used to compare groups) - replaces z-test

T-test of the means of groups. Use the t-test when the population standard deviation is unknown (sigma).

Sample compared to population:
T = sample mean - population mean divided by standard error

df = degrees of freedom, typically n-1

Sample compared to sample:
T = sample1 mean - sample2 mean divided by standard error

df = n1 +n2 - 2

Pre-post comparison: (repeat measures format)

Page 335 for formula

Chapter 10

Chapter 10 – Designing Experiments

Causality
What is the cause of phenomena?
3 Conditions of internal validity:
1. X comes before Y (antecedence)
2. X and Y are in the same space and time (contiguity)
3. Z is explained away (necessary connection)

Experiments
Prediction and control…independent variable (we manipulate), dependent variable (we measure).
Pre-test -> Treatment -> Post-test
Pre-test -> Control -> Post-test
*Randomly assigning participants to treatment and control groups. This is not random sampling a population. Both groups are equivalent.
External validity: generalization from lab to real world.
Internal validity goes up (control goes up) then external validity goes down (generalizability to real life)

Between groups and repeat measure are the basic experimental design.
Time related effects are the huge critic against repeated measure cause. (pp 279-285).

Experiments and quasi-experiments

ROXOA
R=Randomization
O=Observation
X=Treatment
A=Analyze data

Experiments:
ROXOA
RO OA

R XOA
R OA

Threats to validity: R

Selection (messed up the random assignment)
Mortality (participants drop out of groups unequally) If most of the females drop out in one group, it throws off the experiments. Called mortality because it references the use of rats and rats dying at unequal rates.

Threats to validity: O

Testing: the testing sensitizes participants to treatment
Instrument: measurement devices are messed up)

Threats to validity: X

Experimenter bias (treat groups unequally)
Experiment diffusion (something contaminates the control group)

Threats to validity: O - O (multiple observations)

History (something affects participants outside of the experiement like TV show, breaking news, etc.)
Maturation (something within the participants changes)

Threats to validity: A

Statistical regression (extreme scores are not repeatable, tend to move toward the mean in second observations)
Statistical conclusion (improper or faulty analysis)


Quasi-experiments

Do not include randomization, so groups are not equivalent.

1. Nonequivalent control group: OXOA compared with O_OA
2. Simple interrupted time-series: OOOOOXOOOOOA (no random and no group compare)
3. Combined (Time series with nonequivalent control group): OOOXOOOA compared with OOO_OOOA.

SPSS

SPSS definitions:

p-value = Significance (SPSS)

pearson r = Pearson Correlation (bivariate SPSS)

Results section

"A significant correlation was observed between stress3 and coursgrad, r=-0.83, p=0.000."

Discussion section

"I interpret the correlation...." Correlation is for prediction, not causal. Avoid the impression that readers may have that you view it as causal.

r squared is the percentage of variance in y that is systematically varying with x. R-squared is the name of the game. The higher the better with the least number of independent variables.

y-intercept is the number in the constant row under Unstandardized Coeffificent B column (y = slope * x + y-intercept) (y=bx + a) See image above.

slope is the number under the constant row in the same area. (b**)

**If you standardize b, you get r.

The Ed Psych Data Directions in Blackboard is what we need to know.

Regression

In a regression line, for each x score you get a normal distribution of y scores with the mean on the regression line. See page 222.

Regression lines should not go beyond the original data points.

Error is regression is the difference between the average predicted Y and the actual Y.
(Y-Ybar). Observed minus expected. This is called standard error of the estimate, but it is the standard deviation using the Y and expected Y along (running) the regression line. Also known as coefficient of non-determination. (1-r squared).

Opposite of the error is the coefficient of determination (variability accounted for).

How much variance is error and how much is accounted for by a correlation with another variable?

Total variance = variance accounted for + error.

Variance accounted for is r squared (pearson r squared)

The connection between correlation and regression is r = a standardized slope of the regression line. r = b (s sub x / s sub y)