Bio 112 Lecture Notes; Scientific Method

Transcription

1 Bio Lecture ote; Scientific Method What Scientit Do: Scientit collect data and develop theorie, model, and law about how nature work. Science earche for natural caue to eplain natural phenomenon Purpoe of cience to determine caue and effect to gain inight into natural event Science doe not include abolute Science provide tentative eplanation to eplain natural phenomenon Fundamental bai of cience: The Principal of Uncertaint Science cannot prove anthing, nor i it a earch for the truth. Science develop tentative anwer for guee (hpothee) baed on evidence Theor - when upporting evidence i ver trong! Science I a Search for Order in ature Identif a problem Find out what i known about the problem Ak a quetion to be invetigated Gather data through eperiment Propoe a cientific hpothei Make tetable prediction Keep teting and making obervation Accept or reject the hpothei Scientific theor: well-teted and widel accepted hpothei Characteritic of Science and Scientit o Curioit o Skepticim o Reproducibilit o Peer review o Openne to new idea o Critical thinking o Creativit Page

2 Scientific Method:. Obervation The awarene of a natural event or natural phenomenon directl or indirectl b mean of our ene.. Quetion Our initial attempt to eplain an oberved phenomenon 3. Hpothei: A gue potulating an anwer to the quetion. Thi eentiall our initial quetion rephraed a a tatement. Mut be relevant and tetable 4. Eperiment Additional obervation gathered to tet the hpothei. Eperimental deign: pecificall tet validit of hpthei 5. Concluion/Evaluation I hpothei validated or rejected? Eperimental Difficultie Bia Eperimental Error Sample Size Controlled Eperiment Two ide-b-ide eperiment. Control: o change. Treatment: Change one eperimental variable onl 5. Evaluation Concluion Statitical Approach to Science How doe cience develop theorie? A theor i a hpothei which i olidl upported b evidence. Support for hpothee come from tatitic Uing a ample, the mean of an eperimental population can be determined along with other tatitical parameter The abolute true mean (denoted a ) cannot be determined. Intead we etimate a mean () for our ample population. We can etimate a confidence interval in which the true mean of the population lie at a given level of probabilit Thi honor the Uncertaint Principal in Science Page

3 Statitical Method There i a high degree of variabilit in living thing: cell, organim, population Sample a portion of a population mut be ufficientl large, but obtained randoml Random election reduce bia Frequenc table and hitogram We can tabulate and graph data to obtain a frequenc table and a hitogram, repectivel. ormal Ditribution: The hpothetical frequenc of outcome plotted againt the range of poible event. Thi bell-haped frequenc ditribution i o prevalent in nature that it i conidered normal. The mathematical characterization of uch a ditribution form the foundation of ome tatitical anale. Page 3

4 Elementar Statitic otation and Smbol: i igma (Greek capital S) Thi mean to add, or um, all obervation of variable i (inde variable, or counter) The inde variable i ued to identif an obervation (e.g. tet ubject number, meaurement number 8, etc.) i the total number of obervation i : i the value of obervation number i (e.g. the actual height of tet ubject, the actual temperature meaured for obervation 8). : the mean; a um of value divided b number of obervation i the hpothetical mean for ALL population. For eample, we cannot meaure the height of ever individual peron on earth, but we know there a univeral mean. repreent the theoretical tandard deviation for ALL population. ull hpothei; b default, predict no pattern in eperimental obervation Alternate hpothei; b default, upport a ignificant pattern i Graphing Data Conventionall, the variable i alo called the independent variable. When comparing two et of data, the ai repreent the dependent variable. In the eample below, the urviving frog i dependent on the number of paraite. Page 4

5 Page 5 Mean: the average value of obervation; determined b adding up all value then dividing them b the number of obervation. Thi parameter i limited to decribing the mean of onl our oberved value. Variance: i an etimate of the range of value: Standard deviation i another etimate of the range of value in relation to the mean. The quare root of the variance equal one tandard deviation (ditance) from the mean: i i i i

6 Confidence Interval: probabilit that a pread of value will lie within a pecific part of the ditribution range (00% of obervation hould fall inide the bell hape). Thi alo provide our level of confidence for teting hpothee. ote that 95% of data fall within the non-haded part of the curve and ~ tandard deviation, while the haded tail contain the remaining 5%. t-ditribution: Allow u to compare two population uing the relative ditance between their repective mean. CI X X t n n Critical Value: Thi value i derived from a t-ditrubution table (ee page 9) and can be viewed a the ditance (in tandard deviation) among the population mean being compared. t df t- Statitic value: Thi value i calculated uing eperimental data and compared to the Critical Value. When the t-value i greater than the critical value, a ignificant difference eit between two group. p-value: The probabilit of arriving at an incorrect concluion baed on the data being analzed. Page 6

7 Appling Statitic: The Student t-tet We can compare population (or an data et) b plotting their repective frequenc ditribution a in the following eample. otice how the plotted ditribution in Eample are o far apart that one could eail conclude that there a ignificant difference. One could not eail conclude that there a difference among the group in Eample. Unfortunatel, we can t bae our concluion on impl viewing the data. Thi i where tatitical anale become a valuable tool Count Count TAXO Pelv Porph Eample - A clear, ignificant difference 5 0 TEMP Count Count Eample - A ubtle difference Page 7

8 There are a great man tatitical procedure ued to analze data. Which method are applied depend on the nature of the data and the hpothei we re teting. Remember that in the cientific method, hpothee mut be falifiable. Statitical anale provide a wa to mathematicall determine whether we can reject (or fail to reject) hpothee with a certain level of confidence. The Student t-tet i one method for comparing two group or the equalit of two mean. B convention, the ull Hpothei () i that there no ignificant difference between the mean (=). The Alternate Hpothei () i that a ignificant difference doe eit ( ). Pleae note that we can tet our hpothee no matter what we predict the outcome will be. If we believe there i a ignificant difference among group, we impl hope our data will allow u to reject the ull Hpothei. We ll chooe a level of confidence then calculate the probabilit (p-value) that we ll erroneoul reject the ull Hpothei. The Student t-tet wa developed b William S. Goet ( ), an emploee of the Guinne Brewing Compan in Ireland. Becaue Guinne did not allow publication of it reearch, Goet publihed under the peudonm Student. Comparing more than two mean T-tet work when we want to determine the equalit of two mean. What if we have 3 or more ample population to compare? There are additional tatitical anale performed on more than two population, but the depend on the tpe of data and on the quetion we re aking. Tpicall, thee reult in what cientit call model. Tpe of Data Categorical- qualitative data that fall into ditinct categorie. Further divided into two tpe: ominal- decriptive (color, gender) Ordinal- where order i important (mature, immature) umerical- quantitative, meaured numerical obervation, alo ubdivided into two tpe Dicrete- onl certain value are poible (number of eed, offpring etc.) Continuou- an value within an interval i poible and limited onl b the reolution of the meauring device (height, weight, concentration, temperature) Page 8

9 DVI The General Linear Model Ued for comparing multiple population or data et Anali of variance- like a t-tet on 3 or more group 9 6 TEMP 3 0 HC HCS LP MP SITE Correlation- tet whether two variable are correlated (dipla a linear relationhip) Regreion anali- once correlation i etablihed, determine how well a dependent variable (- ai) predict the value of an independent variable (-ai) DVI v Leaf Chloropll R² = Chlorophll g/cm Page 9