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Statistical Analysis

Statistical Analysis. Biology 1.0. All DP biology students should be able to:. Perform the basic algebraic functions (addition, subtraction, multiplication and division) Recognise basic geometric shapes

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Statistical Analysis

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  1. Statistical Analysis Biology 1.0

  2. All DP biology students should be able to: • Perform the basic algebraic functions (addition, subtraction, multiplication and division) • Recognise basic geometric shapes • Carry out simple calculations with a biological context involving decimals, fractions, percentages, ratios, approximations, reciprocals and scaling • Use standard notation e.g. 3.6 x 106 • Use direct and inverse proportion • Represent and interpret frequency data in the form of bar charts, column graphs and histograms, and interpret pie charts and nomograms • Determine the mode and median of a set of data • Plot and interpret graphs (with suitable scales and axes) involving two variable that show linear or non-linear relationships • Plot and interpret scatter graphs to identify a correlation between two variables, and appreciate that the existence of a correlation does not establish a causal relationship • Demonstrate sufficient knowledge of probability to understand how Mendalian ratios arise and to calculate such ratios using a Punnett grid • Make approximations of numerical expressions • Recognise and use the relationships between length, surface area and volume

  3. 1.1.1 State that error bars are a graphical representation of variability of data • If we plot the mean with the range this shows the spread of the data around the mean. • The graph shows how variable the data (measurements) are in comparison to the mean where: • a wide spread the mean is unreliable. • a narrow spread the mean is more reliable. Example of the mean with the full data range: Comparison of the shell length of two samples of gastropod from different locations. Marine population: mean= 30.7, Range = 23-43       Brackish population: mean = 41.3, Range = 32-51

  4. The rules for using error bars: Rule 1: Always state on the graph which type of error bar is being used.  • Mean + Range • Mean +/- SD (standard deviation) • Mean +/- SE (standard error)  Rule 2: Always state the number (n) of the sample size in the legend of the graph. • if there where 20 repeats/measurements then we add n=20 Rule 3: Error bars and statistics should only be shown for independently repeated experiments, and never for replicates. • If we wanted to find the mean height of sycamore trees then you would measure the height of different trees (independently repeated experiments) not the same tree many times (replicates). 

  5. Calculating the mean & standard deviation • Data collected from an experiment falls into three categories: • The arithmetic mean or average is a measure of the central tendency (middle value) of the data. • The sum of all values in data divided by the total frequency of data:

  6. Calculating the mean & standard deviation Standard deviation: • A measurement of the spread of data above and below the mean. • 68% of data fall within ± 1 standard deviation of the mean

  7. Calculating the standard deviation YOU MUST MEMORISE THIS EQUATION! • Yes – you can use a calculator! • Calculators are allowed for Papers 2 and 3 but not Paper 1 σ = standard deviation of the sample Σ = summation of X – = difference between x value and mean N = number of values

  8. Calculating the standard deviation Find the STDEV for both these data sets: Shell length (mm) for two populations of a mollusc species • Find the mean and number of samples • Calculate X - for all sets of values • Find (X - )2 for all values • Σ (X - )2 See excel spreadsheet to see calculations

  9. What does the standard deviation mean? Used to summarise the spread of values around the mean • 68% of the values fall within 1 standard deviation (±1SD) • 95% of the values fall with 2 standard deviation (±2SD) • A sample with a small standard deviation suggests that the set of data has a narrow variation (less error/ less uncertainty) • A sample with a high standard deviation suggests that the set of data has a wide variation (more error/ more uncertainty)

  10. What does the standard deviation mean? • When presenting data as a graph, you can show: • Mean +/- Range • Mean  +/- Standard deviation • These graphs will allow you to evaluate the reliability of your data Graph B: mean +/- SD • The graph show an overlap of the SD bar. • If two SD error bars overlap you can conclude that the difference is not statistically significant. • Sample A and Sample B are not significantly different. Graph A: mean +/- SD • BUT If the two SD bars do not overlap then we CANNOT conclude that they are statistically different.

  11. The t-test This is a how we can test the reliability on whether 2 sets of data are statistically different. • Takes into account: • Means • Amount of overlap • This is so we can be certain whether the two sets of data are significantly different or not. • With the t-test, we always start by stating the null hypothesis H0 = “there is no significant difference” • If the t-test tells us to accept H0, then there is no significant difference between the means of the 2 data sets • If the t-test tells us to reject H0, then there is a significant difference between the means of the 2 data sets

  12. The t-test tells us the probability of two data sets being the same • If P = 1, the 2 sets of data are exactly the same. • If P = 0, the 2 sets of data are not at all the same • P ≤0.05, gives us a 95% confidence that the data has a significant difference.

  13. The t-test in excel • We can calculate the t-test in excel (easy for lab reports) See excel spreadsheet to see t-test • For the examples you'll use in biology: • Tails is always 2 , • Type can be: • Paired • Two samples, equal variance • Two samples, unequal variance

  14. What do the results mean? • Using excel, we found that P = 0.003 (2-tailed test) • P< 0.05, therefore we reject the null hypothesis... H0 = “there is no significant difference” SO: ‘There is a significant difference between the height of shells in sample A and sample B' In an exam, you will be provided with a t – value which you need to compare to the critical value on the t-test table: • Significance is the confidence (P) • df is the degrees of freedom (total sample size minus 2) • Use these values to get a critical value

  15. Using the t-test in the exam • H0 = there is no significant difference in the wingspans of these 2 hummingbird species. • Calculate the degrees of freedom • df = (n1 + n2) -2 • = (12 + 13) -2 = 23 • P = 0.05 (you will be given this value) • cf = 1.174 A researcher measured the wing spans of 12 red-throat and 13 broad-billed hummingbirds.

  16. What do the results mean? • If t=2.15 (as per a complicated equation you don’t need to do, as you will be provided with this value) • And the critical value (CV) = 1.714 If t < CV; then accept H0 If t > CV; then reject H0 2.15 > 1.714 t > CV So we REJECT the null hypothesis. “There is a significant difference between red-throat and broadbill hummingbirds in terms of wingspan”

  17. Correlations • Correlations can suggest relationships between sets of data

  18. Correlations • It is important to remember that correlations do not prove causality. • If a correlation exists, further research is needed to determine if the relationship is causal • Temperature vs enzyme activity • Concentration vs rate of diffusion • CO2 concentration vs rate of photosynthesis Some causal relationships

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