2 Topic 1.1: Statistics1.1.1: State that error bars are a graphical representation of the variability of data1.1.2: Calculate the mean and standard deviation of a set of values1.1.3: State that the term standard deviation is used to summarize the spread of values around the mean, and that 68% of values fall within on standard deviation of the mean1.1.4: Explain how the standard deviation is useful for comparing the means and spread of data between two or more samples1.1.5: Deduce the significance of the difference between two sets of data using calculated values for t and the appropriate tables1.1.6: Explain that the existence of a correlation does not establish that there is a casual relationship between variables
3 Why do we use Stats in Biology? Steps to Scientific MethodAsk a Question/ObservationDo Background ResearchConstruct a HypothesisTest Your Hypothesis by Doing an ExperimentAnalyze Your Data and Draw a ConclusionCommunicate Your Results
4 Why do we use Stats in Biology? In science, observations result in Numbers!!What is the height of bean plants growing in sunlight compared to the height of bean plants growing bean plants growing in shade?Write Specific Question!!!Set up ExperimentSample!!
5 Why do we use Stats in Biology? Statistics is a branch of mathematics which allows us to sample small portions from habitats, communities, or biological populations, and draw conclusions about the larger populationsMeasures the differences and relationships between sets of dataUsing example from previous page—how would be determine if there is a difference between the control and variable?
6 Statistical analysis Mean: is the average of data points Range: range is the measure of the spread of dataStandard Deviation: is a measure of how the individual observation of data set are dispersed or spread out around the mean
7 Mean Problems1. Sandra is playing in a tennis doubles tournament. The rules say that the average age of the pair of players on each side must be ten years old or younger. Sandra is eight years old. Her partner must be _____ years old or younger.2. Juan has played in four baseball games this season. He struck out an average of twice per game. In the last three games, he didn’t strike out at all. How many times did he strike out in the first game of the season? 3. Jerome took five spelling tests in the last marking period. He scored 100% in all but one. His lowest score was 80%. What was his mean score for the spelling tests in the last marking period?4. Lucy bought seven pens. Four of the pens cost a dollar each. Three of the pens cost 30 cents each. What was the average cost of each pen?
8 Range ProblemsCheryl took 7 math tests in one marking period. What is the range of her test scores? 89, 73, 84, 91, 87, 77, 94The Jaeger family drove through 6 midwestern states on their summer vacation. Gasoline prices varied from state to state. What is the range of gasoline prices? $1.79, $1.61, $1.96, $2.09, $1.84, $1.75A marathon race was completed by 5 participants. What is the range of times given in hours below? 2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr
9 Error Bars Are a graphical representation of the variability of data Can be used to show either the range of data or the standard deviation of a graphThe value of the standard deviation above the mean is shown extending above the top bar of the histogram and the same standard deviation below the top of each bar of the histogram
10 Standard DeviationWe will use standard deviation to summarize the spread of values around the mean and to compare the means and spread of data between two or more sampleIn a normal distribution, about 68% of all values lie within ±1 standard deviation of the meanThis rises to about 95% for ±2 standard deviation from the mean
11 Standard Deviation Use Bean plant experiment as an example! If we plot all the data points of the 100 plants we should get a bell shaped curveY-axis- number of bean plantsX-axis-heights
12 Standard Deviation Most sets of numbers are not this perfect!!! Sometimes the bell-shape is very flatThis indicates that the data is spread out widely from the meanSometimes the bell shape is very tall and narrowThis indicates the data is very close to the mean and not spread out
13 Standard DeviationThe standard deviation tells us how tightly the data points are clustered togetherWhen standard deviation is small—data points are clustered very closeWhen standard deviation is large—data points are spread out
14 Standard Deviation Why is this important? Tell how many extremes are in the data
15 Standard DeviationHeight of bean plants in the sunlight in centimeters ±0.1 cmHeight of bean plants in the shade in centimeters ±0.1 cm12413112060153160982121231171426515615512813914595Total: 1300Remember in statistics we make references about a whole population based on just a sample of the population
16 Standard Deviation First, determine the mean for each set of data Height of bean plants in the sunlight in centimeters ±0.1 cmHei128ght of bean plants in the s1hade in centimeters ±0.1 cm12413112060153160982121231171426515615512813914595Total: 1300First, determine the mean for each set of dataSecond, determine the range for each set of dataLook at the two sets of data is there variation among the two sets of data
17 Standard DeviationHow can we mathematically quantify the variation that we observed?Standard DeviationUse Graphing Calculator: Code: 4242PUse website : deviation.phpUse excel:stdexcel.htm
18 Standard Deviation What does this number mean? High Standard deviation—indicates a very wide spread of data around the mean.This would make us question the experimental designExperimental error
19 Standard Deviation Problem Residents of upstate New York are accustomed to large amounts of snow with snowfalls often exceeding 6 inches in one day. In one city, such snowfalls were recorded for two seasons and are as follows (in inches): , 9.5, 14.1, 11.5, 7.0, 8.4, 9.0, 6.7, 21.5, 7.7, 6.8, 6.1, 8.5, 14.4, 6.1, 8.0, 9.2, What are the mean and the population standard deviation for this data, to the nearest hundredth?
20 Standard Deviation Problem Neesha's scores in Chemistry this semester were rather inconsistent: 100, 85, 55, 95, 75, 100. For this population, how many scores are within one standard deviation of the mean?
21 Standard Deviation Problem The number of children of each of the first 41 United States presidents is given in the accompanying table. For this population, determine the mean and the standard deviation to the nearest tenth. How many of these presidents fall within one standard deviation of the mean?
22 T-testAll of these (mean, range, and standard deviation) still does not tell us whether there is a difference between two sets of dataThe t-test compares two sets of data and tells us if there is a significant difference between the two sets of dataLook at Table of t values on Pg 7 in handout
23 T-test p(probability value)-chance alone could produce the difference 0.5, 0.2, 0.1, 0.05, 0.01, 0.001Most science uses 0.05 column.This means there is a 5% chance that the difference between the two numbers are by chance alone95% chance that the difference between the two numbers are because of the variable in your experiment. (bean plant-variable would be light)
24 T-test Degrees of Freedom This is the sum of the sample sizes of each of the two groups minus two.T-test: cfm
25 SignificanceNow you have the p-value, the t-test value, and the df. What does all these numbers mean?You are going to compare the p-value with your t- test resultsIf:T-test value is greater than P-value—significantT-test value is smaller than P-value—not significant
26 Practice Problems t-test Older AdultsYounger Adults45343822521548272537394151244619552636Mean =S =S2 =A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. Compute the appropriate t- test.
27 Practice Problems t-test A researcher hypothesizes that electrical stimulation of the lateral habenula will result in a decrease in food intake (in this case, chocolate chips) in rats. Rats undergo stereotaxic surgery and an electrode is implanted in the right lateral habenula. Following a ten day recovery period, rats (kept at 80 percent body weight) are tested for the number of chocolate chips consumed during a 10 minute period of time both with and without electrical stimulation. The testing conditions are counter balanced. Compute the appropriate t-test for the data provided below.StimulationNo Stimulation128734111465910Mean =S =S2 =
28 Practice Problems t-test Control over PlantNo Control over Plant2335122162615241817537223416103814411927832Mean =S =S2 =Researchers want to examine the effect of perceived control on health complaints of geriatric patients in a long- term care facility. Thirty patients are randomly selected to participate in the study. Half are given a plant to care for and half are given a plant but the care is conducted by the staff. Number of health complaints are recorded for each patient over the following seven days. Compute the appropriate t- test for the data provided below.
29 Correlation does not mean causation The correlation is one of the most common and most useful statistics. A correlation is a single number that describes the degree of relationship between two variables.
30 Correlation does not mean causation We use the symbol r to stand for the correlation.r will always be between -1.0 and +1.0.if the correlation is negative, we have a negative relationshipif it's positive, the relationship is positive.
31 Correlation does not mean causation Correlation is not a causeTo find the cause of the observed correlation requires experimental evidenceAssess the statements (handout) to determine whether you think they represent a correlation or if there is a causal connection