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Statistics - Coggle Diagram
Statistics
Chi-Squared Test
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Our expected ratio(s) will often differ from our reality - observed ratio(s), the Chi-squared test will tell us if this difference is significant or not
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everyday use
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We could use it to see if dice are fair or biased. We expect a ratio of 1:1:1:1:1:1 between all the numbers.
- Our expected ratio(s) will often differ from reality (our observed ratio(s)).
- The Chi-Squared test will tell us if this difference between the expected and observed ratio is significant or not
- If we roll a fair dice 60 times, it is unlikely that we will get all the numbers being If we roll a fair dice 60 times, it is unlikely that we will get all the numbers being
use in biology
In this genetic breeding experiment, two heterozygous parent plants are crossed. We would expect a ratio of green:yellow seeds of 3:1 in the offspring.
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conclusion
e.g. there is a significant difference between the expected and observed ratios at the 5% probability level
standard deviation
Standard deviation is a measure of variation. It measures the amount of variation or spread from the mean.
A low standard deviation indicates that the data have a narrow range and the points are closely grouped to the mean. This could indicate greater reliability
A high standard deviation indicates that the data points have a larger range and are less well grouped. This might have a larger range and are less well grouped. This might
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normal distribution
Scores near the mean are most common and the outliers are rarer; this is called a normal distribution.
- To show a normal distribution, 68% of the leaves should lie within the data spread (which was 75.62 – 93.58mm)
- Also 95% of the leaves should lie within 2 standard deviations from the mean (66.64 – 102.56mm).
- Our data does therefore show a normal distribution
uses;
You can add the standard deviation to bars or plotted points to show how spread out the individual repeats were about the mean by using error bars.
Error bars extend by one standard deviation above the mean and one standard deviation below it so the length of an error bar is twice the standard deviation.
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Spearman’s rank
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Correlation coefficient
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If the correlation we see is not significant, then we can’t really have much faith in our results; they could simply be down to chance
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e.g. A biologist is investigating whether there is a significant correlation between height and weight for a group of 10 people.
- Describe the correlation between height and weight
- Is the correlation significant at the 0.05 level? What could the biologist conclude from their results?
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statistical significance
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Statistical significance helps us determine whether a result is likely due to chance or to some other factor of interest - allows us to feel confident our result is real.
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Unpaired v Paired t-Test
Unpaired t-Test
An unpaired t-test (also known as an independent t-test) is a statistical procedure that compares the averages/means of two independent or unrelated groups to determine if there is a significant difference between the two.
Paired t-Test
A paired t-test (also known as a dependent or correlated t-test) is a statistical test that compares the averages/means and standard deviations of two related groups to determine if there is a significant difference between the two groups.
The groups can be related by being the same group of people, the same item, or being subjected to the same conditions.
Paired t-tests are considered more powerful than unpaired t-tests because using the same participants or item eliminates variation between the samples that could be caused by anything other than what’s being tested.
Unpaired v Paired t-Test
• A paired t-test is designed to compare the means of the same group or item under two separate scenarios. An unpaired t-test compares the means of two independent or unrelated groups.
• In an unpaired t-test, the variance between groups is assumed to be equal. In a paired t-test, the variance is not assumed to be equal.
the 5 significance level
This means there is a 5% or lower probability that our results are due to chance then we say our results are significant
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