Exam 2 Review Quant Methods 1
Two tailed tests have both a positive and negative critical values: T or F?
True
Cohen's d
a measure of effect size that assesses the difference between two means in terms of standard deviation, not standard error
Observed score
actual score
Distribution of sample means will always be_______
approximately normal
body vs tail
bigger piece of graph vs. smaller area
When do we fail to reject the null hypothesis?
- When the p-value greater than our alpha (i.e. p>0.05 in our case) -DOES NOT MEAN WE ACCEPT THE ALTERNATIVE HYPOTHESIS
What is a critical region?
A region of the probability distribution which, if the test statistic falls within it, would cause you to reject the null hypothesis
Step 1 of Hypothesis Testing is:
Identify a research question
Hypothesis Testing
make and test an educated guess about a problem/solution
Sampling with replacement
our way of keeping probability consistent-and not changing
Critical region
the area in the tails of the comparison distribution in which the null hypothesis can be rejected
States there is a meaningful change and/or a relationship between two groups:
Alternative Hypothesis
Critical value
the actual + specific z-score
Calculate z-score from a population?
z=X-μ/σ
What is an alpha level (a)?
- maximum permissible error margin - the probability of making a type I error
What is our default alpha level when not given?
.05
How many critical values does a one-tailed test have?
1
Steps for determining probability of getting a sample mean (M) greater than x-amount/value?
1. Calculate z-score 2. Plot z-score 3. Body, Tail or Middle? 4. Unit Normal Table
2 scenarios that would result in perfect normalcy in distribution:
1. Sample means pile up around the pop. mean 2.
Rules of Probability 1-2
1. p must be lest than or equal to zero and equal to or greater than 1 2. The total probability of all outcomes must add up to 1.00
How many critical values does a two-tailed test have?
2
Rules of Probability 3-5
3. Probability that event does not occur-1-(p does occur) 4. If events are mutually exclusive- p(A or B)=P(A)+p(B) 5. If 2 events are independent- p(A and B)= p(A) * p(B)
We keep proportions original at
4 decimal points
one-tailed test
A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in one tail of its sampling distribution.
Null hypothesis (Ho) represents?
A prediction that there is no difference between groups or conditions
States there is no meaningful change or difference between two groups:
Null Hypothesis
Why do we calculate an effect size?
Our obtained z score only tells us the probability that the result occurred by chance, while effect size tells us the size and magnitude of the treatment effect
Probability has the same interpretation as..
Proportion
For a two-tailed hypothesis test, you get an obtained z score of -2.11. Assuming you chose an alpha of .05, what decision should you make based on this obtained z score compared to your critical z score(s)?
Reject the null because the obtained score was within the critical region
Critical values depend on your specific______?
Research Question
What is the estimated mean?
Same as the population mean
Example of Alternative hypothesis in words
Spending time with therapy dogs will lead to a change/or meaningful difference in happiness
Example of Null hypothesis in words:
Spending time with therapy dogs will not have a meaningful impact on happiness
What does the symbol σM represent?
Standard Error of a Sample Mean
Setting criteria for a decision, is what step in Hypothesis Testing?
Step 2
In the equation: z=X-M/σ , what does "X" represent?
Value of interest
When do we reject the null hypothesis?
When P ≤ 0.05
two-tailed test
a hypothesis test in which the research hypothesis does not indicate a direction of the mean difference or change in the dependent variable, but merely indicates that there will be a mean difference
Standard Normal Distribution
a normal distribution with a mean of zero and a standard deviation of one
Probability is
a ratio of outcomes divided by the total number of possible outcomes
We assume that differences are due to ___________
chance-unless given sufficient evidence to say otherwise
How do we find the proportion that is above a z-score?
either find body or tail in Unit Normal Table
How do we find the proportion of scores between a mean and the z?
multiple the proportions for both scores in column C in unit normal table
Symbol for probability:
p
How do we find the Standard Error of the Mean?
taking the standard deviation and dividing it by the square root of the sample size
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
Obtained score
the observed score of a student on a particular test on a given day
Alternative Hypothesis (Ha) represents?
there is a difference/relationship between groups
Calculate z-score from a sample:
z= X-M/s
