Psych Stats Exam 1

Population

The group your research questions are about

Sample

The subset of the pop that you collect data from

Variable

Something that differs across all people

Constant

Something that is the same across all people (demographic characteristics)

Discrete Variable

Amounts of things with exact values

EX: how many kids do you have? 1 2 or 3

Continuous Variable

Amounts of things with infinitely many values.

EX: How many minuets do you study the scriptures a day

Nominal Scale

categories with no magnitude, numbers are randomly assigned and have no order

EX: Male (1) Female (2)

Write up: mode

Ordinal Scale

Numbers mean less or more of something, but not exactly

EX: Strongly agree, somewhat agree

Write up: mean, SD, range, skewness

Ratio Scale

Precise numbers with meaningful magnitude (can do math)

EX: How many stats classes have you taken

Write up: mean, SD, range, skewness

Experimental Design

Random assignment, manipulation of independent variable

DETERMINES CAUSALITY

Correlational Design

Real world validity because it studies things as they naturally occur.

CANNOT DETERMINE CAUSALITY

Positive=both variables go up or down

Negative= Variables go different directions

Cross-sectional

Measure group one time

EX: survey people once

Longitudinal

Measure group of people over time

EX: Study group of kids every year as they grow up

Research conclusions are constrained more by…

research design than the data analysis.

Types of data collection methods:

survey, behavioral observation, physiological(measure heart rate), interview

Distribution Characteristics

Shape, Central tendency, and variability

Categorical variable

kind of things, this or that

Nominal

Descriptive stats

Describe the sample (mean, median, mode, variance, SD, Frequencies)

Inferential Stats

Calculated using sample data to make inferences about the pop. (z-test, t-test, ANOVA, correlation, chi-squared)

Frequencies

Number of people with each score in data

Bar Graph

Bars don’t touch, used for nominal data

Histogram

Bars touch, used for ordinal and ratio (magnitude)

Unimodal- Distribution characteristic: Shape

One hump in distribution=one kind of people

Bimodal

Two humps in distribution=two kinds of people

Positive Skew

Hump is on the left, skew is right. The slide goes to the right. Usually undesirable things you are asking about, or there is a floor.

EX: Drug use (most people don’t use or admit to drugs)

Negative Skew

Hump on the right slide to the left. Usually desirable, easy answer, or ceiling effect.

EX: How nice are you? people answer higher

EX: The max score an an exam is 100, scores pile there

Skewness: Normal, moderate, high

Normal: Less than 1

Moderate: Between 1 and 2

High: Above 2

Mode

Most frequently occurring score. Can be used with nominal, ordinal, and ratio variables

Median

Middle score. Used for ordinal, ratio

Mean

Average of scores, or balancing point of the distribution. sensitive to extreme scores. Used for ratio or ordinal

Variability

How spread out scores are. SD squared, not as useful as SD.

Range

Distance from smallest to largest. Limited because it does not say variation between top and bottom.

Sum of Squares

Sum of squared deviations from mean. Foundation for variance and SD

Variance

Average squared deviation from mean. Difficult to interpret

Standard Deviation

Average deviation from the mean. In original units so its easy.

-Not effected by sample size

Outliers

Beyond 3 standard deviations away from mean.

-Might be bad data

-might be a totally different kind of person

-make distribution skewed

When adding or subtracting from data…

You only add or subtract from mean NOT SD

When multiplying or dividing from data…

Mean and SD are also multiplied or divided

Sample Stats

Characteristics of the sample

M and N

Pop parameters

Characteristics of the population

u and sd symbol

Three Pieces of info

Raw score: data point

Location(z-score): location of data point relative to mean

Percentages: Percent of scores above and below location

Z-score

Indicate the location of the raw scores in data. Standardizes the distribution. Is in SD units

-Top of formula centers M at 0

-Bottom of formula shrinks/expands SD to 1

EX: Z=1 (one SD above the mean)

Within 1 SD

68% of scores

Within 2 SD

95% of scores

Within 3 SD

99% of scores

Beyond 3 SD from the mean, what percent of scores?

1%

Sampling Error

The expected variation in the sample versus the population. It is inevitable that the sample will be slightly different than the population

-Increases sampling error: Larger pop. SD

-Decreases sampling error: Larger sample size

Sampling Distribution

Distribution of all possible means of a given sample size drawn from a population (pile of all sample means)

-Mean of sampling distribution=population mean

Standard Error

The average degree to which we might expect sample means to error from the population mean.The SD of the sampling distribution.

-Larger pop. SD(variability) = Larger Standard Error

-Larger Sample size = Smaller Standard Error

Central Limit Theorem

Sampling distributions are normally distributed, regardless of pop. distribution

If sampling error did not exist…

Every sample mean would be the same as the population mean and the distribution would be a vertical line.

Smaller z-score means…

a less extreme, more probable mean

Null Hypothesis Significance Testing

Used to determine whether there is evidence for an effect in the population

-To reject or retain the null

Null Hypothesis H0

Nothing is going on (no effect)

-If you reject, you claim something is happening

-if you retain, you claim nothing is happening

Alternative Hypothesis H1

Opposite of Null, there is an effect

Research Hypothesis

Which of the hypotheses you think of true in the population.

-Your proposed answer to the research question

General Logic of Hypothesis testing

Compare your sample mean to pop. mean and decide whether that difference happened by chance or if there is an effect or reason in the population. Then decide to reject or retain.

Why test null if most people are interested in the alternative hypothesis?

It is easier to find evidence AGAINST null than FOR alt.

-More scientific

Steps to hypothesis testing

1. state hypothesis

2. run statistical test (z-score)

3. make statistical decision

4. Interpret results

Single Sample z-test

Compares sample mean to known population.

-Must know pop mean and SD

Alpha Level

If p<.05, it is statistically significant and we reject the null

P-Value

Probability of getting results as extreme or more than yours

• The percent of scores in a given area is the same as probability of getting score in given area

Rejection region

2.5% to the left and right (5% total). Beyond the critical value is where you reject the null.

Critical Value (z-crit)

1.96

• Z Less than 1.96 = Retain Null

• Z Lager than 1.96 = Reject Null

Statistically Significant means you…

Reject the Null

What increases Z

Sample mean farther from population mean

Smaller p-value indicates…

-larger z-score

-More evidence against the null

-Greater likelihood of rejection

Effect Sizes (ES)

Asks: If there is an effect, How big is the effect?

• Assumes Alt. is true

• Not influenced by sample size

• Exists at the population distribution

Cohen’s d

The difference between two pop. means in SD units.

• How far apart the sample mean and pop mean are

• Small: d=.20

• Medium d=.50

• Large d=.80

Pont Estimates

Estimates of population parameters based on sample stats

Confidence Interval (CI)

How precise is our estimate?

• Assumes Alt. is true

• Occur at the sampling distribution level

• Big sample size means smaller interval

• One MOE below point estimate, to one MOE above point estimate

• Does not use effect size

Margin of Error (MOE)

How much the sample result might differ from the true population value.

Confidence Interval Interpretation

If we sampled all possible samples from alt. hypothesis population, 95% of the confidence intervals would include the population mean.

• CI will include null pop. mean where you retain the null

• CI will not include the null pop. mean when you reject the null

Is there an effect?

Hypothesis Test

How big is the effect?

Effect Size

How precise is the estimate?

Confidence Interval

How likely are we to detect the effect?

Power

Power

Probability of rejecting the null if the alt. hypothesis is true (correctly rejecting the null)

• Want power of at least 80%

• Assumes Alt. hypothesis is true

• On sampling distribution of alt. hypothesis

What drives power?

Effect size and sample size

• Larger difference between sample mean and population mean=more power

• Smaller population SD=more power

• Larger sample size=more power

A Priori Power Analysis

Run before collecting data to know what sample size should be to get good power

Beta

Probability of type 2 error (Retain when should reject)

• 1-power=beta

• 20%

Type 1 Error

False Reject (should have retained the null)

Claim something is there when it isn’t

False Alarm

• Alpha 5% chance of type 1 error

• 95% chance of a correct retain

• Assumes Null hypothesis is true

Type 2 Error

False Retain (should have rejected the null)

Claim nothing is there when it is

Miss something

• Beta 20% chance of type 2 error

• 80% chance of a correct reject

• Assumes Alt. Hypothesis is true

Alpha Level

Type 1 error rate 5%.

p<.05 means outer 5% you could falsely reject null