Revision of Basic Concepts PDF

Revision of basic concepts Dr. M Asnong  Learning outcomes At the end of this lecture, students should understand the ff: - Define and some common terminologies used in Experimental design and analysis Dr. M Asnong  Major branches of statistics Ther...

Revision of basic concepts Dr. M Asnong  Learning outcomes At the end of this lecture, students should understand the ff: - Define and some common terminologies used in Experimental design and analysis Dr. M Asnong  Major branches of statistics There are two major branches : 1. Descriptive statistics (deductive statistics)- They are used for organizing and summarizing data in ways that are meaningful and useful. It includes – the construction of graphs, charts, and tables – calculation of various descriptive measures such as means, standard deviations etc. 2. Inferential statistics (Inductive statistics) It consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population. – Involves generalizing from a sample to the population and assessing the reliability of such generalizations.  Some terminologies Population: The entire group (collection) of individuals or objects about which information is desired Sample: is a subsets selected for study from the whole group (the population) An algebraic expression calculated from sample data is termed as statistic while a parameter is obtained or calculated from population data.  Variables: is any characteristic whose value may change (varies) from one individual or object to another If the variable can assume only one value it is called constant. Variables could be classified as Categorical (qualitative) or numerical (quantitative). Dr. M Asnong 5 Categorical (Qualitative) variables They yield non-numerical information or categorical responses; examples – gender, , wood colour, fin types, Species type Categorical variable could be – nominal (they have no natural order of ranking eg gender) or – ordinal (have natural order of ranking eg responses on liker scales). Dr. M Asnong 6 Numeric(quantitative) variables They yield numerical information (or numbers). They can f be: A continuous variable: values form some interval of numbers. A discrete variable: values can be listed. They usually arise when observations are determined by counting, Dr. M Asnong 7  Variable Categorical Numeric Variable Variable Nominal Ordinal Continuous Discrete Dr. M Asnong 8 Variables could also be grouped as: Independent variables Dependent variables Controlled variables Extraneous and confounding variables Dr. M Asnong 9 1. Independent variables: The variables that the experimenter vary over different experimental units It may also be called predictor variable or explanatory variable A continuous independent variable is usually called covariate or regressor whiles categorical independent variable is called a Factor or categorical variable/predictor Dr. M Asnong 10 2. Dependent variable This is the variable expected to change as a result of the experimental manipulation of the independent variable(s) It is the variable measured and analysed to address the objectives of the experiment It is also called response variable, predicted variable, measured variable, explained variable or outcome variable Dr. M Asnong 11  3. Controlled variables A controlled variable is one which the researcher holds constant (controls) during an experiment Lack of awareness of control variables can lead to faulty results or what are called "confounding variables." Dr. M Asnong 12 4. Extraneous and confounding variables An extraneous variable is a variable other than the IV which CAN or MAY have the POTENTIAL to have an effect on the DV, which therefore affects the results of an experiment in an unwanted way. A confounding variable is an extraneous variable that DOES cause a problem because it is empirically related to the independent variable Dr. M Asnong 13 Factor It is a categorical independent variable – variable proposed to affect or predict another (the dependent) variable. Levels The different values of a factor used in the experiment. Each factor has two or more levels. Dr. M Asnong 14  Treatment- The combination of levels from each factor applied to an experimental unit. If an experiment has a single factor, then each treatment would correspond to one of the levels ie the treatment are the levels Dr. M Asnong 15 Example: A study is conducted to investigate the effect of soil type (loamy, sandy, clay) and light intensity (low, high) on germination of Gmelina seeds. What is/are the factors, the levels and treatments? Dr. M Asnong 16 Dr. M Asnong 17 Some important graphs Dr. M Asnong 18  1. Pie chart A chart that indicates relative frequencies by slicing up a circle into distinct sectors. Most effective for summarizing data sets when there are not too many different categories.  2. Bar chart It is a graph of a frequency distribution of categorical or discrete data It displays the distinct values or classes on a horizontal axis and the frequencies (or relative frequencies or percentage) on a vertical axis 3. Histogram Displays the frequency distribution of a particular variable (quantitative data). Observations are grouped into artificial classes or the distinct values (discrete data). Horizontal label-The classes (class marks, class midpoints or class limits) Vertical -frequency (relative frequency, percent)  Boxplot Box plots (also called box-and-whisker plots) provide a succinct summary of the overall distribution for a variable. Mean Outliers  Mean Plot (Error Bar Plot) Categories are display on the horizontal axis and the corresponding quantitative values (the mean) on the vertical axis. Scatter plot 5 min Break Dr. M Asnong 28  Learning outcomes At the end of this lecture, students should understand the ff: - Why we need to design our experiments - The three basic principles of experimentation - Some basic steps in experimentation Dr. M Asnong 29  Prince is a shoe shop manager and he has two locations picked for a possible new shop. He needs to conduct a mini-study to make a decision. Location A is smaller, and he notices that there is a high school two blocks away, some business offices close by, and a car wash next door. Location B is larger and next to a supermarket with some business offices scattered around the area, amidst several vacant plots. If you are hired by Prince, which location would you recommend ? Defend your answer  What is an experiment? Investigators in all fields carry out experiments to obtain answers So what is an experiment? An experiment is a planned inquiry that either answers new questions or hypothesis; confirms or denies previous results. Dr. M Asnong 31  Experimental Unit The physical entity or subject to which the treatment is randomly applied or exposed to Any two experimental units must be capable of receiving different treatments and must be independent of one another – thus bounded or physically defined in such a way that what transpires in one can have no effect on the other. Dr. M Asnong 32 Experimental unit- the plant pot Dr. M Asnong 33  Measurement or Observational units: They are the actual objects on which the response is measured. This may or may not be the same as the experimental unit. Dr. M Asnong 34  An Ichthyologist wants to evaluate the effect of polluted river water on fish lesions. Two aquaria, each with 7 fish are set up. A water treatment (polluted vs. control) are randomly assign to each of the aquaria. After a month, 5 fish from each aquarium are caught and the number of lesions counted. What is the experimental and observational unit and how many are they? In this study the animals are all housed in one cage and the treatment is given by injection to each animal. What is the experimental unit? Why?... What is the observational unit and how many are they? Dr. M Asnong 35  Control/Reference group The control group is a natural normative category or A group used as the baseline for comparison Dr. M Asnong 36  Experimental error It is the random variation present in all experimental results. Is defined as the difference between the true value of a measurement and the recorded value of a measurement. Error can be described as: Random or Systematic. Dr. M Asnong 37 Random Errors Measurements subject to random errors differ from each other due to random, unpredictable variations in the measurement process. Random errors are unpredictable and are chance variations in the measurements over which the researcher has little, if any, control. Impact can be reduced by increaseing sample size because the results can be “averaged”. Dr. M Asnong 38  Systematic Errors Is a consistent and repeatable bias or offset from the true value Due to-miscalibration of the test equipment, or Experimental procedure or the design of the experiment They skew the data consistently in one direction. Can not be rectify by increasing sample size; except by changing the experimental setup. Dr. M Asnong 2017/18 39 Forty bean plants, growing in pots, were covered one afternoon by individual glass containers and left in the laboratory overnight. Next morning, the inside of the lid of each container was found to be covered in droplets of a fluid which proved to be water. Conclusion: Plants generally give off water vapour Will this conclusion be accurate? Dr. M Asnong 2019/20 40 What is Experimental Design(ED)? ED refers to the manner in which the experimental units are arranged or grouped, and how the treatments are assigned to them. It uses statistical approach to provide a logical structure for the experiment and collection of data This ensures appropriate data can be obtained, which may be statistically analysed to yield valid conclusions Dr. M Asnong 41  The ED used will influence the statistical analysis that could be used for the data When selecting an experimental design the experimenter should always base the choice of design on those designs that will effectively address the question or test the hypothesis Dr. M Asnong 42 The three basic principles of experimentation 1. Randomization: The process of randomly allocating treatments to the experimental units to avoid any bias in the experiment that could result from the influence of some extraneous unknown factor. avoids possible bias on the part of the experimenter, thereby increasing the accuracy of the estimation It helps obtain representative samples Dr. M Asnong 43 2. Replication Is an independent repetition of the experiment in order to obtain a more precise result. An experiment therefore contains replication if the set of all the treatment combinations to be compared in an experiment are applied independently to two or more experimental units. Dr. M Asnong 44  Replication also provides more observations, which reduce the standard error and improve precision. For example if σ2 is the variance for the data and there are n replicates then the variance of the sample mean is σ2/n ; So as n increases, the variance decreases Dr. M Asnong 2017/18 45 Does increasing the number of observational units increase replication? Yes/NO 1 measurement per pot Experimental unit=50 Measurement unit= 50 Treatment=2 Replicate= 25 4 measurements per lot Experimental unit= 50 Measurement unit(N)= 200 Treatment=2 Replicate= 25 Dr. M Asnong 46 3. Blocking This is the process of partitioning the experimental material into groups that are similar to one another (homogenous) It reduces the sources of variability and increase precision. It helps account for and eliminates the effects of a known extraneous variable (systematic bias) that could influence the response variable Dr. M Asnong 47  48 Dr. M Asnong Research questions Is the question that the research project sets out to answer. The methodology used for a study, and the tools used to conduct the research, all depend upon the research questions. Three main questions types: Dr. M Asnong 49 1. Causal Questions Compares two or more phenomena and determines if a relationship exists. Often called relationship research questions. Example: Does the amount of calcium in the diet of lion cubs affect the number of cavities they have per year? Dr. M Asnong 50 2. Descriptive Questions Seek to describe a phenomena and often study “how much”, “how often”, or “what is the change”. Example: How often do cocoa parasite attack cocoa trees planted under shade? Dr. M Asnong 51 3. Comparative Questions Aim to examine the difference between two or more groups in relation to one or more variables. The questions often begin with “What is the difference in...”. Example: What is the difference in caloric intake of mudfish and Tilapia? Dr. M Asnong 52  Hypotheses “Hypothesis is a formal statement that presents the expected relationship between an independent and dependent variable.”(Creswell, 1994) “An hypothesis is a statement or explanation that is suggested by knowledge or observation but has not, yet, been proved or disproved.” (Macleod Clark J and Hockey L 1981) Dr. M Asnong 53 Nature of Hypothesis It should be testable – verifiable or falsifiable It should be a prediction of consequences Dr. M Asnong 54 Example: Consider the example of a simple association between two variables, Y and X. 1.Y and X are associated (or, there is an association between Y and X). 2.Y is related to X (or, Y is dependent on X). 3.As X increases, Y decreases (or, increases in values of X appear to effect reduction in values of Y). Dr. M Asnong 55 Types of Hypotheses NULL ALTERNATIVE HYPOTHESES HYPOTHESES Designated by: Designated by: H1 or HA H0 or HN Dr. M Asnong 56 The null hypothesis The null hypothesis is the hypothesis that nothing is going on Every hypothesis will have an associated null hypothesis (H0) and most statistical tests use the null hypothesis as a starting point. Dr. M Asnong 57 The alternate hypothesis Opposite of Null Hypothesis.  Only reached if H0 is rejected.  Frequently “alternative” is actual desired conclusion of the researcher! Dr. M Asnong 58  EXAMPLE In a trial of a new fish feed, the null hypothesis might be that the new feed is no better, on average, than the current feed. We would write H0: there is no difference between the two feeds on average. The alternative hypothesis might be that: Dr. M Asnong 59 1. the new feed has a different effect, on average, compared to the current feed. We would write H1: the two feeds have different effects, on average. 2. the new feed is better, on average, than the current feed. We would write H1: the new feed is better than the current feed, on average. Dr. M Asnong 60  Hypothesis Testing Hypothesis testing is a four-step procedure: 1. Stating the hypothesis (Null or Alternative) 2. Setting the criteria for a decision 3. Collecting data 4. Evaluate the Null hypothesis Dr. M Asnong 61  Making a Statistical Decision There are two approaches for making a statistical decision regarding a null hypothesis – p-value (or probability value) approach. – rejection region approach Conclusions from the two approaches are exactly the same Dr. M Asnong 62 P value It is the probability of obtaining an effect extreme as the one in your data if the null hypothesis is true. A value called alpha (α ) is set (usually 5% or 0.05 or 1 in 20). If the P-value is less than (or equal to) α, then the null hypothesis is rejected in favor of the alternative hypothesis. And, if the P-value is greater than α, then the null hypothesis is accepted. Dr. M Asnong 63  Critical values(Fc) A critical value is a point on the test distribution that is compared to the test statistic (calculated value) to determine whether to reject the null hypothesis. If the absolute value of your test statistic (calculated value) is greater than the critical value, you can reject the null hypothesis. Dr. M Asnong 64  Testing & Challenging There are two possibilities 1.Nothing Happened the Null Hypothesis - Ho 2. Something Happened 1.the Alternative Hypothesis - H1 Dr. M Asnong 65  Errors in Hypotheses Two types of mistakes are possible while testing the hypotheses. Type I and Type II sick well What doc says You are sick. Doc Get scared for nothing! sick confirms it RIGHT WRONG-Type II error well Doc missed your real You’re really not sick! illness! RIGHT WRONG-Type I error. Dr. M Asnong 66  Type I Error  A type I error occurs when the null hypothesis (H0) is wrongly rejected. For example, A type I error would occur if we concluded that the two fish hormones produced different effects when in fact there was no difference between them Dr. M Asnong 67  Type II Error:  A type II error occurs when the null hypothesis H0, is not rejected when it is in fact false. For example: A type II error would occur if it were concluded that the two hormones produced the same effect, that is, there is no difference between the two drugs on average, when in fact they produced different ones. Dr. M Asnong 68  Decision Reject H0 Accept H0 H0 Type I Error Right Decision Truth H1 Right Decision Type II Error A type error I is often considered to be more serious, and therefore more important to avoid, than a type II error. Dr. M Asnong 69  Degrees of freedom Degrees of freedom are effectively the number of observations in the testing set which are free to vary Dr. M Asnong 70  The scientific method Is an approach to acquiring knowledge that involves formulating specific questions and then systematically finding answers. The planned and systematic application of the empirical method  The scientific method By combining several different methods of acquiring knowledge, we hope to avoid the pitfalls of any individual method used by itself. The scientific method is a carefully developed system for asking and answering questions so that the answers we discover are as accurate as possible.  The steps of the scientific method Step 1: Observe behavior or other phenomena Step 2: Form a tentative answer or explanation (a hypothesis (guess a reason) Step 3: Use your hypothesis to generate a testable prediction Step 4: Make systematic, planned observations (data collection) Step 5: Use the observations to evaluate (support, refute, or refine) the original hypothesis Dr. M Asnong 2019/20 74 Practical Example… As a nutritionist working in a zoo, you have been tasked to develop a menu plan for a group of howler monkeys. The monkeys need fresh leaves as part of their diet in order to get all the vitamins they need. Dr. M Asnong 75 Practical Example… Choices you consider include leaves of the following species: (a) A (b) B (c) C (d) D and (e) E. You know that in the wild the monkeys eat mainly B leaves, but you suspect that this could be because they are safe whilst feeding in B trees, whereas eating any of the other species would make them vulnerable to predation. Dr. M Asnong 76  You design an experiment to find out which type of leaf the monkeys actually like best: How will you design the experiment Write one hypothesis for the research Dr. M Asnong 77