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# Statistics

### intro hypothesis testing, hypothesis testing with means, statistical significanc

what is the definition of hypothesis testing? a systematic procedure for deciding whether the results of a research study, which examines a sample, support a hypothesis which applies to a population
what is the logic of hypothesis testing? 1. assume IV has no effect on DV 2. conduct a study to gather data that leads to rejection of this assumption 3. conclude IV does have effect on DV
Step 1 of Hypothesis testing? Restate question as a research hypothesis and null hypothesis about the populations
Step 2 of hypothesis testing? Determine characteristics of the comparison distribution. Assume a normal distribution where to population parameters are µ and σ.
Step 3 of hypothesis testing? Determine your cutoff sample. Also known as the critical value (Zcrit) on the comparison distribution at which the null hypothesis should be rejected
Step 4 of hypothesis testing? Determine your samples obtained score on the comparison distribution; Zobt
Step 5 of hypothesis testing? Decide whether to reject the null hypothesis.
What is µ? the mean of the distribution of means
What is µ1? the mean of the research population
What is µ2? the mean of the comparison population
what is the z score for a p<.05 significance level of a one-tailed test? ± 1.64
What is the score for a p<.01 significance level of a one tailed test? ± 2.33
What is the formula to find the samples obtained score? z=(X-µ)÷σ
What is a direction research hypothesis? predicting a particular direction direction of difference between the research and null hypothesis. Also called a one-tailed hypothesis test
What is a non direction research hypothesis? predicting a difference between the populations without stating direction. Also known as a two tailed test
What is the score for a p<.05 significance level for a two-tailed test? ±1.96
What is the score for a p<.01 significance level for a two-tailed test? ±2.57
What is the definition of the distribution of means? of samples of a given size from a particular population
The characteristics of any distribution of means are determined by? 1. the parameters of the population distribution of individuals 2. number of individuals in each sample randomly drawn from the population
Rule #1 of the distribution of means? the mean of a distribution is the same as the mean of the population of individuals. µM= µ
Rule #2a of the distribution of means? the variance of a distribution of means is the variance of the population of individuals divided by the number of individuals in each sample σ2M=σ2÷N
Rule #2b of the distribution of means? the standard deviation of a distribution of means is the square root of the variance of the distribution of means σM=√σ2÷N. Also called the standard error
Rule #3 of the distribution of means? the shape of means is approximately normal if either (a) each sample if N=30 or more individuals or (b) the distribution of the population of individuals is normal to begin with
µM=? The mean of the distribution of means
µ=? the mean of the population of individuals
σM2=? Variance of the distribution of means
σ2=? population variance
N=? number in each sample
What is the central limit theorem? a statement about the characteristics of the sampling distribution of means of random samples from a given population. describes characteristic cs of the distribution of values we would obtain if we could draw infinite # of random samples.
What is the Z test? a hypothesis testing procedure in which there is a single sample and the population parameters of mean and variance are known
Formula for the Z test? Z= (M-µM)÷σM
What is point estimate? the best estimate of the population mean is the sample mean
What is the standard error of the mean? it is the same as σM the standard deviation of the sampling distribution of means
What does SE tell you? how much the means of samples are typically in error as estimates of the mean of the population of individuals
What is Interval Estimate? an estimate of the range of possible means that are likely to include the population mean with a certain degree of confidence
What is another name for the interval estimate? Confidence Interval
What is step 1 for figuring confidence limits? figure the standard error
What is step 2 for figuring confidence limits? figure the raw scores for 1.96 SE (95%CI) or 2.57 SE (99%CI) above and below the mean
What are decision error? possible correct and incorrect decisions in hypothesis testing
What does effect size do? indicates the extent to which two populations do not overlap as a result of the experimental procedure
What is the amount of overlap influenced by? by predicted mean difference and population SD. SE size adjusts the difference between means for the SD.
What is the formula for effect size? d= µ1-µ2÷σ
What are properties of effect size? increases when there is a greater difference between means. increases when there is a smaller SD in the population
what number indicates a small effect size? 0.20
what number indicates a medium effect size? 0.50
What number indicates a large effect size? 0.80
What is meta-analysis? statistical method for combining the effect size from many different studies
What is statistical power? refers to " the probability that the study will produce a statistically significant result if the research hypothesis is true
Power=? 1 - β (that is , beta or Type II error)
gather needed information (a) µM (b) population predicted 1 mean (c)σM
What is step two to calculate power? figure the raw score cut-off point on the comparison distribution to reject the null hypothesis
What is step three to calculate power?
What is step four to calculate power? Using the normal curve table, figure the probability of getting a score more extreme than that Z score
What are five e ways to increase power? Increase the intensity of the experimental procedure, use less diverse population, use standardized testing and/or more precise measurement, use larger sample size, use a more lenient level of signifiance ∝
Created by: taylorjud