1 Quadrat Sampling Chi-squared TestSkills 4.1 Quadrat Sampling Chi-squared Test Testing for association between two species using the chi-squared test with data obtained by quadrat sampling. 

2 General Set Up To obtain data for the chi-squared test, an ecosystem should be chosen in which __________________________________________________________________________________ Sampling should be based on _________ numbers. In each quadrat the ________ or _________ of the chosen species should be recorded. The collection of raw data through quadrat sampling will be done in Bamfield on the Beach

3 Quadrat sampling 101 The presence of two species within a given environment can be determined using quadrat sampling A quadrat is a rectangular frame of known dimensions that can be used to establish population densities Quadrats are placed inside a defined area in either a random arrangement or according to a design (e.g. belted transect) The number of individuals of a given species is either counted or estimated via percentage coverage The sampling process is repeated many times in order to gain a representative data set

4 Quadrat sampling is not an effective method for counting ________________– it is used for counting plants and sessile animals In each quadrat, the presence or absence of each species is identified This allows for the number of quadrats where both species were present to be compared against the total number of quadrats

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6 Quadrats for Population EstimationsActivity 118 Discuss the questions with your group and share your responses Activity 119 Do this in a group of 4 and compare your answers when you are finished. What did you find?

7 T-test or Chi Square??? χ2 test T-Test____________________________________________________________________________ Used for many applications χ2 test ____________________________________________________________________________ Used in Genetics and Ecology for Biology

8 1. Goodness of Fit - GeneticsThe goodness of fit test is normally used in genetics where the genotypic and phenotypic ratios have already been established for a given test and population. Ie. when the expected outcome has already been established. For example: You want to understand the outcome of an experiment that you set in your field based on the test cross given by Mendel. We will use this later in the year

9 Chi-Squared Tests in EcologyWe will use this now and in Bamfield

10 Define Symbiosis

11 Types of Association Association Description Implication PositiveNegative None

12 The Chi-Squared Test (2)The chi-squared test is used to study differences between data sets. It is only used for _______________ (counts), never for measurements. It is used to ___________________________________ ____________________________ It is not a valid test for small sample sizes (_______) It tests the validity of the null hypothesis: ___________ between groups of data. In ecology, chi-squared tests are used to study ___________________

13 A chi-squared test can be completed by following five simple steps:Identify __________ (null versus alternative) Construct a __________________(observed versus expected) Apply the _______________ formula Determine the _____________________(df) Identify the ____________(should be <0.05) Lets Try It

14 The presence or absence of two species of scallop was recorded in fifty quadrats (1m2) on a rocky sea shore  The following distribution pattern was observed: 6 quadrats = both species  ;  15 quadrats = king scallop only  ;  20 quadrats = queen scallop only  ;  9 quadrats = neither species 

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16 Step 1: Identify hypothesesA chi-squared test seeks to distinguish between two distinct possibilities and hence requires two contrasting hypotheses: Null hypothesis (H0): _________________________________ Alternative hypothesis (H1): _________________________________

17 Step 2: Construct a table of frequenciesA table must be constructed that identifies expected distribution frequencies for each species (for comparison against observed) Expected frequencies are calculated according to the following formula:  Expected frequency = (Row total × Column total) ÷ Grand total

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19 Step 3: Apply the chi-squared formulaThe formula used to calculate a statistical value for the chi-squared test is as follows: Where:  ∑ = Sum  ;  O = Observed frequency  ;  E = Expected frequency These calculations can be broken down for each part of the distribution pattern to make the final summation easier

20 Based on these results the statistical value calculated by the chi-squared test is as follows:𝝌2  =  ( )  =  7.90

21 Step 4: Determine the degree of freedom (df)In order to determine if the chi-squared value is statistically significant a degree of freedom must first be identified The degree of freedom is a mathematical restriction that designates what range of values fall within each significance level  The degree of freedom is calculated from the table of frequencies according to the following formula: df = (m – 1) (n – 1)  Where:  m = number of rows  ;  n = number of columns When the distribution patterns for two species are being compared, the degree of freedom should always be 1

22 Step 5: Identify the p valueThe final step is to apply the value generated to a chi-squared distribution table to determine if results are statistically significant A value is considered significant if there is less than a 5% probability (p < 0.05) the results are attributable to chance

23 When df = 1, a value of greater than 3When df = 1, a value of greater than is required for results to be considered statistically significant (p < 0.05) A value of 7.90 lies above a p value of 0.01, meaning there is less than a 1% probability results are caused by chance Hence, the difference between observed and expected frequencies are statistically significant As the results are statistically significant, _____________ ______________________________________________ Alternate hypothesis (H1): There is a significant difference between observed and expected frequencies Because the two species do not tend to be present in the same area, we can infer there is a negative association between them

24 The Flat Periwinkle (Littorina littoralis)

25 Periwinkles feed on a number of seaweed species

26 Food preference is a form of animal behaviorUsing quadrats, the number of periwinkles associated with each seaweed species was recorded.

27 State your null hypothesis for this investigation (H0)H0: There is no difference between the numbers of periwinkles associated with different species. What is the alternative hypothesis (HA)? HA : There is a real difference between numbers of periwinkles associated with different species.

28 Use the chi-squared test to determine if the observed differences are significant or if they can be attributed to chance alone. Enter the observed values and calculate the chi-squared value

29 Here’s how you do it… The expected value (E) would be the mean number of periwinkles associated with the four seaweed species.

30 Now Complete the Chart…Calculate the degrees of freedom: 4-1 = 3

31 Check your Chi-square table for 3 degrees of freedom.57.4 >> 7.82, 11.34 Is H0 accepted or rejected? There is a significant difference in feeding preferences of periwinkles.