Inferential Statistics Flashcards
Inferential Stats
Making inferences beyond our data from distributions
Generalizing beyond the data/comparing different samples
Normal Distribution and z-scores are crucial to this
Criterion for Normal Distribution
Symmetric (right and left side look roughly same)
Unimodal (only one peak in the data, one mode),
Bell-shaped-curve (point of curve is not narrow/sharp/too pointy)
Mean, median, mode are equal: correspond to the center of the distribution
Specific shape depends on the population mean and standard deviation: how spread out it is
MOST VALUES FALL AROUND THE MEAN:
Empirical Rule (68–95–99.7),
About (⅔) 68% of the data lie within 1 SDs of the mean
95% of the data lie within 2 SDs of the mean
About 99.7% of the data lie within 3 SDs of the mean
Examples of human characteristics that are normally distributed:
height, self-esteem, IQ, shoe size, personality traits (extraversion/intraversion)
How to find negative values on a Z-table?
Z-table doesn’t give you negative values: “smaller portion” label is the one that tells you what the negative is
How to work with Z scores on non-standard normal distributions?
Don’t have a mean of zero and SD 1
Transform them into a standard normal distribution
Distribution will look the same but have new mean and SD
We standardize it using the z formula
Z= x — mu/sigma
difference between z scores and area under the curve
z scores are distances along the horizontal scale
areas are REGIONS under the curve
What are probabilities/probable limits?
positive or zero values, areas under the curve, never negative
What is sampling error?
Random variability in observations/statistics due to chance
Cannot be controlled and will impact overall sample
1st and 2nd step of hypothesis testing?
Start with hypothesis that our sample participants represents a population that does not differ from some comparison population or standard: NULL HYPOTHESIS, OPPOSITE OF DIRECTIONAL HYPOTHESIS
The more unlikely the null hypothesis is, the more confidently we can reject the null hypothesis in favour of the alternative hypothesis
What is the central limit theorem?
When you have a population, if you draw a large enough sample size from that population, the mean is closer to the tail: IT WILL BECOME A NORMAL DISTRIBUTION WITH A BIG ENOUGH SAMPLE SIZE
IF SAMPLE SIZES ARE GREATER THAN 30, ARE DRAWN FROM ANY POPULATION, THE RESULTING DISTRIBUTION OF THOSE SAMPLE MEANS WILL BE NORMAL AND CENTER AROUND THE MEAN OF THE ORIGINAL DISTRIBUTION
What happens as n increases?
GREATER SAMPLE SIZE = THE SKINNIER THE NORMAL DISTRIBUTION BECOMES (=better chance of getting closer to the true mean, more precise, bigger samples allow for this )
ANY shape of distribution, with a large enough sample, BECOMES A NORMAL DISTRIBUTION
Sampling distribution of the sample mean
has a mean =population mean
, a variance equal to 1/n times the variance of the population, a SD equal to the population SD divided by the square root of n (ALWAYS TRYING TO GET CLOSER TO THE ACTUAL POPULATION)
