Shared Flashcard Set

Details

Statistical Analyses
Mean, CLT, t-tests, Proportions and Ratios, Chi-squared, p-values, Null hypotheses, CIs, 2X2 tables
25
Mathematics
Undergraduate 3
10/05/2014

Additional Mathematics Flashcards

 


 

Cards

Term
What are alternatives to quantitative studies?
Definition
Qualitative: Key informant interviews, focus groups, participant observation, etc

Mixed Method Studies: Iterative process, combining both Quan. and Qual. research methods
Term
The Mean is a measure of...
Definition
central tendancy
- it's an AVERAGE
Term
Define the central limit theorem
Definition
When the average of a series of means is normally distributed, with a variance of s^2, a std deviation of s, and mean of u.
Term
Which test do we use for all of our means?
Definition
t test
Term
What are the limitations of the CLT?
Definition
1. Need large sample size
2. Need to know std dev of pop'n
Term
When do we need standard error of the mean and how do we get it?
Definition
- used with standard deviation of the sample when standard deviation of the population is unknown (which is often is)
Term
When do we use the t-statistic? (2 reasons)
Definition
1. To test if a single mean is significantly different from zero or;
2. to test if two means are significantly different from one another
Term
Define Proportion
Definition
A type of ratio where the value of the numerator is included in the value of the denominator
Term
Which ways can a proportion be expressed?
Definition
Decimals (0.3), Vulgar functions (1/4), and percentages (20%)

They can only be expressed in a range from 0.0 to 1.0 (or 0% to 100%)
Term
Define Ratio
Definition
A fraction measure where the numberator is NOT included in the denominator
Term
What is the proportion of fish in the sea if the water to fish ratio is 6:4?
Definition
4/(4+6) = 0.4 = 40% = 4/10
Term
Which test do we use to test the significance of proportions/ratios, and why?
Definition
X^2, because proportions/ratios cannot be negative, so we can't use the t-distribution
Term
What is the p-value?
Definition
- The probability that the observed differences (b/w groups) might have arisen due to chance alone

- the probability that a test statistic would be larger than observed (if the null was true)
Term
What is the null hypothesis?
Definition
That there is no difference b/w the two groups
or
That there is no association b/w exposure and outcome
or
that there is no difference b/w a measure and zero
Term
With regards to the null, how can we define the p-value?
Definition
The p-value is the probability of getting the test statistic that we calculated (or a bigger one), IF THE NULL IS TRUE.
Term
What does a high p-value mean?
Definition
That the difference we observed was due to chance.
Term
If p-value is high, should we accept the null hypothesis, or reject it and why?
Definition
Null = there is no association/difference

High p-value = difference due to chance

So, we should accept the null, that there is no association/difference
Term
What does a low p-value mean?
Definition
Less likely that the observed difference was due to chance - means that there IS a difference/association
Term
If p-value is low, should we accept the null hypothesis, or reject it and why?
Definition
Reject the null, but a low p-value means that it's less like that the observed difference was due to chance, so it's more likely that, in reality, there IS a difference.
Term
Define alpha
Definition
The rule to decide if the difference observed is due to chance (not significant), or not due to chance (significant).

0.05 (5%) used as industry std
Term
If p-value is < alpha...
Definition
We reject the null
Term
If p-value is > alpha...
Definition
We accept the null
Term
Define confidence interval
Definition
Reasonable statement about the entire population, based on sample statistics
Term
A 95% CI is defined as:
Definition
Out of 100 samples, we expect 95 of these to fall with in the bounds of the CI (the area in which we expect a certain result)
Term
A 95% confidence interval (CI) of 1.3 - 4.2 means that...
Definition
We can be 95% confident that the observed mean would fall b/w 1.3 and 4.2
Supporting users have an ad free experience!