Needle Length Study Use diata posted on D2L& previous 2 pages of this lab handout for this competition esample study Nendles were collected from3 plors: frees grown in low density, medium density, and high density (what could density be a proxy for ecologically?Three needleas were collected from each tree in each plot D) Research hypothesis 2) Statistical hypothesis (write with mathematical symbols instead of words): 3) Factor of interest (ecological factor): 4) Treatment Levels: 5) Dependent variable(s) (Y): 6) Independent variable(s) (X): 7) Sample size (n) (per treatment level) with units: 8) What are multiple samples from the same individual called? 9) Think about the previous question. What implications would it have for cakculating averages? 10) Averages with measure of variation/error: 1) Type of statistical test (include parameters chosen) and why: 12) p-value(s?): 13) Statistical hypothesis conclusion and why? 14) Research hypothesis conclusion and why? 15) Potential confounding factors (sources of biological and experimental error): 12 Chapter 1 Describing a Population METHOD B: NEEDLE LENGTH IN CONIFERS Outdoor/indoor activityl Research Question How do pine needles vary in length, within and among individual trees? Preparation Locate several pine trees of the same species. Needles of other conifers may be used if they have needles long enough to be measured with a mm ruler. If students cannot collect needles themselves, pine branches can be collected elsewhere, or “pine straw” can be obtained from garden supply firms. Laboratory teams can be larger if greater effort is required to collect and measure 80 needles. Materials (per laboratory team) Metric ruler, marked in mm Procedure Recognize that each needle is a plant organ, developing according to a genetic program influenced by local conditions. A pine needle performs the critically important job of photosynthesis, producing chemical energy for the tree. A needle’s length may affect how well it functions. If the needle is too short, it may lack sufficient photosynthetic tissue to produce an adequate supply of food. On the other hand, needles that are too long may fail to transport luids adequately to the tip, or may accumulate too much ice and break limbs in the winter. Limits on size and shape affecting the performance of a biological trait are called functional constraints, and they help explain why many species’ characteristics remain within predictable ranges. 1. Although needles on the same tree might be expected to conform to a genetically determined size, differences in leaf age, sun or shade, exposure to wind, temperature, or moisture supplied throu sources of variation. Among different trees have conditions. Develop a sampling plan. Your sample size will be 80 needles. If you have access to a grove or row of pine trees, spread out your needle collection to include roughly equal numbers of needles from each of the trees. A sampling plan that includes the same research area is a stratified sample. Decide whether you will pull a needle from a live branch, or pick a fallen needle from the ground. lar branch could influence needle length. Within a tree, we can recognize many a population of trees, the variation is probably even larger because different genes, and probably experience a broader range of environmental 2. number of needles from each tree in your Since pine needles decay slowly, they can be collected long after they the tree. If you collect live needles from the tree, will you always collect from a low branch, or will you try to collect equal numbers of needles from high, mid-height, and low branches? When collecting needles from pines (genus Pinus) you will discover that their needles come in bunches. The brown collar of tissue holding the bunch of needles tugether is actually a dwarf branch, called a fascicle. The number of needles in a bunch is fairly consistent, and is useful for identification. For instance, the Eastern White Pine (Pinus strobus) typically has five needles per fascicle, while Red Pine (Pinus resinosa) has two. Chapter 1 Describing a Population 13 Make a decision about which needle in the bunch you will measure. The longest one? A andomly selected one? What will you do if you encounter a broken needle? Whatever your method, it would be best to measure only one needle per bunch, so that your data are not dlustered into subgroups. Pull the needles apart carefully, so as not to introduce error by breaking le according to your predetermined sampling plan. If the population of pines on campus is not that large, collect all your needles from the same tree. Recognize that this collection is not a population in the biological sense, since only individual produced all the needles. However, your collection is a population in the statistioa sense, because you are measuring a sample of a much larger number of groups can sample different trees so that you can compare yor one needles. Different lab 3. Measure lengths and record observations. Measure each of the 80 needles in your sample. How accurate is your ruler? Record needle lengths in mm on the data pages at the end of this chapter Follow directions on the calculation page to produce a histogram of needle lengths and to calculate standard deviation, standard error, and confidence limits for this population a mean, Interpret your data. What does the histogram show about the variation of needle lengths in this species? Answer the Questions for Discussion that follow the calculation pages. Think about the on evergreen needles, and try to explain the distribution of sizes in biological terms. Check calculated mean fall within the 95% confidence limits you calculated for your own mean? If not, how do you interpret the difference between the two estimates? If two groups sampled from the same tree, then significant differences in your calculated means might result from sampling bias, measurement error, or calculation mistakes. If two lab groups sampled different trees, then the your accuracy. Compare your results with those of another lab group. Does the other group’s data may reflect real biological differences between the two trees. CALCULATIONS (METHOD A OR B) Enter your 80 measurements (x) in the second column of the table, recording 20 measurements per page on each of the next four pages. You may wish to split up this task, with each member of your team completing a page. 1. 2. Sum the measured values (seed weight or needle length) for each page, and then complete calculation of the mean (%) in the calculation box at the end of the tables by adding totals from all four pages and dividing by the sample size (n-80) Subtract the mean from each of the 80 measurements to obtain the deviation above or below the 3. average. (Deviation from mean for sample i d) 4. Square each deviation (d2) 5. Add up all the squared deviations on each page, then sum the totals for the four pages to compute the sum of squared deviations (Ed?). Divide the sum of squared deviations by (sample size -1) to calculate the sample variance (s) Take the square root of the variance to calculate the standard deviation (s). 6. 7. 160 166 160 169 166 160 166 166 166 162 164 163 166 166 160 166 164 163 10 168 160 162 149 148 12 12 13 166 13 164 162 168 14 15 15 15 16 16 16 150 156 156 160.5 Average Standard Deviation Maximum value Minimum Value Confidence Interval