Probability (w5)

Question 1

What is the difference between inferential statistics, descriptive statistics, and probability theory ?

Answer 1

• Inferential statistics help us draw conconclusions about the population.
• Descriptive statistics describe our data.
• Probability Theory allows us to infer conclusions using descriptive statistics

Question 2

How do ‘frequentists’ define probability?

Answer 2

Frequentism defines probability in terms of frequencies of events in repeated trials.
- Looks at probability as long run frequency.
- Only applies to repeatable event (the probability of something happening over many instances)

Question 3

How does a Bayesian define probability?

Answer 3

It is defined as ones degree of belief or uncertainty about a event or parameter. It represents the degree of confidence or plausibility assigned to a particular outcome or hypothesis based on available evidence

Probability is subjective and incorporates prior beliefs and knowledge

Question 4

Describe a ‘Binomial distribution’ ?

Answer 4

The binomial distribution models the number of successes, with each trial has two possible outcomes (success or failure) with a constant probability of success. The binomial distribution is a discrete distribution. The binomial distribution is defined by two parameters: the number of trials (n) and the probability of success in each trial (p)

Question 5

How is a ‘normal distribution’ described?

Answer 5

The normal distribution is a continuous probability distribution as it deals with continuous random variables that can take any value within a range. The normal distribution is defined by two parameters: the mean (μ) and the standard deviation (σ).

Question 6

What is an ‘estimator’? Give an example.

Answer 6

An estimator is anything that you use to try and estimate a population parameter. The sample mean is the estimator for our estimated population mean.

Question 7

Does the sample SD equal the estimated population SD?

Answer 7

No. This has to do with degrees of freedom. When calculating the sample SD one must include (n-1) to account for the loss of one degree of freedom when estimating the sample mean.

Solution: use Bessel-corrected equation.

Question 8

What is a sampling distribution of the mean ?

Answer 8

This is the finding of a total mean out of a ‘set of means’.

Question 9

What difference in shape should the sample distribution of the mean take? As compared to the regular raw distribution

Answer 9

The sample distribution of the mean is scores are going to varaible becasue of the affect of averaging. This means we should see a higher and sharper peak of it’s distribution.

less varaible than population distribution as seen when comparing sd(pop

Question 10

What is the standard error of the mean (SEM)?

Answer 10

It quantifies how much the sample mean is expected to deviate from the true population mean. SEM = sd of sample / √n

A higher sample sample size decreases SEM, indicating a more precise sample mean.

Question 11

What does figure does the SEM resemble?

Answer 11

SEM is exactly the same as the standard deviation of the sample distribution of the mean

Question 12

Are sample means closer or further away to the population mean than each individual score?

Answer 12

They are closer.

Question 13

What is the core tenant of the central limit theorem?

Answer 13

That regardless of what the true distribution of is in the world, the sample distribution of the mean scores is going to become increasingly normal as you increase sample size.

Question 14

Why does the sample distribution of the mean appear more normal as n increases?

Answer 14

You have more means falling closer to the population mean and less extreme scores impacting variation

Question 14

Why does the sample distribution of the mean appear more normal as n increases?

Answer 14

You have more means falling closer to the population mean and less extreme scores impacting variation

Question 15

What does a confidence interval indicate?

Answer 15

This is the range in which we are confident that our mean score fits somewhere in to.

eg. usually a 95% confidence that our sample captures the true mean.

Question 16

What is the main difference between Fisher and Neyman in their thinking about hypothesis testing?

Answer 16

Fisher: One is trying to falsify a single hypothesis.
Neyman: one is choosing between between two rival hypotheses

Both were frequentists

The current ‘Orthodox NHST’ is a blend of these two views that nether man would agree on.

Question 17

What is the difference between a research hypothesis and a statistical hypothesis?

Answer 17

Research hypothesis: makes claims about psychological constructs.
Statistical hypothesis: makes claims about population parameters.

Question 18

What is a Type I error?

Answer 18

Type 1 error is the incorrect conclusion that there is a significant effect or relationship between variables when, in reality, there is no such effect.

A false-positive

Alpha / significance levels (p=0.5) were set up to control for these type I errors

Question 19

What is a Type II error?

Answer 19

This is when you accept the null when it is actually false

A false negative.

Beta (β) is the probability of making a Type II error. Beta safeguards against Type II errors by measuring the power of a statistical test. Higher β = lower prob’ of T II

Question 20

What is a test statistic?

Answer 20

This is a single number that you can calculate only from your observations

Example: mean, SD, the third largest ‘thing’, (n) observations

Question 21

What is diagnostic test statistic?

Answer 21

A test-statistic becomes diagnostic if the null hypothesis and alternative predict different values. Something that tells the difference between the null and the alternative

Question 22

What does it mean - ‘Sampling distribution if the null is true’

Answer 22

This is what would we expect to see as a sampling distribution of the mean IF the null was true. Null assumes no affect, something is as likely to happen and it is not to happen.

The distribution is therefore binominal.

Question 23

What is the observed T in your data?

Answer 23

This is the number that we got from our data or experiment. And then one asks themselves how likely was it to get this number if the null hypothesis was true

Question 24

What are the four-parts for building a statistical test?

Answer 24

1) A diagnostic test statistic, T (e.g mean)
2) Sampling distribution of T if the null is true
3) The observed T in your data
4) A rule that maps every value of T onto a decision

Question 25

A p-value is the probability that the null hypothesis is true, yes or no?

Answer 25

No. A p-value is a claim about how likely you were to see your results if the null hypothesis were true.