# The PENIS of Statistics (L2 & L3) Flashcards

1
Q

What does PENIS stand for?

A
```Parameters
Estimation
Null Hypothesis Statistic Testing
Intervals [of confidence]
Standard error.```
2
Q

What are parameters?

A

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.

3
Q

What makes the mean a statistical model?

A

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

4
Q

Does the mean have error?

A

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.

5
Q

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

A

Sum of squared error (or variance).

6
Q

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

A

Standard error and confidence intervals.

7
Q

What do we use the mean for?

A

To make predictions about the population.

8
Q

What is ‘error’?

A

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

9
Q

How do we calculate the sum of squared error?

A

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

10
Q

How do we calculate mean squared error?

A

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).

11
Q

What is standard deviation?

A

Variance in squared units.

12
Q

How do we calculate standard deviation?

A

SD = squared root of mean squared error.

13
Q

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

A
• The fit
• The variability
• The representation of the population
• Error.
14
Q

What are degrees of freedom?

A

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.

15
Q

What is estimation through the method of least squares error?

A

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)

16
Q

What is the sampling error?

A

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

17
Q

What is the standard error?

A

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

18
Q

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

A

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

19
Q

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

A

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

20
Q

What are confidence intervals?

A

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

21
Q

What does the null hypothesis suggest about the parameter value?

A

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

22
Q

How is significance testing related to sample size?

A

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)

23
Q

What is Cohen’s ‘d’?

A

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

1. 2 is a small value,
2. 8 is a large value.
24
Q

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

A

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

25
Q

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

A

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