Depending on our sample size, we can draw conclusions with a certain level of confidence.

Descriptive Statistics

Error Bars

**B1 Statistical Analysis**

**Learning Outcomes**

1.1.1 State that error bars are a graphical representation of the variability of data.

1.1.2 Calculate the mean and standard deviation of a set of values.

1.1.3 State that the term standard deviation is used to summarize the spread of values around the mean, and that 68% of the values fall within one standard deviation of the mean.

1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples.

1.1.5 Deduce the significance of the difference between two sets of data using calculated values for t and the

appropriate tables.

1.1.6 Explain that the existence of a correlation does not establish that there is a causal relationship between

two variables.

what would you study?

hypothesis?

how will you test it?

how will you measure it?

Samples of bean plants

small enough

large enough

(to manage the data)

(to represent the population)

Statistics measures the differences and relationships between sets of data.

Draw conclusions about a larger population.

90% confidence

95% confidence

100% confidence

Standard Deviation

Measure the spread of our values around the mean.

If our data has normal distribution (meaning our values are clustered around the mean) then we assume that:

About 68% of our values lie within ± 1 SD of the mean.

This number rises to 95% for ± 2 SD from the mean.

Are graphical representations of the variability of the data. Error bars can show either the range of the data or the SD on a graph.

Organisms vary and this variation can be described in a population.

Normal Distribution

A common way that the data is distributed

Bell Curve

Abbreviations for the standard deviation are S.D., s.d. and σ (sigma)

Exercise

The following data show the weights of 24 kangaroos in kilograms:

Tasks

1. Complete

2. Produce a histogram chart

Where

n

is the sample size and

range

is from the smallest to largest value.

Exercise 2

These data show the lengths of shells of two species of mussels.

Have common mussel really got longer shells than green mussels or have the samples just come out that way?

t - test

Compare the means to determine if they are significantly different.

Requires data to show a normal distribution

Populations are more likely to be significantly different if:

the averages (𝑥 ̅) are further apart

the SD are smaller

The t-test provides support for one of two hypotheses:

H (null hypothesis)

H (alternative hypothesis):

o

A

"There is no significant difference between the mean lengths of common and green mussels shells."

"There is a significant difference between the mean lengths of the common and green mussel shells."

The t-test calculates the probability that the data are from different populations (supporting H ) or could be from the same population (supporting H ). A probability of less than 0.05 indicates a significant difference, supporting H .

A

A

O

The t-test requires that two quantities are calculated:

1. The degree of freedom

2. The value of t

The value of P (level of significance) can be looked up on a table of Critical values of t using df and t.

For df = 23 and t = 2.62

P is between 0.05 and 0.01

0.05 > P > 0.01

This suggest that the mussels have significantly different shell lengths and supports the alternative hypothesis, HA.

Do not write that a hypothesis is proven or disproven, the results will support one hypothesis or the other.