The PENIS of Statistics (L2 & L3)

Question 1

What does PENIS stand for?

Answer 1

Parameters
Estimation
Null Hypothesis Statistic Testing
Intervals [of confidence]
Standard error.

Question 2

What are parameters?

Answer 2

Every model has parameters, represented by ‘b’. Regardless of the model, parameters are estimated using the same principles.
All parameters have: standard error, confidence interval & p-value.

Question 3

What makes the mean a statistical model?

Answer 3

The value ascertained by the mean is hypothetical; it is not observed in the data.

Question 4

Does the mean have error?

Answer 4

Yes, as the value obtained will not be correct for every person in the population. However, it has the ‘least error’ due to the squared scores deviating the least.

Question 5

What do we assess how well a model accurately represents data?

Answer 5

Sum of squared error (or variance).

Question 6

How do we assess how well a model accurately represents the population?

Answer 6

Standard error and confidence intervals.

Question 7

What do we use the mean for?

Answer 7

To make predictions about the population.

Question 8

What is ‘error’?

Answer 8

The deviation from what a model predicts (eg. the mean) and the actual data point (the observed value).

Question 9

How do we calculate the sum of squared error?

Answer 9

SS = the sum of (score - mean)squared.

Question 10

How do we calculate mean squared error?

Answer 10

s[squared] = the sum of (score - mean)squared / n-1

Note: why n-1? Because we are calculating for the population (see degrees of freedom).

Question 11

What is standard deviation?

Answer 11

Variance in squared units.

Question 12

How do we calculate standard deviation?

Answer 12

SD = squared root of mean squared error.

Question 13

What do sum of squared error, variance and standard deviation all represent?

Answer 13

• The fit
• The variability
• The representation of the population
• Error.

Question 14

What are degrees of freedom?

Answer 14

The freedom the experimenter has to randomly sample people from the population, in order to keep calculating the same mean.

Note: why n-1? As last person sampled is chosen so the mean continues to calculate a stated value, -1 removes this ‘person’ from the equation.

Question 15

What is estimation through the method of least squares error?

Answer 15

Based on minimising squared error whereby we keep estimation the value of the mean until we find the lowest error for the parameter (b value)

Question 16

What is the sampling error?

Answer 16

The difference between the sample value and the value given to you by the population.

Question 17

What is the standard error?

Answer 17

Tells us something of how a parameter differs from sample to sample (ie. how spread out our samples are)

Question 18

Why is it important to know the spread of sampling distribution?

Answer 18

It can tell you how close to the true value you are.

Question 19

What percentage of the sample fall within 1.96 standard deviations of the mean in a normal distribution?

Answer 19

95%, indicating that 95% of people in the same ‘contain’ the value we are interested in (relates to confidence intervals)

Question 20

What are confidence intervals?

Answer 20

They ‘go around’ the mean.

If confidence interval doesn’t overlap with each other it could be chance, but equally could show that the manipulation has created a population difference (eg. good experimental significance)

If confidence interval doesn’t overlap with the mean, they don’t contain the desired value.

NOT RELATED TO PROBABILITY

Question 21

What does the null hypothesis suggest about the parameter value?

Answer 21

That (b)=0, because the parameter represents the effect/relationship of the parameter and in a null hypothesis there is no effect.

Question 22

How is significance testing related to sample size?

Answer 22

The bigger the sample is, the easier it is to ‘find’ significance (ie. the same experiment could be insignificant with a small but significant with a large sample)

Question 23

What is Cohen’s ‘d’?

Answer 23

A way to quantify the differences between means by dividing by the control groups SD (see equation).

0. 2 is a small value,
1. 8 is a large value.

Question 24

What does a Cohen’s ‘d’ value of ‘d’=1 mean?

Answer 24

That the means are 1SD apart and therefore there is an effect.

Question 25

What does a Cohen’s ‘d’ value of ‘d’=0 mean?

Answer 25

That the means are the same and therefore there was no experimental effect.