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HL Psychology
Internal
Assessment
Inferential Statistics
What you should know
after this PowerPoint:
• A concise review of descriptive statistics
• Differences between descriptive and inferential
statistics.
• Why we use inferential statistics in psychology
• How to properly choose an inferential statistics test.
• How to distinguish between various types of data.
• How to test for statistical significance.
Descriptive statistics provide for..
• Measure of central tendency
o Gives a typical value for the data set
o Tells you where the middle of the data set is
• Measure of dispersion
o Indicates how the data are spread out
o Tells you what the rest of the data are
• The aim of descriptive statistics is to give an
accurate summary of the data
• The wrong choice of statistic gives a distorted
picture of the data
• This can lead to the wrong conclusions being drawn
from the data
• Each measure of CT and D has its advantages and
disadvantages
www.psychlotron.org.uk
Descriptive Statistics
Measures of Central
Tendency
• The mean – total scores divided by the
number of scores
• Use it when the data are normally distributed,
unskewed and there are no outliers
www.psychlotron.org.uk
o Adv: it uses all the values in the set, so is most sensitive to variations in the
data
o Dis: it can be artificially raised or lowered by an extreme value, or by
skewed data
Measures of Central
Tendency
• The median – the middle score in a range
What is the median 2,3,3,4,4,4,4,5,5,6,42?
• Use it when you can’t use the mean because of
skew, outliers etc.
www.psychlotron.org.uk
o Adv: it is based on the order of the data, not their actual values, so not
distorted by extreme values
o Dis: however, this makes it less sensitive to variations in the data
Measures of Central
Tendency
• The mode -most frequently occurring value
• Use when dealing with frequency data,
and/or where there is a clear modal value in
the set
www.psychlotron.org.uk
o Adv: it’s the only measure suitable for summarising category/frequency
data
o Dis: for many data sets there is no modal value, or their may be several
Calculate….
• A psychologist has obtained the following
scores. Answer the questions below.
•
8 1 5 5 2 7 1 1 1 4 6 8 9 9
• The range of these scores is
__________________________
• The mean of these scores is
__________________________
• The mode of these scores is
__________________________
• The median is
______________________________________
Measures of dispersion
• Range-difference between the smallest and largest
value Ex 3,4,7,7,8,9,12,4,17,17,18 =18-3 =16
• Although quick and easy to calculate it is distorted
by extreme values
Standard Deviation
• Standard deviation – a measure of the spread of
scores around the mean
• It is the most sensitive measure of dispersion using all
available data. It can be used to relate the sample
data to the population’s parameters.
SD formula
• Sum of all participant scores divided by the no of
participants = mean
• Subtract the mean from each score
• Square each of these scores
• Total the squared scores
• Divide by one less than the total participants. This is
the variance
• Take the square root of the variance.
Work out the SD….
• Scores – 13,6,10,15,10,15,5,9,10,13,6,11,7
Graphs
• Bar chart –Shows data for categories that the
researcher is interested in comparing
Histogram
• Shows data for all categories even those with zero
value
Frequency polygon/line
graph
• Shows two sets of data on one graph
Pie charts
• Show the proportion of all scores gained by various
categories
Inferential
Statistics
HL IA ONLY
Inferential Statistics
• With inferential statistics, you are trying to reach
conclusions that extend beyond the immediate
data alone. For instance, we use inferential statistics
to try to infer from the sample data what the
population might think.
• Or, we use inferential statistics to make judgments of
the probability that an observed difference
between groups is a significant one or one that
might have happened by chance in this study.
Inferential Statistics
• Thus, we use inferential statistics to
make inferences from our data to
more general conditions; we use
descriptive statistics simply to describe
what's going on in our data.
What you are bring asked
to do (HL IA).
• An appropriate inferential statistical test has been
chosen and explicitly justified. Results of the
inferential test is accurately stated.
• The null hypothesis has been accepted or rejected
according to the results of the statistical test. A
statement of statistical significance is appropriate
and clear.
What you are bring asked
to do (HL IA).
• The information you have obtained from
participants takes the form of raw data. This should
go into the appendices, and you should use your
results to calculate descriptive statistics appropriate
to your to data.
• The test you choose is dependent on the level of
measurement of your data and whether you used
independent samples or repeated measures.
Levels of Measurement
• Nominal-frequency headcount; things can
only belong to one category ex the no of
students wearing yellow shirts.
• Ordinal –data which is ranked or put in
order. It is not known what the interval
between each rank is ex 1st,2nd,3rd time in a
swimming trial
• Interval/ratio- measurement on a scale
where the intervals are known and equal
(ratio has a true zero point; interval can
move into negs. Ex of ratio is time in secs.
Levels of data: nominal
• Which newspaper paper do you read regularly?
• We can put these into categories.
Levels of Data: ordinal
• What grade did you get for each of your portfolio?
• These can be put in order… highest to lowest
Levels of data: interval
• How quick is your reaction time?
• We can measure and compare the exact
time because the intervals on the ruler are
equal.
Inferential tests
• Provide a calculated value based on the results of
the investigation
• This value is then compared to a critical value
(statistical tables) to determine if the results are
significant
• In chi square, sign test, spearman’s rho the
calculated value must exceed the critical value.
Choosing an inferential
test
• Nominal data and independent measures design = Chi
square test
• Ordinal data and independent measures design = Mann
Whitney U
• Interval and ratio data and independent measures
design = Unrelated T-test
• Nominal data and repeated measures design =Sign test
• Ordinal data and repeated measures design = Wilcoxon
test
• Interval or ratio data and repeated measures design =
related T-test
• More info: http://hs-psychology-ibhl.ismonline.org/files/2011/09/Choosing-an-inferential.pdf
A directional hypothesis
• Very often, we state before we test the hypothesis in
which direction of the results will fall. Our hypothesis
is usually directional (meaning we are predicting an
increase or decrease in a time or score)and the
appropriate statistical test of the hypothesis is called
one-tailed.
• Once you have collected the data. Decide which
test you need to administer. Only one person in
your group needs to work out the mathematics.
Using Tests of Significance – The General
procedure
• Choose appropriate statistical test
• Calculate statistical test
• Compare the test with the critical values. These can
be found in the back of the Research methods text
book, or mathematics statistic books, or online.
• Decide which side of the critical value your result is
on.
• Report the decision.
Inferential statistics- indicating
how significant results are.
• A significant result is one where there is a low
probability that chance factors were responsible for
observed difference
• 5% level of significance, in psychology, is
acceptable (P is less than 0.05)
• There is less than a 5 % likelihood that the difference
was due to chance.
Key Terms you will need to look up
and define.
Critical value
Degrees of freedom
P value/level
Significance
One-Tailed Test
Two-Tailed Test
Type 1 error
Type 2 error
Interval
Ordinal
Nominal