# Exam prep week 13 Inferential statistical analysis Flashcards

Measures of

variability/dispersion

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

Range

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

Variance

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

Standard deviation

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

Advantages of the standard

deviation

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

Inferential statistics

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

Confidence interval (CI) & sample size

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

Hypothesis testing

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

Research hypothesis vs null

hypothesis

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

Level of significance

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

Statistical power

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

Power analysis

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

Statistical tests

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

Statistical tests:

How do they work?

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

Statistical tests:

How do they work?

Example

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