Chapter 2: The SPINE of Stats Flashcards
what does SPINE stand for?
S: standard error
P: parameters
I: interval estimates (CIs)
N: NHST
E: estimation
what is a statistical model?
the mean can be used as a simple stats model
a model is a representation for a purpose
special type of math model that is informed by data and incorporates uncertainty and randomness
useful for:
1. identifying patterns in data
2. untangling multiple influences
3. predicting future outcomes
4. assessing efficacy of interventions
degree to which a statistical model represents the data is known as the fit of the model. multiple models can fit the same data
population
the complete collection of entities of interest
vary in size
broader populations are usually of greater importance
we use samples and inferential stats to make conclusions about pops
parameter
model is made up of variables and parameters
number that describes some aspect of the population
the number can summarize the population or can capture how variables relate to each other
usually constant
estimated from sample data
assessing the fit of the model
- degrees of freedom are the number of pieces of info we have to estimate population parameters
- the fit of a model can be assessed with either the sum of squares (SS) or the mean squared error
- small numbers relative to the model indicates a goof fit, large numbers indicates a poor fit
estimating parameters
- estimation methods are the different methods for estimating parameters
- the method of least squares or ordinary least squares (OLS) estimates parameter values by minimizing the errors in prediction (more precisely, the squared errors)
- for models consisting of a single number, the mean is the value that minimizes the squared error
standard/sampling error
- the difference between a sample statistic and the parameter being estimated is called sampling error
- sampling error = statistic - parameter
- the SE of the mean tells us how mch error to expect in our estimate of the population mean
- have their own sampling distribution and SE
SE = SD / sq root N
confidence intervals
for any parameter, not just mean
the SE of the mean can be used to create a CI
- CI is an interval estimate of the pop mean
- lower boundary: mean - (1.96 x SE)
- upper boundary: mean + (1.96 x SE)
- We are 95% confident that the population mean is between the lower bound and the upper bound
- set the CI to what makes the most sense (i.e., 99% when you need to be really confident the parameter falls in the CI, 80% when missing an effect is of serious consequence)
- larger sample sizes result in narrower CIs
- in small sample sizes, the sampling distribution may not be normal, so use a t-distribution
comparing the means of two groups using CIs
- if two CIs overlap, the pop means might be the same or different, it’s unclear
- if the CIs do not overlap, the pop means are likely different
what is an effect?
- umbrella term for different types of association
- does not imply causation
- X –> Y (temporal precedence, covariation, rule out alternative explanations
NHST overview
- a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population, or if it is just due to sampling error
- dominant inferential approach in psychology with many shortcomings
- general process: assume there is no effect in the pop, collect data, find the prob of the data is there is no effect in the pop, and if the prob of the data if there is no effect is low, you condlude there is an effect inthe pop
- it is impossible to conclude there is no effect in the pop w/ NHST, you can only say you did not observe an effect
steps of NHST
- determine null and alt hypotheses
- set alpha and do a power analysis to determine sample size: alpha is the probability of falsely finding an effect if no effect exists (prob of rejecting the null if the null is true)
- collect data
3.5: test statistic - p-value: the prob of obtaining the observed test statistic or an even more extreme test statistic if the null is true
- make a decision (null is tenable, reject the null)
test statistics
signal/noise, effect/error
many different types: z, t ,f
- variance explained by the model/variance not explained by the model
- come from known distributions, which allows us to find the probability of the test statistic
- bigger test statistics are less likely to occur if there is no effect (bigger test statistic = lower p value )
- the value of the test statistic (positive/negative) depends on wheter the difference or direction of the relationship is positive or negative
1 vs 2 tailed tests
- directional hypothesis (direction of the effect specified): option of doing a one tailed test
- nondirectional hypothesis (doesn’t specify the direction of the effect)
- one tailed tests are more likely to detect an effect than two tailed tests if the effect is in the expected direction (pos or neg)
- two tailed tests are the norm, one tailed tests looked upon with suspicion
type I and type II error
type 1: rejecting the null when the null is true (false positive)
type 2: failing to reject the null when the null is false (false negative)
- power is the probability of correctly rejecting the null when the null is false
- familywise alpha is the probability of making at least one type one error across a series of NHSTs
