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1 Leaning diary: research methodology Name: Juriaan Zandvliet Student number: (1) a short description of each topic of the course, (2) desciption of possible examples or exercises done in relation and (3) your perspective, links, references, ideas and intrerest related to the topic and issues where you would need further training 1. Set up Science produces accurate facts that can be checked, scientific laws and theories. You can say the results of science are repeatable and the theories are falsifiable. The sciencecouncil.org states the following about science: the pursuit and application of knowledge and understanding of the natural and social world following a systematic methodology based on evidence. Science is carried out during a research process. A research process consists out of four stages; problems, theories, criticism and new problems. This research process can be carried out by the following method: 1. Observe some aspect of the universe 2. Invent a tentative description, called hypothesis 3. Use the hypothesis to make predictions 4. Test those predictions by experiments and modify the hypothesis 5. Repeat steps 3 and 4 until there are no discrepancies There are two examples of scientific research processes. The first one is called pure scientific research, this is about explaining the word around us and explaining how the universe operates. Something can be called science when it is falsifiable. For instance the theory of gravity, when I throw a rock into the air and it fall back the theory will stand. If I throw a rock into the air and it will not fall back the theory is refuted. An example of a not falsifiable theory it the existence of a god. Because it is not falsifiable it is not scientific. There is a wide variety of examples of scientific research. Scientific research can be a publication in a scientific paper. Two well-known journals with a relatively broad spectrum of subjects are Nature and Science. Recognised publishers of academic journals are Elsevier, Wiley-Blackwell and Springer. Reference

2 2. Main concepts Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies. Statistics studies methodologies to gather, review, analyze and draw conclusions from data. Statistics is a term used to summarize a process that an analyst uses to characterize a data set. If the data set depends on a sample of a larger population, then the analyst can develop interpretations about the population primarily based on the statistical outcomes from the sample. Statistical analysis involves the process of gathering and evaluating data and then summarizing the data into a mathematical form. Mean A mean is the mathematical average of a group of two or more numerals. The mean for a specified set of numbers can be computed in multiple ways, including the arithmetic mean, which shows how well a specific commodity performs over time, and the geometric mean, which shows the performance results of an investor s portfolio invested in that same commodity over the same period. Variance σ2 Variance is a measurement of the span of numbers in a data set. The variance measures the distance each number in the set is from the mean. Variance can help determine the risk an investor might accept when buying an investment. Standard Deviation σ, Variance σ2 Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. If the data points are further from the mean, there is higher deviation within the data set.

3 Normal distribution A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme. Height is one simple example of something that follows a normal distribution pattern: Most people are of average height, the numbers of people that are taller and shorter than average are fairly equal and a very small (and still roughly equivalent) number of people are either extremely tall or extremely short. Degrees of freedom Df = n-1 Standard Deviation vs. Mean In its simplest form, the mean is simply the average of all the data points in a given set. In investing, for example, you might want to know the mean closing price for the last 20 days. This can be obtained by adding the closing prices for each session and dividing by 20. Because markets are fickle at best, traders and analysts use moving averages that adjust daily to incorporate the most updated data. This

4 means the calculation is always taking into account the most recent sessions' movements, and older sessions drop off as they become less relevant. An exponential moving average (EMA) is calculated by weighting each data point, giving greater significance to more recent data. Standard deviation is calculated based on the mean. The distance of each data point from the mean is squared, summed and averaged to find the variance. Or to put it another way: Variance is derived by taking the mean of the data points, subtracting the mean from each data point individually, squaring each of these results and then taking another mean of these squares. Standard deviation is simply the square root of the variance. Calculating Standard Deviation The formula for standard deviation uses three variables. The first variable is to be the value of each point within the data set, traditionally listed as x, with a sub-number denoting each additional variable (x, x1, x2, x3, etc.). The mean, or average, of the data points is applied to the value of the variable M, and the number of data points involved is assigned to the variable n. To determine the mean value, the values of the data points must be added together, and that total is then divided by the number of data points that were included. For example, if the data points were 5, 7, 3 and 7, the total would be 22. The total of 22 would then be divided by the number of data points, in this case four, resulting in a mean of 5.5. This leads to the following determinations: M=5.5 and n=4. The variance is determined by subtracting the value of the mean from each data point, resulting in - 0.5, 1.5, -2.5 and 1.5. Each of those values are then squared, resulting in 0.25, 2.25, 6.25 and The square values are then added together, resulting in a total of 11, which is then divided by the value of n-1, which is 3 in this instance, resulting in a variance approximately of The square root of the variance is then calculated, resulting in the standard deviation of Range The range is the highest value minus the lowest value in a ascending) series of numbers. The range of for example the number series 11, 12, 13, 13, 16, 18, 19, 20, 22 is 11. This is calculated as = 11. Standard Deviation vs. Variance The variance helps determine the data's spread size when compared to the mean value. As the variance gets bigger, more variation in data values occurs, and there may be a larger gap between one data value and another. If the data values are all close together, the variance will be smaller. This is more difficult to grasp than are standard deviations, however, because variances represent a squared result that may not be meaningfully expressed on the same graph as the original data set.

5 Standard deviations are usually easier to picture and apply. The standard deviation is expressed the same unit of measurement as the data, which isn't necessarily be the case with the variance. Using the standard deviation, statisticians may determine if the data has a normal curve or other mathematical relationship. If the data behaves in a normal curve, then 68% of the data points will fall within one standard deviation of the average, or mean data point. Bigger variances cause more data points to fall outside the standard deviation. Smaller variances result in more data that is close to average. All the definitions are further explained in the next video: Reference Verhoeven, N. (2015). Statistiek in stappen. Amsterdam: Uitgeverij Boom

6 3. Tests Test are used when samples of whole population have to be taken care of and needs to be generalized. There is always insecurity during generalizing, statistics tries to control this by testing assumptions to make decisions. For instance when comparing two populations with each other, statistics is used to make decisions. Comparing two populations is done with the help of the t-test. T-test A t-test is a parametric statistical test that can be used, among other things, to determine whether the population average of a normally distributed quantity deviates from a certain value, or whether there is a difference between the averages of two groups in the population. Using a t-test, you can then determine an exceedance probability or a confidence interval. A t-test can be used if certain conditions are met. For the t test for one sample, the sample concerned must be a random sample from a normal distribution, with possibly unknown variance. In the case of two samples, both samples should come from a normal distribution. The two samples must either be independent of each other or have to be paired. In the case of two independent samples, the two populations should have the same variance when applying the standard t test. If both populations have a different variance, an adapted t-test can be used. The case of paired observations amounts to a t-test for the single sample of the differences. Violations of these assumptions have consequences for the robustness and the distinctive character of the t-test. With the help of an F-test it can be tested whether the variances in both groups differ significantly from each other. The normality of the populations can be tested using the Kolmogorov- Smirnov test. If the conditions of the central limit theorem are met, the t-test can be approximated for large samples. The sample averages required for the calculation of the test quantity are then almost normally distributed. Anova Anova is a testing procedure to determine whether the population averages of more than 2 groups differ from each other. In that sense it is a generalization of the t-test for two samples.

7 Levene test The Levene test is a statistical test to measure if two variations for two different population a different of each other. When the out coming p-value is lower than the alfa there is a significant difference in variation between the two populations. A good example of what statistical test to use is the following youtube video: Reference Verhoeven, N. (2015). Statistiek in stappen. Amsterdam: Uitgeverij Boom

8 4. Regression methods and models Correlation Correlation is the statistical relationship between two variables. These can be two sets of measurements, or possible values of two random variables. The strength of this relationship is expressed in a correlation coefficient. The degree of correlation between two variables is expressed in the correlation coefficient. Their value can vary between -1 and means no linear coherence, +1: perfect positive linear coherence and - 1: perfect negative linear coherence. The further the correlation coefficient is removed from 0, the stronger the correlation rate. R and R2 R² is a measure that provides information about the extent to which a model approaches the actual data. If all predicted values match the actual values, then R² = 1. Note that a (perfect) relationship says nothing about the causality in the data. Regression Analysis Regression analysis determines the extent to which specific factors such as interest rates, the price of a product or service, or particular industries or sectors influence the price fluctuations of an asset. This is depicted in the form of a straight line called linear regression. The line summarizes the relationship between x and y The residuals need to be distributed according to a normal distribution. The error term has a normal distribution with a mean of 0.

9 Models Linear regression technique tries to predict the values of the outcome Y via a linear relation from the values of X. The outcome variable Y is called the dependent variable, and the predictor X the independent variable. Simple regression is when you predict the outcome with one predictor. In practice, this will in many cases not be sufficient and it is desirable to analyse the effects of two or more predictors. Like with models predicting the tree volume, multiple predict. We then speak of multiple (also multiple or multivariable) linear regression. A model tries to predict value y with the help of Y = β 0 + β 1 x. The model line is created where the sum of squares of model residuals is minimized. In the example β 0 is the constant, and is also called the interceptor. β 1 is the variable: income, it is also called the slope. The dependent variable is price. This coefficients table show the correlation between income and price. The value for β1 is.564 and is significant, this means this value cannot be zero which means there would be no correlation. The significance of β0 explains nothing about the correlation between the two variables price and income.

10 Standard Error (SE) The standard error of an estimate shows the precision of that estimate. The standard error is used to indicate how certain you are of an estimated value. Formally, the value represents the spread of the estimate if there were multiple samples, with the estimate being made again for each sample. The formula for standard error is as follows: When the number of samples increases (n) the standard error will decrease because the outcome of dividing true a bigger number will give a smaller number. A good example is given in the following Youtube video about simple linear regression: Reference Verhoeven, N. (2015). Statistiek in stappen. Amsterdam: Uitgeverij Boom

11 5. Other response variables Homoscedasticity is when the residuals show a trend and get wider or smaller. In heteroscedasticity date the variance is constant. There are other data types like: count data, proportional data, binary response data and survival data (age-at-death data). Count data Count data is non-negative integer values (0,1,2,3, ) arising from counting rather than ranking. Example is the number of days a student is absent in one school year. This data can never be less than zero. That is why a normal regression model would not work because the model will eventually turn negative. Proportional data Proportional data gives a proportion of two or more categories, for instance the proportion voting for two different parties or the proportion of dead and alive trees after a storm. Just like count data the data has to be converted before using a linear model because values cannot exceed 100% or can be less than 0%. The variance of the response variable is likely to increase with the mean. Binomial data Binomial data is data consisting out of 0 and 1. Zero stands for normal and one stands for special. For instance healthy people (zero) or sick people (one). Just like count data and proportional data linear model will not acknowledge that the data cannot exceed the values of one and zero. A transformation is therefore required Generalized Linear Models (GLMs) Generalized linear models is count-, proportional or binomial data that has undergone a transformation so a linear model can be utilized. This is done by transforming the predictor to a logistic scale bar or logit. The following youtube video give examples of different statistical data types and how generalized linear models work: Reference Verhoeven, N. (2015). Statistiek in stappen. Amsterdam: Uitgeverij Boom

12 6. Visualizations Visualizations is a big part of academic research. It is about showing the data and communicate information using efficient visuals. Sometimes data can be presented in misleading ways to give the data more impacts. In general complex ideas should be communicated with clarity, precision, and efficiency. There are five design principals for visualising data. 1. Proportions in graphics should accurately represent raw data 2. Labels should be clear, accurate, and descriptive 3. Data should vary, not design 4. There should be no more dimensions shown than dimensions in the data 5. Graphics must not quite data out of context Figures and tables Figure legend is placed under the figure and table heading above table. Every figure and table included in the paper must be referred to for the text. Each column of the table should have a title or a label. Vertical lines should be avoided and do not use a table when you wish to show a trend or pattern. The figure on the right is a bad example of data visualisation. It clearly violates rule 3 listed above: data should vary, not design. Also the proportions of the data do not represent the raw data (rule 1). All the percentages in the figure add up to 243%, 100% would be the right proportion.

13 7. GIS A geographic information system, abbreviated to GIS, is an information system with which spatial data or information about geographical objects, so-called geo-information. This can be stored, managed, processed, analyzed, integrated and presented. There are a lot of spatial analyst tools in GIS to analyse the data and make calculations: clip, intersect, merge, buffer and dissolve. Clip: Extracts input features that overlay the clip features. Intersect: Computes a geometric intersection of the input features. Features or portions of features which overlap in all layers and/or feature classes will be written to the output feature class. Merge: Combines multiple input datasets of the same data type into a single, new output dataset. This tool can combine point, line, or polygon feature classes or tables. Buffer: Creates buffer polygons around input features to a specified distance. Dissolve: Aggregates features based on specified attributes. A possible exam question will be the difference between topology and topography. Topography is the study of the description of characteristics of places and areas. Topography also includes the study of the location and the names of places, waters, mountains, regions, countries and other geographical forms. Topology is a kind of geometry, but topology does not deal with metric properties such as the distance between points. It is the property that describe how the space is composed, such as coherence and orientation. 8. R statistics R is a program that can be used for statistic to make calculations and analyse data. The program uses script language to execute commends. It is a great programme for data analysis and statistical computing with vector and matrix calculations. Frequent codes used in the R programme are: summary(data) sd(data) hist(data) boxplot(data) plot(model) length(data)