Discovering Statistics

Question 1

What is validity?

Answer 1

The degree to which a theory/model reflects a true/accurate picture.

Question 2

What is reliability?

Answer 2

The replicability of results

Question 3

What are the characteristics of a normal distribution?

Answer 3

Symmetrical
Bell shaped curve
Standard Deviation determines steepness
Unimodal
Continuous

Question 4

What percentage of values fit within +/- 1.96 standard deviations in a normal distribution?

Answer 4

95%

Question 5

What is the standard error?

Answer 5

The standard deviation (variability) of the sampling distribution

Question 6

What are point estimates?

Answer 6

Single numbers used to guess corresponding population parameters.

Question 7

What are examples of point estimates?

Answer 7

Measures of central tendency such as mean median and mode
Measures of dispersion such as range and standard deviation
Relationships such as correlations

Question 8

What are interval estimates?

Answer 8

uncertainty quantified around point estimates (smaller intervals mean more confidence and less uncertainty)

Question 9

What are confidence intervals?

Answer 9

range of values that’s likely to include a population value with a certain degree of confidence. E.g 95% Confidence interval means that 95% of samples will include the population mean

Question 10

What is the t-distribution?

Answer 10

A way of approximating confidence intervals if the sampling distribution mean is not known. It is centred around 0, symmetrical and its shape changes based degrees of freedom (df=infinity, the distribution is normal)

Question 11

What are the three levels of hypothesis?

Answer 11

Conceptual
Operational
Statistical

Question 12

What is the scientific method?

Answer 12

Observation
Theory
Hypothesis/predictions 
Test hypothesis 
Interpret data
Reach conclusions + generate more hypotheses

Question 13

What is the linear model?

Answer 13

To obtain the value of an outcome from one or more predictors

Question 14

What is the equation for the general linear model?

Answer 14

Outcome = b0 (intercept) + b1(predictor) + e (error)

Question 15

What is b0 (intercept)?

Answer 15

The value of the outcome when the predictor is 0

Question 16

What is b1?

Answer 16

The change in the outcome for every unit change in the predictor (slope)

Question 17

What value is used to establish the significance of b1?

Answer 17

T value measures how many SD our estimate is from 0, we want it faraway from 0 as possible to reject null hypothesis

Question 18

How is model fit evaluated?

Answer 18

R2 and adjusted R2

Always lies between 0 and 1, near 0 means does not fit the variance, 1 means good fit

Question 19

What is the F stat?

Answer 19

The statistic that indicates whether there is a relationship between outcome and predictor. The further the f is from 1 means there is a relationship

Question 20

What are outliers?

Answer 20

A value in the data that does not follow the trend

Question 21

How can outliers be detected in the GLM?

Answer 21

Graphs
Standardised residuals (if difference between observed and predicted is more than 3 its is outlier)
Cooks distance (more than 1 is outlier)

Question 22

If outliers are present, what should be done?

Answer 22

A robust estimation model should be used instead of OLS model as they are more resistant to their influence

Question 23

What are the assumptions of the linear model?

Answer 23

Linearity and additivity
Normally distributed
Independent errors
Homoscedastic errors

Question 24

What are the differences between errors and residuals?

Answer 24

Errors refer to difference between observed and predicted values of the population - this cannot be observed
Residuals refer to difference between observed and predicted values of the sample

Question 25

What are independent errors?

Answer 25

Errors in one prediction that are unrelated to errors in another

Question 26

What are homoscedastic errors?

Answer 26

Variance of residuals should be consistent at different levels of the predictor variable.

Question 27

What is heteroscedasticity?

Answer 27

The number of residuals are more on one side of the spread creating a funnel shape

Question 28

What should be done if the assumption of normal distribution is not met?

Answer 28

Normality can be ignored as long as sample size is big enough die to central limit theorem (at least 30 samples), if small sample size is used - bootstrapping can be used.