Quiz 2 Flashcards
Standard Deviation
- amount of variability from the individual data values to the mean (in the original units of data values)
- dispersion of sample data relative to the mean
- provides info as to how good of a representation the mean is for a spread
Standard Error (of the mean)
- degree of discrepancy there is likely to be in a sample mean relative to the population mean
- the SD of the sampling distribution of the mean
- SE = SD / (√N)
______ quantifies how confident we are in our estimate of the population mean.
the standard error
What happens when we clump scores together into a sample mean?
the value becomes closer to the population mean than the individual scores.
Standard Error Equation
Sigma sub xbar = SD / (√N)
Standard Error of the Mean equation (explanation)
The standard error is calculated by dividing the standard deviation by the sample size’s square root. It gives the precision of a sample mean by including the sample-to-sample variability of the sample means.
The smaller the standard error, the _____ representative the sample will be of the overall population
more
Sampling Distribution
Approximates normal even when population distribution shape is not normally distributed
Standard error is the standard deviation of the sampling distribution
If the sampling distribution has less variability between sample means, would we be more or less confident in the mean?
More → smaller variability means the sample means are closer to the population mean
Central Limit Theorem
- states that a sampling distribution always has significantly less variability than the population, from which it has drawn
-The sampling distribution will look more and more like a normal distribution as the sample size is increased - 30+ rule
Different Kinds of Distributions
- Distribution of a pop of individuals
- Distribution of a particular example
- Distribution of means (aka sampling distribution
Confidence Intervals
- Gives us an estimated range of values which is likely to include an unknown population parameter
- It is the estimated range calculated from a set of sample data
Confidence Intervals Calculation
- 95% CI = M ± Zsub a/2 * (SE)
- sample mean ± 1.96* (SD/√N)
- Step 1: figure out the middle of the CI → sample mean
- Step 2: Decide how confidence you want to be: 90%, 95%, 99%
- Step 3: look up the z-scores for the CI you want and apply
- E.g. 1.96 for 95% CI because 95% of
scores in a Z distribution fall between
±1.96 (standard normal curve) - Step 4: use SEs instead of SDs since using samples not individuals
- Step 5: once you have the mean of your sample, just add it to 1.96 x SE (95% CI) to get the upper boundary and subtract 1.96 x SE to get the lower boundary
What happens to the size of the CI as sample size increases?
CI becomes narrower as number of scores increase because les variability between sample means in a sampling distribution
Total Variance = ?
Effect + Error
Effect
- variance we CAN explain
- the portion of variance that is explained by predictor variables
- E.g how much biological sex explains
variation of height
- E.g how much biological sex explains
- With more predictor variables, amount of effect will increase
- Summed total variance explained by predictor variables
Error
- variance we CANNOT explain
- portion of variance that remains unexplained after we account for predictor variables
- With more predictors, amount of error will decrease
We want the value of the ratio effect/error to be _____ because _______________
We want the value of the ratio to be LARGE because it means that you have more effect than error
MEANING –> model has MORE explanatory power than unexplained variance
Test Statistics
- effect/error ratio
- A statistic for which the frequency of particular values is known
- Observed values can be used to test hypotheses
p value
- A conditional probability
- tells us that:
- if the null hypothesis is true,
what is the chance of drawing a random sample from that population that gets a statistic that is equal to or greater than the observed result (observed test statistic value)
- if the null hypothesis is true,
As the test statistic value becomes greater, it becomes ______ likely to observe that value (or greater) if the null hypothesis is true
less
95% CI = _______
significance level (a) of .05
When the p value is lower than our alpha (.05), _______________.
we reject the null
Three Problems with NHST (Null Hypothesis Statistical Tests)
- NHST don’t tell researchers what they want to know (i.e. the probability of the null being true given the data we have ≠ probability of the data we have given that the null hypothesis is true)
- Alpha levels are arbitrary
- We convert a continuum of uncertainty into two dichotomous decision-roles - Statistical significance does NOT mean importance
- Does not tell us the size or magnitude of effect
Type I Error
- Occurs when we believe that there is a genuine effect in our population when in fact there isn’t
- Incorrectly rejecting the null when it is true
- The probability is at the alpha-level (usually set at .05)
Type 1 error occurs at 5% - Higher bar for avoiding type I error rather than for type II
Type II Error
- Occurs when we believe that there is no effect in the population when, in reality, there is
- Incorrectly NOT rejecting the null hypothesis
- Type 2 error rate is 20%
- Power = The probability of finding an effect when it exists in the population
- Convention of power is .8
(80%)
