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1. Topic 6.1
Statistical Analysis

2. MEAN, SD AND V

3. Mean 6.1.2
• Mean is the average.
• The mean is obtained by adding all the values
together and dividing the total by the number
of individual values.

4. Standard Deviation 6.1.2
• The standard deviation is a measure of the
spread of the scores around the mean.
SD

5. Normal Distribution 6.1.3
• When scores are normally distributed 68% fall
within + 1SD and 95% within + 2SD of the
mean.

6. Standard Deviation 6.1.4
• Standard deviation helps
compare means and the
spread of data between
two samples
– A small SD indicates that
the data is clustered closely
around the men value
– A large SD indicates a wider
spread around the mean

7. SD – Who Cares?
• SD helps us observe differences between data
sets (text p. 139)
– Mean may be similar, SD adds information to
mean value
• SD helps us understand what is “normal” and
what might be statistically significant
– Watch the video on my topic 6 page.
• “Standard Deviation explained and visualized”

8. Coefficient of Variat5on 6.1.3
• The coefficient of variation represents the
ratio of the standard deviation to the mean.
• It is a useful statistic for comparing the degree
of variation from one data series to another,
even if the means are drastically different
from each other.

9. ERROR BARS

10. Error Bars 6.1.1

12. Error Bars
• Error bars can show variance in
data between two samples and
the graphed means (text
example - Saaed /Asif)
• Error bars can show the
variance in trials by the same
person and their means (p139 –
top example with golfer).
• Error bars can show standard
error
• ***We must define how we are
using the Error Bars!!!!

13. T-TEST

14. T-test
• The t-test can be used to measure whether
there is a significant difference between the
means of two populations.
– EXAMPLE – If you calculate the weight of the
people on two different islands, the t-test will
determine whether there is a significant difference
• The formula will be based on the difference between
the means and the degree of variation among them.

15. State the Null Hypothesis
The Null Hypothesis ALWAYS says, “There is NO
SIGNIFICANT difference between _____ and
______.
• We either reject or accept the
• If the P value is ABOVE 0.05 – we ACCEPT
• If the P value is BELOW 0.05 – we REJECT

16. t-test
• Measures whether there is a significant
difference between the means of 2 populations
In the first two graphs, there is
a large amount of cross-over of
the two graphs.
What this tells us is that the test
creates similar results despite
the changed variable.
(P scores OVER .05)
This means that there is NO
significant differences.
SOURCE - http://mrkubuske.com/2014/08/29/running-a-t-test/

17. Understanding the t-test
• T-test generates a score(t)
– A table of critical t-values is used to determine the
probability (p) based on degrees of freedom
– In EXCEL – this is all calculated for us
– In EXCEL we need to know the type of test to
ensure the correct “tables” are accessed by EXCEL

18. Types of t-tests
Paired (dependent)
• The two group of scores
are related
• Man on Diet example
• DOF is single group - 1
– Two groups of subjects
are matched on one or
more characteristics OR
– One group of subjects is
tested twice on the
same variable.
Unpaired (Independent)
• The most frequently
used t test
• Mary Roisin (p. 157)
• DOF is TOTAL group -2
– Do two groups training
at different levels of
intensity differ from
each other on a measure
of cardiorespiratory
endurance?

19. Reminder….
• The t-test can be used to measure whether
there is a significant difference between the
means of two populations.
• You need to know the TYPE of test!
• The t-score and resulting Probability is based
on this formula related to the degrees of
freedom

20. Determining Probability
• We need to know this because we are using
the t-test to determine…..
• The t-test can be used to measure whether
there is a significant difference
between the means of two
populations.

21. Confidence in my scores?
• P = Probability
• P > .05 – there is MORE
than a 5% chance my
results are by CHANCE so
they are not significant.
• P< .05 - there is a LOW
chance it was by chance
and it IS SIGNIFICANT

22. State the Null Hypothesis
The Null Hypothesis ALWAYS says, “There is NO
SIGNIFICANT difference between _____ and
______.
• We either reject or accept the
• If the P value is ABOVE 0.05 – we ACCEPT
• If the P value is BELOW 0.05 – we REJECT

23. Confidence in my scores?
• P = Probability
• P > .05 – there is MORE than a
5% chance my results are by
CHANCE so they are not
significant. We accept the
Null Hypothesis.
• P< .05 - there is a LOW
chance it was by chance and it
IS SIGNIFICANT and we reject
the Null Hypothesis