Topic 6.1

Statistical Analysis

MEAN, SD AND V

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.

Standard Deviation 6.1.2

• The standard deviation is a measure of the spread of the scores around the mean.

SD

Normal Distribution 6.1.3

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

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

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”

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.

ERROR BARS

Error Bars 6.1.1

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!!!!

T-TEST

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.

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

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/

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

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?

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

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.

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

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

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