FOLLOW 0B – Statistics for IB Biology PP



IB Statistics Notes????????Objectives of this Unit:Types of Data, Types of Graphs, Applications and Statistics to match your dataBar Graphs, Line Graph, Scatter Plot, Histogram, Pie ChartMean, S.D., Regression, Chi Square Analysis,State that error bars are a graphical representation of the variability of dataRange and standard deviation show the variability/spread in the dataCalculate the mean and standard deviation of a set of valuesUsing Excel formulasGiven a mean and S.D. state the range for different parametersState the term standard deviation is used to summarize the spread of values around the mean68% of all data +/- 1 standard deviation, 95% within 2 SDExplain how S.D. is useful for comparing the means and spread of data between two or more samplesGreater S.D. shows greater variability of dataThis can be used to inter reliability in methods or results BUT in Biology we also expect variabilityDeduce the significance of the difference between two sets of data using calculated values for t and tablesUsing t value and t table and critical valuesDirectly calculating P values using excel in lab reportsDifference between P and TExplain that correlation does not establish that there is a causal relationship between two variablesProper Lab FormatDesigning Lab ProcessApplications of Statistics in relation to Biology, diversity, variability, living systems etc.FOLLOW 0B – Statistics for IB Biology PPWhat are Statistics?Statistics are numbers used to: ________________ and ________________________________about DATAThese are called descriptive (or “univariate”) and inferential (or “analytical”) statistics, respectively.Variables:A variable is anything we can ______________________________________Three types:___________________: values span an uninterrupted range (e.g. height)___________________: only certain fixed values are possible (e.g. counts)___________________Categorical: values are qualitatively assigned (e.g. low/med/hi)Dependence in variables: “Dependent variables depend on independent ones”___________________ variable – variable you are changing___________________ variable – variable you measure to see result___________________ variables – variables that can also impact the dependent variable that you identify as needed to not vary*** Experimental Control – NOT the same as controlled variablesGraphs:Outlier - An?outlier?is an ________________________________________________________ in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal. Before abnormal observations can be singled out, ___________________________________________________________________________________LineScatterHistogramBarAppropriate for data when:Important Features IncludeSample and other notesThe Mean:Most important measure of “central tendency”Variance:Most important measure of “dispersion”The Friendly Histogram:Histograms represent the distribution of dataThey allow you to visualize the mean, median, mode, variance, and skew at once!Normal Distribution: Occurs frequently in natureEspecially for measures that are based on sums, such as:sample meansbody weight“error”Many statistics are based on the assumption of normalityYou must make sure your data are normal, or try something else!40538403429000Properties of a Normal Distribution:Symmetric Mean = Median = ModeTheoretical percentiles can be computed exactly~68% of data are within 1 standard deviation of the mean95% within 2 standard deviations>99% within 3 s.d.Example Question: If the average tail length of a newt is 2.34cm with a standard deviation of 0.12cm, what is the range of tail length that would include 95% of the population?Flipped Notes From the VideoIn General, what are the two scenario possibilities when comparing two groups?Define the following terms: Mean, Median, Range, NumberWhat is Standard Deviation? What does it tell us, what is the formula, when is it useful?What does a t-test represent?What does a t-test tell us? What is it’s formulaExplain what a Null Hypothesis is and when it should be rejected or accepted170370538163500Summarize the steps to drawing a conclusion from a t-testTHE VIDEO. DO NOT DO THE EXAMPLE PROBLEM4727144-18986500Inferential Statistics – Part 2Inference: the process by which we _______________________ about an unknown based on _________________ or prior experience. In statistics: make conclusions about a population based on _________________ _________________________________Important: Your sample _______________________________ you’re interested in, otherwise your conclusions will be misleading! Statistical Hypothesis:Should be related to a scientific hypothesis!Very often presented in pairs:Null Hypothesis (H0): the “boring” hypothesis of “__________________________”Alternative Hypothesis (HA): the interesting hypothesis of “_____________________________”Statistical tests attempt to (mathematically) _____________________________Significance: Your sample will never match H0 perfectly, _____________________________________________The question is whether your sample is ___________________________ from the expectation under H0 to be considered ___________________________________________________________________________________, then you reject H0.P-Value:The p-value of a test is the probability of ________________________________________________, assuming H0 is trueIf p is very small, it is _________________ that H0 is true(in other words, if H0 were true, your observed sample would be unlikely)How small does p have to be?_____________ is a common cutoffIf p<0.05, then there is less than 5% chance that you would observe your sample if the null hypothesis was true. “Proof” in Statistics:Failing to reject (i.e. “accepting”) H0 __________________________ that H0 is true!And accepting HA _____________________ that HA is true either!Why?Statistical inference tries to draw conclusions about the population _____________________________By chance, the ______________________________Example: if you always accept H0 at p=0.05, then 1 in 20 times you will be wrong!Instead we say that the data supports or rejects hypothesis, and my suggestion is that you Never use the word prove in a LabWhy is this biology?Measurement Uncertainty versus Variance (standard deviation)CUT AND PASTE THIS INFORMATION BELOW INTO AN EXCEL SPREADSHEET. Table 1: Raw measurements of bill length in A. colubris and C.latirostris nA. Columbris bill length (mm) (+/-0.1mm)C. latirostris bill length (mm) (+/-0.1mm)113.017.0214.018.0315.018.0415.018.0515.019.0616.019.0716.019.0818.020.0918.020.01019.020.0You MUST be able to use Excel/Sheets proficiently. You will need to be able to graph properly and to calculate mean, standard deviation, t-tests. Make notes here if you need to help you remember how it is done. (We will learn several other stat methods when we need them in upcoming units of study)2657475952500The overlap of a set of error bars gives a clue as to the significance of the difference between two sets of data. left42481500Null Hypothesis: There is NO Significant DifferenceThis is the ‘default’ hypothesis that we always test. In our conclusion, we either accept the null hypothesis or reject it.A t-test can be used to test whether the difference between two means is significant. If we accept H0, then the means are ______________________________ If we reject H0, then the means are __________________________. Remember:We are never “_______________”to get a difference. We design carefully-controlled experiments and then analyze the results using statistical analysis. What is DF?What is T-value?What is P-Value?59594751524000*Do not confuse P with TIn Excel TTEST (____________,_______________,_________________,_________________)CUT AND PASTE THIS INFORMATION BELOW INTO AN EXCEL SPREADSHEET.Table 2: Correlation between bill length and body weight in A. colubris bill length (mm) (+/-0.1mm)13.014.015.015.015.016.016.018.018.019.0weight (g) (+/-0.05g)2.72.82.82.92.92.93.03.13.43.6Make some Notes on how to graph and analyse thisCorrelation and Causation:Correlations can suggest a relationship Correlation does NOT suggest causationR2 is a goodness-of-fit measure for linear regression models. It indicates the percentage of the variance in the dependant variable that the independent variables explain. It’s Lab Time!Chips Ahoy Practice Lab – this is optional if you need extra practiceIA Caffeine Lab – Submit to Turn it In Design Lab – Done in class in groups and presented orally ................
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