Introduction to Statistical Analysis

Question 1

Why do we analyse data?

Answer 1

=To discover implicit structure in the data (finding patterns in experimental data which might
in turn suggest new models or experiments)
=To confirm or refute a hypothesis about the data

Question 2

What are the types of data and the scales within them?

Answer 2

=Qualitative
-Categorical scale
-Ordinal scale
=Quantitative
-Interval scale
-Ratio scale

Question 3

What is categorical scale?

Answer 3

Each data item is drawn
from a fixed number of categories, where the
names of the categories may occur in any
sequence and are not orderable
-Nationality: French, Japanese, Mexican, etc.
-Can be called nominal

Question 4

What is Ordinal scale?

Answer 4

Data on an ordinal scale has a recognized
ordering between data items, but there is no
meaningful arithmetic on the values
-Finishing position in a race: 1st, 2nd, 3rd etc.

Question 5

What is Interval scale?

Answer 5

a numerical scale (usually with real
number values) in which we are interested in relative
rather than absolute value
(Celsius temperature scale)
=The differences between the numbers are
interpretable, but the variable doesn’t have a
“natural” zero value
=Subtraction and average are meaningful, but addition
or multiplication are not

Question 6

What is Ratio scale?

Answer 6

Ratio scale: a numerical scale (again usually
with real number values) in which there is a
notion of absolute value (response time/ age in years)
=Zero really means zero
=Subtraction, average, addition and
multiplication are meaningful

Question 7

What is the difference between continuous and discrete data?

Answer 7

Continuous variable: it is possible to have another
value between any two values
 e.g. response time
• Discrete variable: a variable that is not continuous
 e.g. graduation year

Question 8

What scales are continuous and discrete?

Answer 8

Continuous= interval and ration (quantitative)
Discrete= nominal, ordinal, interval, ratio (all)

Question 9

Describe normal distribution

Answer 9

Any normal distribution is described by two
parameters:
 The mean μ is the centre around which the data
clusters.
 The standard deviation σ is a measure of the
spread of the curve

Question 10

What are the percentages associated with standard deviations?

Answer 10

1= 68% within
2= 95% within
3= 99.7%

Question 11

What is a statistic?

Answer 11

single value computed from data that captures some overall property of the data

Question 12

What measures are we interested in when describing data?

Answer 12

=Central tendency- idea of what a typical or common value for a given variable is (mean, median, mode)
=Dispersion- idea of how
spread out data values are
(range, variance, standard deviation)

Question 13

Describe the mean

Answer 13

-Total divided by the number of values
-Appropriate for both interval and ratio scales;
it does not depend on an absolute zero in the
scale. Does not work for qualitative
-Affected by outliers

Question 14

Descriptive vs inferential data

Answer 14

• Descriptive= present information to summarise and visualise
• Inferential= generalise to larger populations

Question 15

Describe the median

Answer 15

middle value
when the values are ranked in ascending or
descending order
-Non-decreasing order= x((N+1)/2) for N odd or any value between x(N/2) and x(N/2)+1 for even
=Appropriate for qualitative ordinal data and
quantitative interval and ratio data. It does
not make sense for categorical data, as that
has no appropriate ordering.
• Median is a good summary statistic for data
where there is a forced cutoff at one end, or
possible distortion by extreme outliers

Question 16

Describe the mode

Answer 16

most commonly
occurring value
It is most typically used for ordinal or
categorical data.
• It is not particularly informative for
quantitative data with real-number values,
where it is uncommon for the same data
value to occur more than once

Question 17

Describe the range

Answer 17

difference
between the highest and the lowest values.
• Often the minimum and maximum values are
also reported
The interquartile range is an alternative
measure that is less influenced by extreme
values. This is used a lot

Question 18

What is variance?

Answer 18

Mean square deviation from the mean

Question 19

Describe standard deviation

Answer 19

The standard deviation makes sense for both
interval and ratio data; but has no meaning for
qualitative data scales.
• This is perhaps the most popular
measure of dispersion

Question 20

How do you take a representative sample?

Answer 20

• Random

- Sample as large as practically possible

Question 21

How do we estimate the variance of the whole population using the sample mean?

Answer 21

Bessel correction= denominator (n-1) rather than n

Different equation than the normal variance equation