Stats - Exam II

Factors that influence a hypothesis test

- variability of scores --> more variability means more likely there will be a difference
- number of scores in a sample

Type 1 Error

Rejecting null hypothesis when it is true

- more harmful because these results get posted in journals even though they are not actually true

Type 2 Error

failing to reject a false null hypothesis

- less harmful because the results do not get posted and ppl will replicate the study

Assumptions for a hypothesis test w/ z scores

- random sampling
- independent observations --> assumed that there is no relationship between the variables
- the value of standard deviation is unchanged by treatment
- normal shaping distribution

Effect size

provides a measurement of the absolute magnitude of a significant difference, independent of size of the sample

Statistical power

the probability that the statistical test will correctly REJECT a FALSE null hypothesis

Factors that affect power

- effect size --> as effect increases power increases
- sample size --> larger sample sizes decreases standard error which increases power
- alpha level --> higher alpha (.05) increases power lower alpha (.01,.001) decreases power
- one tailed vs two tailed test --> one tailed increases power (lower critical region ex. 1.63) two tailed decreases power (higher critical region ex. 1.96)

Steps to a Hypothesis Test

1. State a hypothesis (Null & Alternative)
2. Set Criteria for a Design (alpha level & critical region)
3. Collect data and Compute Sample Statistics (z score)
4. Make a decision (reject or fail to reject null hyp)

The Law of Large Numbers

the larger the sample size (n), the more probable it is that the sample mean is close to the population mean

Central Limit Theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution. (happens when sample size hits 30)

The Distribution of Sample Means

the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population

- the distribution is of the frequency of obtaining certain SAMPLE MEANS, not scores

Finding the proportion between two scores on either side of the mean

1. Calculate z scores
2. find proportion for each side of the mean
3. add them together

Finding the proportion between two scores on one side of the mean

1. Calculate z scores
2. Find proportion for tail w/ z score that is closest to the mean
3. Find proportion for tail w/ z score thats farthest from the mean
4. Subtract the latter from the former

Random Sampling

each member of a population has an equal chance of being selected

Independent random sampling

equal chance of being selected plus the probability of being selected remains constant for each selection

sampling WITH REPLACEMENT

To make full use of the unit normal table remember...

-The body always corresponds to the larger part of the distribution and the tail is always the small section
-Because the normal distribution is symmetrical the proportions on the right hand side and the left hand side are the same → to find proportions for negative z scores you must look up the corresponding proportions for the positive value of z
-Although z scores change from positive to negative the proportions are always positive

To standardize a distribution you have to...

-Transform the raw scores into z scores
-Transform the z scores into new X values so that the mean and standard deviation are obtained

If every x value is transformed into a z score then the disrtibution of z scores will have...

-Shape - exactly the same shape as the original distribution of scores
-A mean of 0
-A standard deviation of 1

Purpose of z scores

-To make raw scores more meaningful that contain more information
-Standardize an entire distribution of scores