Sally Bui's Biology HL Blog: August 2012

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7. Give an example to explain how correlation does not indicate or prove causation. Very infants develop the symptoms of autism shortly after the normal time in childhood when the MMR inoculation is administered. Some parents of these autistic children came to blame the vaccination for the child’s condition. This confusion lasted for several years and the numbers of children received vaccination felt to dangerously low levels. Fortunately, detailed studies then was able to convince the majority of parents that MMR inoculation and the onset of autism were not causally linked. Therefore, even if we have applied statistical tests that indicate the possibility of a correlation, we cannot then assert that one event is the cause of the other.

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6. Explain what the T-test is, why it is useful and when you would use it. T-test provides a way of measuring the overlap between two sets of data; hence using T-test, you are able to tell how significant the difference between two data sets. For instance, a small value of t indicates large overlap; hence the difference between two data sets are highly unlikely to be significant. The t-test is normally applied to sample sizes of between 5 and 30 of normally distributed data.

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5. Show a picture and explain what 1 and 2 standard deviations from the mean are and what this means for normally distributed data in terms of how many of the values lie in this range.

Standard deviations can be used to decide whether the differences between two related means are significant or not. If standard deviations are much larger than the difference between the means, then the differences in the means are highly unlikely to be significant. On the other hand, when standard deviations are much smaller than the differences between the means, then the differences between the means is almost certainly significant.

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4. Explain what normally distributed data is and compare it to skewed or unequally distributed data. Give an image or two to help you explain. Normally distributed data is the data values that group symmetrically around a central value, when the data is plotted into a curve. Here, as you can see, in the normal distribution curve, the mode, median and mean coincide.

Whereas, in the skewed or unequally distribution curve, values reduce in frequency more rapidly on side of the most frequently obtained value than the other. Hence, the measurement of inequality of the data is the difference between the mean and mode.

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3. What does it mean if data has a small standard deviation? If the data has a small standard deviation, this indicates that the data is clustered closely around the mean value.

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2. What is the measure of how much readings in a sample vary from the mean called? How do you calculate it? Why is it useful? The measure of how much readings in a sample vary from the mean is called standard deviation. In order to calculate standard deviation, you need the equation:

Or you can follow these steps: 1. Calculate the mean (x) 2. Measure the deviations (x-x) 3. Square the deviations (x-x)2 4. Add the squared deviations (x-x)2 5. Divide by the number of samples (n) Standard deviation is useful because it tells us how spread out are the readings; hence, this will give you a better picture of the data than just the mean alone (i.e. by using standard deviation we have a ‘standard’ way of knowing which data is normal and which is not).

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1. What is the point of error bars? Why is this useful? Error bar represents the range of values obtained at each reading from the highest to the lowest. This is useful as you are able to see how variable or consistent a particular result is.