First year Statistics

Question 1

Give the types of data.

Answer 1

Discrete:
Nominal - lowest form, categorical, basic
Ordinal - has a rank, but categorical e.g. Likert Scales

Continuous:
Interval - regular intervals, ranked, no absolute 0 e.g. height, time
Ratio - highest power, ranked, absolute 0 e.g. %s

Question 2

What are the assumptions for the different types of tests?

Answer 2

Sample size, data type, skewness, peakedness

Non-parametric: <30, all discrete tests, continuous data that is not normally distributed

Parametric: >30, continuous data that is normally distributed

Question 3

Name the inferential statistical tests for both types.

Answer 3

Non-parametric: Chi-Squared, Mann-Whitney, Kruskal-Wallis

Parametric: T-tests 1 and 2-tailed, ANOVA

Question 4

Name the types of relational statistics.

Answer 4

Measure correlation (not causation) based on distance from 0.

Non-parametric: Spearman’s Rank
Parametric: Pearson’s r

Question 5

What are the different confidence intervals?

Answer 5

0. 05 = 95%
1. 01 = 99%
2. 001 = 99.9%

Question 6

What is Simple Linear Regression? What does it permit us to do?

Answer 6

Permits us to make numerical predictions of one variable by reference to another
Involves the comparison of a dependent variable (changed) and independent variable (measured)

Attempts to predict the changes in Y based on changes observed in X; proportion of changes in Y explained by X

Question 7

What is variance?

Answer 7

Sum of squares/degrees of freedom

Explained = diffrence between mean and predicted values

Unexplained = difference between observed and predicted (a.k.a. RESIDUAL)

Question 8

What are the outputs of a simple linear regression model? Explain their significance.

Answer 8

R-square = type and strength of relationship; +1 is strong positive, -1 strong negative

F-ratio = explained / unexplained variance;
The further from 1, the better the model at explaining changes in Y

Test statistic = if P > 0.05, then can accept alternative hypothesis and reject the null, and conclude that the model explains a significant proportion of changes in Y

Question 9

Summarise the overall aim of simple linear regression.

Answer 9

To maximise explained variance which is implied by a large F-ratio. The higher the R-square, the more variance in Y explained by C i.e. there is a higher proportion of variance explained by the model. This also suggests values were closer to the line