Introduction to Statistics

Question 1

What is ‘statistics’?

Answer 1

Statistics are the study of a representative sample to find out what happens in an entire population

Question 2

When do we use statistics? What is the objective?

Answer 2

When we want to study a characteristic and we can only access a sample of the population, not everyone on the planet. The objective is to explain the variability/ to reduce uncertainty

Question 3

What is a ‘variable’?

Answer 3

A variable is a characteristic that varies. Why this variable varies is what we study in statistics.

Question 4

What is probability theory?

Answer 4

This is the theory underlying statistics. The idea we have an educated guess for the population based on our sample.

Question 5

Why do we use descriptive statistics?

Answer 5

To familiarise ourselves with the data. Make sure you do not have errors, mistypes or typos in your data. Data cleaning.

Question 6

What is a categorical variable?

Answer 6

Qualitative - words. Can be nominal or ordinal

Question 7

What is a numeric variable?

Answer 7

Quantitative - numbers. Can be discrete or continous

Question 8

What is an Ordinal variable and give an example

Answer 8

Words, but ranked. For example, income: poor, average, wealthy

Question 9

What is a Nominal variable and give an example

Answer 9

Words, with no order or rank. For example, gender, eye colour, etc

Question 10

What is a binary variable and what is an ordinal variable?

Answer 10

Binary is when there are only TWO choices, e.g. gender male or female - can be ordinal or nominal but must be only two categories.
An ordinal variable is when there are more than two choices. It can be nominal or ordinal data.

Question 11

What is a discrete variable?

Answer 11

Distinct value. Whole numbers, not decimals or precise numbers. No ranking is required. For example, shoe size, Age 1yr/2yrs/3yrs etc

Question 12

What is a continuous variable?

Answer 12

Specific numeric value which is on a scale (interval) and can be ranked. For example, weight, height, IQ, BMI, etc.

Question 13

If we have categorical data, what kind of descriptive statistic should we use?

Answer 13

We are interested in the frequency, how many people are in each category. Hence, we need to create a frequency table. We can also create bar charts or a pie chart. This to visualise the data to see what we have.

Question 14

In a frequency table, it will show us the ‘percentage’, the ‘valid percentage’ and the ‘culmuative perecentage’. What do each of these percentages mean and which one should we pay the most attention too?

Answer 14

The percentage, is the percentage including the missing values and outliers.
The valid percentage is the percentage removing the misisng values.
The culmuative percentage adds the percentages of each region from the top of the table to the bottom, culminating in 100%. This is more useful when the variable of analysis is ranked or ordinal, as it makes it easy to get a sense of what percentage of cases fall below each rank. (wikipedia)

Question 15

If we use a frequency table and realise there is a missing value or a piece of incorrect data, what is our two options?

Answer 15

1. remove and delete the missing or incorrect participant data (although loose information on all the other variables, so want to avoid) - Although remember to keep an original data document
2. Fill in with the predicted value of what it is supposed to be

Question 16

What type of descriptive statistic would we use for numerical data?

Answer 16

Histograms and Box Plots. This is because we are interested in the VARIANCE, not the frequency. We would also look at the central tendacy measurements, and the measurements of dispersion.

Question 17

With numerical scale data, we are not interested in the frequency of the catergories, we are interested in ….

Answer 17

Variance

Question 18

What is the mean, median and mode?

Answer 18

Central tendancy measurements. The median is the middle value in the data, the mode is the most common value, and the mean is the average of all the values

Question 19

Why is the mean sometimes not useful?

Answer 19

The mean is not useful as if the range is really big it could skew the mean value. It also does not tell us about the distribution of the values.

Question 20

How do you work out the variance?

Answer 20

Caluclate the difference between the mean value and each individual value. The variance is the average of the values’ distance from the mean. This is how much the data varies from the mean

Question 21

How would you work out the standard deviation?

Answer 21

The standard deviation is the distance either side of the mean. This is the square root of the variance.

Question 22

What are the measures of dispersion?

Answer 22

SD, Variance and min/max values

Question 23

What is the interquartile values?

Answer 23

We need to order the values in order, then we split the values at 50%, and then 25% and 75%, the values at these percentages are the interquatile values

Question 24

What is a standardised value?

Answer 24

A standardized value is what you get when you take a data point and scale it by population data. It tells us how far from the mean we are in terms of standard deviations.

Question 25

What does the central limit theorem in probability theory mean?

Answer 25

Even if the events follow different distributions to the curve of distribition, given enough data they become normal, that is they end up to look bell shaped

Question 26

If the data is symmetrical you report the…

Answer 26

mean and SD

Question 27

If the data is asymmertical/skewked you report the…

Answer 27

median and range/min/max

Question 28

If the curve of distribution is skewed …… then it should go mode, median, mean

Answer 28

Positive

Question 29

If the curve of distribution is skewed …. then it should go mean, median, mode

Answer 29

Negative

Question 30

If a box plot’s 50% line is skewed to the left, what kind of skew is this?

Answer 30

Positive

Question 31

If a box plot’s 50% line is skewed to the right, what kind of skew is this?

Answer 31

negative

Question 32

What is the descriptive indices for:
A) Catergorical variables
B) Numerical variables

Answer 32

A) frequencies and proportions

B) Measurements of centeral tendacy and measures of dispersion

Question 33

What are the plots/displays for:
A) Catergorical variables
B) Numerical variables

Answer 33

A) pie charts, bar charts

B) Histograms, box plots

Question 34

Ordinal data can be considered either categorical or discrete numerical.
If there are less than 4 points -> treat them as ?????
If there are 5 or more than 4 points -> treat them as ?????

Answer 34

1. categorical

2. numerical