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DV ( y-axis ) of the relation /association between measure : average r2 . of y value is function of a amount of variance between - ( x-axis ) IV and generates regression line I " y= ab ✗ p= ← i ' ' DV accounts for ' - how well a i. e- , linear ' Allows you to make predictions affect y ? ✗ Alternative hypothesis ( Ha) : , distribution of Either A associates with B ( positive association ) null hypothesis ( Ho ) Chi squared ( x2 ) goodness of fit test A does or , : N exponential regression logistic regression * cannot : e. r use for non linear ' regressions - or causality association is likely e. not associate with any association is tests if categorical variables fall within HA sample data do not follow the expected : N species A and species B statistically significant association between variables i. no example . This does not determine correlation . statistically significant association between variables i. : : : . tests if a relationship between categorical variables exist Ecology example significant association between Ho : sample - . of the nature of a relationship between continuous variables squared ( x2) test for independence \ Genetics I variability of y is explained by variability in ✗ other 11% of variance is explained by other factors understanding How does \ . r 89% of regression Allows an i r2 = 0.89 ex : P . - O Iv DV or the variation in the data - • Chi fits ' regression line ' ( at bx) - - 2 variables It e- a non - random species are dependent B ( negative association ) likely due to chance specified distribution sampled population is not representative of entire population distribution expected ( Mendelian ) phenotypic ratios difference between observed and sampling error or difference suggests gene linkage suggests genes data follow the expected distribution unlinked are Bothx-lestscalculatedthesa.me# p - value : probability of obtaining the observed effect \ significance =p data obtained X' 2 - CF XZ CF : : fail to reject null hypothesis we an don't accept Ho calculated ✗ 2 as we , evidence allows us to = probability extreme) results where strength reject or I 12.71 63.66 636.62 2 4.30 9.93 31.60 3 3.18 5.84 12.94 reject null hypothesis at p= 0.01 12.3 ( DF -_ 2) haven't proven affect doesn't exist rather the of the * reject null hypothesis ex: * of obtaining similar ( or more 5% or less likelihood the Ho is correct Ho is true degrees of freedom significance level (a) (number ofgroups-DO.050.010.CI expected expected XZ i. e. Not data expected observed = 0.05 Ho is true dataset if in the not . Since I > 9.93 Assuming in 1% no we effect of studies , can we due would obtain to random error } observed differences or critical values more ( CF) f- test : 2- sample HA : there Ho : no is used to determine significant difference a if there is a significant difference between the between 2 (s )2 + = t CF t , (5) ni Nz 2 = 5- St dev ( is A larger than B) tailed : compares differences in only 1 direction n = sample size two tailed : compares differences - paired related /dependent groups compares : \ assumes : ✓random (is A smaller either direction in - reject null hypothesis : - mean fail to reject null hypothesis : CF ✗ difference due to treatment and not chance or sampling error - one (x,-~ i. e. . or larger than B) ( before + after ) test same group 2x sampling ✓ DV continuous + normally distributed > 20) for ✓ groups are dependent n= ) unpaired : compares unrelated /independent groups \ assumes : ✓random test separate groups ( control us treatment sampling ✓ DV continuous + normally distributed > 15 ) ( or ✓ A- NOVA ( Analysis of variance) : used to determine if there is a significant difference why can't we HA at least : do multiple t tests one group is significantly different Type increases - Ho : no statistically significant difference between F MS between group variance Ms within group variance independent error : the PIO 05 . any groups all random One way error F F crit : fail to reject null hypothesis F F crit : reject null hypothesis there 3 or more groups probability that you incorrectly rejected null hypothesis means - equal is a difference amongst groups ANOVA : \ assumes : Types of ANOVAs - way ANOVA \ Post hoc tests control - Tukey 's Post hoc : - 4 groups : A , what for Type 1 errors ✓random groups differ specifically ( post , so even the B C, D requires comparisons : among B and are , treatment pair only statistically significant difference these groups ✓ groups have equal variance - hoc " = A between A - - - B providing p where two examine ✓ after this an value IV interaction between residuals ( value - mean are considered IVs ) have equal variance sampling if many comparisons are made, the A i. also \ assumes : ✓ DV continuous all possible combinations between groups 6 + compares 3. + groups can compares , : , - - considered IV is one normally distributed ✓ groups are ✓random > 15 ) ( or independent sampling ✓ DV continuous post hoc Post hoc test : used to determine where compares 3. + groups n= to determine which groups differ " error i. e. following a statistically significant ANOVA ) constant rate remains adjusted p value for each treatment pair value 0.89 B - p 0.01 C grouping * C 0.21 B - D 0.04 D 0.11 C - D 0.25 't } only B and C B and D are and significantly different from each other C ( p -0.01 ) and B and D ( p -0.04) - - * the Dunnett 's Post hoc : compares all treatment groups to - ex : equal variance from the rest Two ex : of means groups have - = - if 1 between the ✓ groups are n= * groups Types of t tests statistically significant difference between both groups t groups and St. Dev of two means I control (A) 3 , treatment groups ( B. C D) , more comparisons made, the less statistical power only control group treatmentpairpvalue A - A - A - B 0.03 't C 0 D 0.10 . I 1 only group 13 * differed from control significantly because fewer comparisons, higher statistical power a) how , data within groups examine likely Trials µ . unusually high or low values are identified ? be they can \ point that differs significantly from others making them unusual in dataset data Outlier : 1 outliers | outliers I 2 3 a 8 8 2 b 9 10 8 c 2 4 5 • } compared to other bars • : • in trial , values Terror • outlier ' ✓ very low alters L0BF_ • • b) why are they important ? \ outlier c) how \ mean ( Tor b) error in error in measurement and entry data sampling outliers any time measured in incorrect sample 2 outliers - occur , occur can identify them clearly significant : the it does not mean the ✗ - evidence is not fail to reject we null null \ an error : remeasure ( if possible ) or as we know its an error : remeasure ( if possible ) or remove an do not are \ p mean value your can as removed , clearly justify why ? 0.0s p an effect exists hypothesis is true an look important , but ③ what does it \ mean if it means that . : we \ the reject value p the the \ be may is , and but alternative or it's possible : is false effect size i. e. too small for is size proof there is no you to effect detect too small is variability is too high for hypothesis test to detect didn't work random significant error 10=-0.05 ? strong enough to suggest an effect may exist in the population hypothesis stronger the evidence against the Ho lower the p value , the ✗ it does not mean population important caution against drawing conclusions based on differences that evidence is null in the hypothesis investigation failed be data doing so skews remove , sample ✗ it does not remove analysis without as a comparison strong enough to suggest effect may exist an know its outliers if * is non . do ? we as we - what does it mean if p value the - naturally doing it means that statistical power conditions consider \ do reduces . outliers cannot be removed, * increases within group variation - sample not of target pop - unusual \ natural variation if this . d) what - * St D and increases they caused ? are \ alters the null to replicate need we hypothesis is false and or the lower the probability of and alternative is true i. e. proof of statistically significant results several times before we an effect can have a false positive confidence " s, ✗ it does not relate to the strength of the investigation or its importance , i. e. Ivp value = Ronald Fisher good investigation Fur thering Frost , J . 2020 . Hypothesis Testing Biology for life .com : An intuitive guide for making data driven decisions statistics html Statistics solutions .com - free - resources directory of statistical analyses - - - . Statistics By Jim Publishing