Johnny, CH.2 - SPINE

Question 1

Why do Scientists use statistical models?

Answer 1

1. models represent real world processes to predict how these processes operate under certain conditions
   - We can have little confidence, not complete confidence in the predictions models make
   - Outcome (data) = model +error. This equation means that the data we observe can be predicted from the model we choose to fit plus some amount of error

Question 2

What is the relationship between samples and populations when it comes to psychological research?

Answer 2

Scientists are usually interested in finding results that apply to an entire population. Because we can’t collect data from every being in a population, we use a sample and use these data to infer things about the population as well

Question 3

What is one of the most common statistical methods?

Answer 3

The Linear Model:
Y1 = b0 + b1X1 + e1
(This equation is expressed as we want to predict the value of an outcome variable Y from a predictor variable X.
- b0: intercept of a line (determines the vertical height of a line, represents the overall level of the outcome variable when predictor variables are 0)
- b1: slope

Question 4

SPINE of Statistics

Question 5

What does SPINE stand for?

Answer 5

S: Standard Errors
P: Parameters
I: Interval Estimates (CI)
N: Null Hypothesis Significance Testing (NHST)
E: Estimation (of Parameters)

Question 6

Parameters

What are Parameters?

Answer 6

Parameters are a numerical or other measurable factor that define a system or define the conditions of how the system works
(Very general, don’t memorize)

Question 7

Parameters

What do parameters represent?

Answer 7

Some fundamental truth about the variables in the model.
- !!! Parameters are not measured !!!
- We can predict values of an outcome variable based on a model

Question 8

Parameters

What are some important things to note on parameters?

Answer 8

• Always use the word “estimate”: When we calculate parameters based on sample data they are only estimates of what the true parameter value is in the population
• the model variables have no error
• See Picture 1

Question 9

Parameters

What is error in statistics?

Answer 9

A discrepancy between observed values and true values
(See Picture 2 for formula and explanation)
- deviance: outcome - model
- error: observed - predicted

Question 10

Parameters

What is the total error (Or else, sum of errors)?

Answer 10

(See Picture 3 for explanation and examples)

Question 11

Parameters

How do you estimate the mean error in the population (mean squared errors)?

Answer 11

• total error / degrees of freedom
• total error: sum of differences between observed and predicted scores, squared
• degrees of freedom (df): N - 1
  (See Picture 4)

Question 12

Parameters

What is the fit of a model and how do you estimate it?

Answer 12

The fit of a model is how representative of the real world a model is.
- We estimate it using the sum of squared errors and the mean squared error
- ~As Sum of Squared Errors decreases, the fit of a model increases

Question 13

Estimation of Parameters

What is the method of least squares?

Answer 13

A method used to minimize the sum of squared errors
(I think the method is rather unimportant to mention, there hasn’t been anything in slides or exercises as well, if you guys want me to put it then let me know)

Question 14

Estimation of Parameters

What is the maximum likelihood estimation?

Answer 14

An estimation method whose goal is to find the values that maximize the likelihood.
- Likelihood refers to how well a sample provides support for particular values of a parameter in a model (In other words, when we are calculating likelihood we are trying to determine if we can trust the parameters in the model based on the sample data that we have observed)

Question 15

Standard Error

Why is the standard error important?

Answer 15

It is important becuase it shows us how representative our samples are of the population of interest

Question 16

Standard Error

What is Sample Variation?

Answer 16

Samples vary because they contain different members of the population

Question 17

Standard Error

What is A sampling distribution?

Answer 17

A frequency distribution of sample means
- Average of all sample means: Value of the population mean
- Use it to tell us how representative a sample is of the population
- SD is also known as standard error of the means (or standard error)

Question 18

Standard Error

What is the Central Limit Theorem?

Answer 18

As samples increase, the sampling distribution becomes normal with a mean equal to the proportion mean and a SD equal to = (See Picture 5)

Question 19

Interval Estimates (CI)

General Info

Answer 19

• Confidence level (e.g. 95%), we can be 95% confident that the parameter in question is within this range
• Boundaries of a CI (See Picture 6)
• If we have small sample, we don’t use a normal but a t distribution (See Picture 7 for boundaries)
  (Picture 8 also contains an example of how to represent visually CI)

Question 20

Null Hypothesis Significance Testing (NHST)

What are the 2 philosophical frameworks leading in NHST?

Answer 20

• Fisher Paradigm (Father of P-value). He created the concept of the Ho
• Neyman-Pearsonm: included the Ho and created the concept of the Ha
  !!! IN GENERAL: If P-value is significantly low, reject Ho !!!

Question 21

NHST

What are the differences between Ho and Ha?

Answer 21

(This table was in the lecture but Johnny didn’t explain it well, I think just remember the general outline of it, no need to understand it really)
Ho:
- Skeptical point of view
- No effect
- No preference
- No correlation
- No difference
Ha:
- Refute skepticism
- Effect
- Preference
- Correlation
- Difference

Question 22

NHST

What are the 2 main aspects of Frequentist Probability?

Answer 22

• Objective Probability: The likelihood of an event occurring based on empirical data and concrete measures
• Relative frequency in the long run

Question 23

NHST

What is the standard error?

Answer 23

The Variability of the Sampling Distribution (in other words, if I repeat my experiment over and over again how much variability will there be in the outcome of that experiment?)
- As variability increases, so does SE
(See Picture 9 for formula)

Question 24

NHST

How do we use the SE?

Answer 24

To do parameter estimation. It is crucial in designing Confidence Intervals, since it determines the boundaries and how wide the CI will be.
- If we want to design a 95% CI, as our SE increases, so will the width of our CI, in order to be 95% sure that our CI entails the true parameter. So we can have two 95% Ci intervals with the first being wider than the other, if that first one has a bigger SE
(See picture 10)

Question 25

NHST

What is the general process of NHST?

Answer 25

See picture 11

Question 26

NHST

What is the significance level α?

Answer 26

A value that determines when to reject Ho
(determines how strict we must be to reject the Ho)

Question 27

NHST

What is the statistical power (1-β)?

Answer 27

The probability of rejecting the Ho when the HA IS TRUE

Question 28

NHST

What do 1-α and β represent respectively?

Answer 28

• 1-α is the probability of correctly accepting Ho
• β is the probability of not rejecting Ho when it’s false (error type II)

Question 29

NHST

How do you calculate the test statistic?

Answer 29

See picture 12

Question 30

NHST

What is true about the usual size of tests in NHST?

Answer 30

Usually we have small tests, large tests are more uncommon

Question 31

NHST

What are the different types of tests according to the directionality of the hypothesis?

Answer 31

• If a statistical model tests a directional hypothesis -> one-tailed test (e.g. we want to see if watching a film increases or decreases the likelihood of buying the equivalent book. Ho is that there is no increase or decrease, Ha is either there is a decrease or increase. If we have a directional hypothesis, we only look at one of the two options, increase or decrease. So we look at Ho<Ha, or Ho>Ha, but not both
• If a statistical model tests a non-directional hypothesis -> two-tailed test (in the same example as above, now we look at both Ho<Ha, and Ho>Ha)

Question 32

NHST

What are the two types of errors?

Answer 32

• Type I error
• Type II error

Question 33

NHST

Type I error

Answer 33

When we believe there’s an effect in the population, when in fact there isn’t one (False positive)
- By specifying a we specify how often we are ok with making a Type I erroR
- ~ Given that a usually equals 0.05, probability of making a Type I error is usually 0.05
(In other words, out of 100 data collection process times, 5 times we obtain a statistic making us think there’s an effect when there isn’t one)
- Depends on sample size (Because a larger sample size is a better approximation of the population, as sample size increases, error decreases, so it is easier to find the signal, thus there are lower probabilities of making a Type I error)

Question 34

NHST

Type II error

Answer 34

When we believe there isn’t an effect in the population, when there is one actually (False Negative)
- Is equal to b-level
- Usually 0.2
- Depends on sample size (Because a larger sample size is a better approximation of the population, as sample size increases, error decreases, so it is easier to find the signal, thus there are lower probabilities of making a Type II error)

Question 35

NHST

What is the relationship between Type I and II errors?

Answer 35

As the probability of making a Type I error increases, the probability of making a Type II error decreases, and vice versa
(in terms of α and β, if α decreases, then we decrease the probability of making a Type I error, but at the same time it is more difficult to find an effect, thus more likely that we will make a Type II error

Question 36

NHST

How is the chance of making a Type I error affected by many testings?

Answer 36

If Type I error probability = 0.05, then the probability of no Type I error = 0.95. If we have 3 tests, then the probability of no Type I error across these three tests is 0.95x0.95x0.95=0.857, so the probability of Type I error across 3 tests is 1-0.857 = 0.143
This shows that the probability for a Type I error increases over many tests. This also gives the following formula:
- experiment wise error rate = chance of making a Type I error in testing = 1 - (0.95)^h, where h is the number of tests

Question 37

NHST

How can we combat the buildup of errors?

Answer 37

Use the Bonferroni correction:
- Pcrit = α/k, where a is singificance calue and k is the number of tests.
This formula is used to ensure that α<0.05 always

Question 38

NHST

Other general info regarding α and β

Answer 38

• If we know 3 out of the following: 1-β, α, size of effect and sample size, we can calculate the power of a test and the sample size necessary to achieve a given level of power
• Sample size affects whether a difference between samples is deemed significant or not (e.g. in large samples even small differences can be significant

Question 39

NHST

What is the effect size of a test?

Answer 39

A quantitative measure of the strength of a phenomenon
- Larger absolute values always indicate a stronger effect
- Important in power analysis, meta-analyses etc.