Statistics Primer Flashcards
Histogram
- How many people awnser the same
- Creates a bell curve
- The awnser that is the most is in the middle
Mode
Most common number
What three things have a central tendency?
- Median
- Mean
- Mode
Histograms ____ things together. The larger the ____ the less information on the graph. The smaller the ____ the more precise the data.
bin (all 3)
____ is the best way to talk about distibution of responses
Standard Deviation
SD is related to the average
Flatter and wider distribution = ____ SD
larger
% distributions on a bell curve
The distribution of observations for a sample approximates a normal distribution
* 68% of observations within 1 SD of mean
* 95% of observations within 1.96 SD of mean
* 99% of observations wihtin 3 SD of mean
- Mean ± 1 SD commonly reported (68% of data)
The other 5% of the ND is considered
rare
Split 2.5% on each tail
What is inferential statistics?
Estimated population characteristics using sample data
Inferential statistics looks for effects through ____ and ____
- Hypothesis Testing (How different two groups are)
- Relationships (How similar two groups are)
Inferential statistics - sample characteristics
- Inclusion/exclusion criteria define the population
- These criteria limit your generalization
- The more cases you sample, the more confident you can be your sample represents the population well (greater precision)
The looser the sample criteria =
better general application
Sampling Error
- Each sample results in a different estimate of the population mean
- Larger samples = better estimates of the population mean (more accurate, therefore less error)
Standard error of the mean (SE)
- Estimate of how close a particular sample mean is likely to be the population mean
- This is different than SD
- SE = sample SD/sqrt(sample size)
- Larger samples allow us to be more accurate of the actual population mean (smaller SE)
Samples that are smaller end up =
flatter and wider distribution
More SD
Having a distribution table that have more than ____ allows for normal distribution tables. The probability is ____ that any random sample falls within this range.
- 50 samples
- 95%
Not always possible; the more powerful the measure the less samples needed.
95% Confidence Interval
Range of values expect the true population mean to lie within estimated confidence interval.
Explain effect of sample size on distribution with graph
- Small sample size = wider distibutions
- The more subjects decreases the range of scores you would expect by chance alone
Can determine sample size through g power
For smaller samples, what statistic do we use?
- t-test for 95% confidence interval
- As n (number) increases, SE decreases = more narrow confidence interval
- 50 - infinitity = normal distibution
When do we want to be 99% confident over 95% confident?
- High risk situations
- Drug interactions
The width of the confidence interval is affected by what three things?
- Sample size
- How confident you want to be (95% vs 99%)
- Sample Variability (SD); measurement error
Confidence intervals tell you..
- What values you should and should not expect by chance
Hypothesis testing looks at the chance that the data occurs…
by chance or is real data
Alpha
- Describe the possibility of concluding groups are different when they are not
- Alpha influences Type 1 error
- Used in hypothesis testing
increasing the alpha =
not accepting randomness as much
Alpha level
- Your tolerance for declaring a sample mean as significantly different if it falls outside the expected range by chance
- Typical error tolerane is 5%
Explain whether these groups are the same or different
- If accepting a 5% chance these are different by chance (a = 0.05), then these groups are different.
- The means have to overlap into the 95% of the other group to be similar.
By changing from a 5% alpha to a 1% (99% confidence) this results in…
- Decreased chance of false significant conclusions
- Type 1 error: have an increased probability of NOT finding a difference
Beta
- Probability of incorrectly concluding that the groups are not different (Type II error)
- Typical value acceptable for clinical research is 20%
How to determine the power of test?
1 - Beta
(1 is true value; B is the probability of incorrectly concluding the groups are not different)
Power of a test must be ____ to be acceptable for clinical research
80%
What are the 4 factors that can affect power?
- Alpha level
- Difference between group means
- Within group variability
- Sample Size
How does alpha affect the power level?
- Raising the alpha level increase power
- Also increases Type 1 Error
- One tailed tests also increase power BUT you must justify why you are not looking at the other tail
One tailed
How does the difference between groups affect power?
- Larger group differences increase power (Better chance they are different)
How does within group variability effect power?
- More precise outcome measures: SD is decrease, decreased score variability = increases power
- Less precise outcomes measure: SD increases, increased score variability = less power
How does a sample size affect power?
- More subjects = more power
- More likely to be closer to true population
When comparing two distibutions, what does it mean when they overlap a lot?
They are similar! Less likely to see significant difference.
