Statistical Analysis
IB SEHS
MEAN 6.1.1
 Mean or average of a group of values describes a middle
point or central tendency, about which data points vary
 A way of summarizing a group of data and stating a best
guess at what the true value of the dependent variable (what
you measure in the experiment and what is affected during the experiment)
value is for that independent variable (a factor that can be varied or
manipulated in an experiment) level
Calculating the Mean of Grouped
Data using Excel
 http://www.youtube.com/watch?v=M7oON5Yvq-c
ERROR BARS
 Graphical representatives of the variability of data
 Any individual measurement you make in a lab will lack
perfect precision, this leads a researcher to take multiple
measurements at some independent variable level
 The error bars shown in a line graph represent a description
of how confident you are that the mean represents the true
value.
 The more the original data values range above and below
the mean, the wider the error bars and less confident you
are in a particular value.
How to Plot Good Science Graphs in Excel
 http://www.youtube.com/watch?v=-3WgNXh4K8Y
How to Add Error Bars to Excel Graphs
 http://www.youtube.com/watch?v=90zGaV0KLuk
STANDARD DEVIATION 6.1.2
 SD: the spread of scores around the mean or average.
 A small SD indicates that the data is clustered closely
around the men value
 A large SD indicates a wider spread around the mean
6.1.3
For example, the average height for adult men in the United
States is about 70 inches, with a standard deviation of around
3 inches. This means that most men (about 68%, assuming a
normal distribution) have a height within 3 inches of the
mean (67 inches – 73 inches), while almost all men (about
95%) have a height within 6 inches of the mean (64 inches –
76 inches).
6.1.4
 If the standard deviation were zero, then all men
would be exactly 70 inches high.
 If the standard deviation were 20 inches, then men
would have much more variable heights, with a typical
range of about 50 to 90 inches.
Standard Deviation Equation
How to Compute Standard Deviation in Excel
 http://www.youtube.com/watch?v=BCmhlz8rPf8
Coefficient of Variation 6.1.5
 The standard deviation expressed as a percent
 Important measure of relatively
t-test 6.1.6
 Measures whether there is a significant difference between
the mean of 2 populations
Independent t-test
 Determines whether two sample means differ reliably from
each other
 Do two groups training at different levels of intensity differ
from each other on a measure of cardiorespiratory
endurance?
Dependent t-test
 The two group of scores are related in some way.
 Two groups of subjects are matched on one or more
characteristics OR
 One group of subjects is tested twice on the same variable.
Two tailed t-test
 The two-tailed test is a statistical test used in inference (the
process of drawing conclusions from data that is subject to random variation), in
which a given statistical hypothesis, will be rejected when
the value of the test statistic is either sufficiently small or
sufficiently large.
One tailed t-test
 Only one of the rejection regions "sufficiently small" or
"sufficiently large" is preselected according to the
alternative hypothesis being selected, and the hypothesis is
rejected only if the test statistic satisfies that criterion
t-test in Microsoft Excel
 http://www.youtube.com/watch?v=BlS11D2VL_U
Correlation 6.1.7
 Determining a relationship between two things
 Is there a correlation between athletes’ ages and times for
the 5,000 meters?
 Solve for r-
Coefficient of Determination (𝑟 2 )
 The square of the correlation
 Usually, expressed as a percentage
 Even if the percentage is high it does not mean that age
causes the athlete to run the 5,000 meters faster. It simply
means that age and speed are related.
Understanding Statistical Correlation
 http://www.youtube.com/watch?v=l-sa3YlspLk
Coefficient of Determination
 http://www.youtube.com/watch?v=F54cdyvcyRA
Correlation Coefficient in Excel
 http://www.youtube.com/watch?v=s2TVkYmmCAs