Exam prep week 13 Inferential statistical analysis

Question 1

Measures of

variability/dispersion

Answer 1

 Concerned with the spread of data
 Variability answers:
-Is the sample homogeneous or heterogeneous?
-Are the samples similar or different?
 Measures of variation describe extent to which
individuals/scores in sample vary
 Most common measures are:
-range
-variance
-standard deviation

Question 2

Range

Answer 2

 Simplest & most unstable measure of
variability
 The difference between the highest &
lowest scores
 Disadvantage: depends on the 2 extreme
scores only (outliers)
 Can use difference between other scores
e.g. semi-quartile range

Question 3

Variance

Answer 3

 Measure of the variability that includes every score in
the distribution rather than only 2 scores
 Some of the scores will be > mean
 Some of the scores will be

Question 4

Standard deviation

Answer 4

Standard deviation is the square root of the variance –
therefore in same units as original measurements
 The most frequently used measure of variability
 A measure of average deviation or distance of each
score from the group mean in a normal distribution
 Should always be reported with the mean

Question 5

Advantages of the standard

deviation

Answer 5

 Takes all the scores into account
 Can be used to interpret individual scores
 SD allows reader to get a feel for the
variation the data contain
 Used in calculation of many inferential
statistics

Question 6

Inferential statistics

Answer 6

 Descriptive statistics - summarise data
 Inferential statistics – allow inferences or
conclusions to be drawn from data
 Usually two purposes:
1. Estimate how well a sample statistic
reflects the population parameter
2. Test hypotheses or predictions about
the population

Question 7

Confidence interval (CI) &
sample size

Answer 7

CI can be calculated from sample mean,
sample standard deviation and sample size
 Greater the sample size, smaller the CI:
i.e. the greater the confidence we have
that sample statistic estimates population
parameter

Question 8

Hypothesis testing

Answer 8

 Inferential statistics provide objective basis
for decision-making
 Statistical hypothesis testing based on
disproving: ie it is easier to disprove
something than to prove it

Question 9

Research hypothesis vs null

hypothesis

Answer 9

Research (alternative) hypothesis (HA
): statement
about expected relationship between dependent and
independent variables
e.g. wounds will heal more quickly with a gauze
dressing than with no dressing
 Null hypothesis (H0
): statement that there is no
relationship between dependent and independent
variables
e.g. there is no difference in wound healing time
between gauze dressing & no dressing
 In statistical hypothesis testing we accept the
research hypothesis by rejecting (disproving) the
null hypothesis

Question 10

Level of significance

Answer 10

 In statistical hypothesis testing we try to
minimise the chance of making a Type I
error
 To do this we set a low probability that our
statistical test will reject a true null
hypothesis - ie will conclude that there is a
relationship between dependent and
independent variables when in fact there is
no relationship
 This probability is called the  level or level
of significance:
0.05 (5%); 0.01 (1%); 0.001 (0.1%)

Level of significance is set at the start of
the research study
i.e. before undertaking the statistical test,
not after
 Minimum level of significance always 0.05
 More stringent levels of significance (0.01
or 0.001) set when making Type I error
would have serious consequences

Question 11

Statistical power

Answer 11

Power of a statistical test
is the probability of not
making a Type II error
ie of correctly rejecting a
false null hypothesis
 Power determined by
amount of variation in
data, strength of
relationship between
dependent & independent
variables (effect size) &
sample size

Question 12

Power analysis

Answer 12

We do not set a significance level for Type II error,
but we would like power to be ≥80%
 For a given sample size, Type I () & Type II (β)
error levels are inversely proportional - ie the more
stringent the  level, the lower the power of the
statistical test
 The only way to reduce both Type I & Type II errors
is to increase sample size
 Power analysis can be used to determine the sample
size needed to maintain 80% power in a statistical
test at a given level of significance

Question 13

Statistical tests

Answer 13

 HA: there is some specified relationship
between dependent & independent
variables
 H0
: there is no relationship between
dependent & independent variables
 A statistical test enables you to reject HO
with a certain degree of confidence
e.g. at the 0.05 significance level, you have
a 95% chance of being right in rejecting H0
and a 5% chance of being wrong

Question 14

Statistical tests:

How do they work?

Answer 14

Set a desired significance level – 0.05, 0.01 or 0.001
 Calculate a test statistic that summarises the
relationship between dependent and independent
variables: usually the greater the test statistic, the
stronger the relationship
 Calculate the probability of obtaining the value of
the test statistic if in fact there is no relationship
between dependent and independent variables
(probability value or p value)
 If p value significance level, then accept H0 &
reject HA

 If p value is significance level, result of
statistical test is said to be not significant

Question 15

Statistical tests:
How do they work?
Example

Answer 15

 Example: Pressure areas (indicated by redness of
skin) are developing in your patients in an aged care
ward. Which of 2 types of preventative treatment
(sheepskin cover, air mattress) should you use to
reduce the size of the pressure areas?
 How would you test this?
 What is the dependent variable?
 What is the independent variable?
 t = 3.5, P

Question 16

Statistical significance & clinical

significance

Answer 16

Statistical significance should not dictate our
actions, it should guide our actions
 Statistically significant test means that we can reject
HO with only a 5% (or less) chance of being wrong
 A result may be statistically significant, but of little
clinical significance
Example: diameter of pressure areas reduced by 2
mm when using new air mattresses rather than the
current sheepskin covers. This difference is
statistically significant (t-test, p

Question 17

Statistical significance and
clinical significance (cont.)

Answer 17

Clinical significance depends on the effect size ie:
the strength of relationship between dependent &
independent variables. For a finding to be clinically
significant, it should be statistically significant &
have an appropriate effect size
 Example: diameter of pressure areas reduced by 50
mm when using new air mattresses rather than the
current sheepskin covers. This difference is
statistically significant (t-test, p