The principles of statistics, the assumptions on which statistical tests are based, sampling, and the preparation of data for analysis

Question 1

Type 1 error

Answer 1

The incorrect rejection of a true null hypothesis (a false positive)

Question 2

Type 11 error

Answer 2

Incorrectly retaining a false null hypothesis (a false negative). Low power means high type 2 error

Question 3

How does power relate to type 11 error

Answer 3

Power = 1-B, where B = the probability of making a type 11 error

Question 4

List 4 factors which affect power

Answer 4

Effect size (large effect size increases power)
Alpha (decreasing alpha decreases power, increasing alpha increased power but also increases chance of making a type 1 error)
Variance of the distribution (decreasing the variance of the distributions increases power)
One tailed test increases power

Question 5

What do you need to calculate power

Answer 5

Effect size
Sample size
Alpha

Question 6

Assumptions for independent measures designs

Answer 6

Normally distributed variables (skewness and kurtosis, Shapiro-Wilks tests for both)
Linear relationship between variables
No multicollinearity or singularity
Homogeneity of variance (Tested using Levene’s test of homogeneity. If significant, the assumption has been violated). When data violates this it is heteroscedastic. Heteroscedastic=bad.

Question 7

Assumptions for repeated measures designs

Answer 7

Normally distributed variables (skewness and kurtosis, Shapiro-Wilks tests for both)
Linear relationship between variables
No multicollinearity or singularity
Sphericity (only univariate ANOVA, not RM MANOVA)
•Tested using Maulchly’s test. Assumes that all pairs of levels of the within-subjects variable have equivalent correlations. In RM ANOVA, violations of sphericity can increase type 1 error rate. It is only relevant when there are more than two levels. If violated, use a correction, which are provided in the output in SPSS. Two available corrections are the greenhouse geisser (GG) and the huynh-feldt (HF).

Question 8

Nominal data

Answer 8

Discrete data, categorical variables (qualitative)

Question 9

Ordinal

Answer 9

Quantities that have a natural ordering but the intervals between each value are not equal. (e.g. when you rank things in order) (qualitative)

Question 10

Interval

Answer 10

Like ordinal except the points on the scale do have equal intervals. For example temperature, and Likhert scales with numbers on them. (quantitative)

Question 11

Ratio

Answer 11

Like interval but with a neutral 0 point. (distance, time)

quantitative

Question 12

Sampling error

Answer 12

The sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter. The smaller the sample, the greater the sampling error.

Question 13

Random error

Answer 13

Random errors in experimental measurements are caused by unknown and unpredictable changes in the experiment. These changes may occur in the measuring instruments or in the environmental conditions. When averaged, random error should become 0.

Question 14

Probability sampling

Answer 14

The sampling technique in which every element of the population has an equal, non-zero probability of being selected.

Question 15

Categorical variable

Answer 15

Categorical variables contain a finite number of categories or distinct groups. Categorical data might not have a logical order. For example, categorical predictors include gender, material type, and payment method.

Question 16

Discrete variable

Answer 16

Discrete variables are numeric variables that have a countable number of values between any two values. A discrete variable is always numeric. For example, the number of customer complaints or the number of flaws or defects. If a discrete variable has enough levels, you can treat it as a continuous variable in a statistical analysis. If not, you may consider treating it as a categorical variable.

Question 17

Non probability sampling

Answer 17

In non-probability sampling, not all members of the population have a chance of participating in the study unlike probability sampling, where each member of the population has a known chance of being selected. Non-probability sampling is used in studies where it is not possible to draw random probability sampling due to time or cost considerations.

• convenience sampling (i.e. students)
• quota sampling (recruiting 250 males and 250 females)
• snowball sampling

Question 18

Volunteer sampling

Answer 18

Non-probability sampling. Participants self-select into the survey

Question 19

Quota sampling

Answer 19

Non-probability sampling. Research decides how many people to recruit who possess particular characteristics, such as gender or ethnicity.

Question 20

Random sampling

Answer 20

Each item from the population has an equal, non-zero chance of being selected for the sample.
Can be achieved using a lottery system where all of population given a number and numbers are then randomly selected. Can be done using computer software for random selection

Question 21

Descriptive statistics

Answer 21

A methods for organising, displaying and describing data. Includes measures of central tendency and measures of dispersion

Question 22

Inferential statistics

Answer 22

The estimation of parameters and the testing of statistical hypotheses

Question 23

Systematic error

Answer 23

Systematic errors are errors that are not determined by chance but are introduced by an inaccuracy (involving either the observation or measurement process) inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged.

Question 24

Positive skew

Answer 24

Tail to the right, in the positive direction. Bulge to the left of the graph.
The median and mode will likely be to the left of the mean, i.e. have a smaller or more negative value than the mean.

Question 25

Negative skew

Answer 25

Tail to the left, in the negative direction. Bulge to the right of the graph.
The median and mode will likely be to the right of the mean, i.e. have a larger or more positive value than the mean.