Methodological glossary
In this glossary you will find only a very short description of each concept. If you need a more detailed explanation, please follow one of the external links.
- Analysis of variance
- Research data are often based on samples drawn from a larger population of cases. This is true of most types of questionnaire surveys, among other examples. When, on the basis of the analysed results of such sample surveys, we conclude that the same results are valid for the population from which the sample has been drawn, we are making a generalisation with some degree of uncertainty attached. Analysis of variance is a method that allows us to determine whether differences between the means of groups of cases in a sample are too great to be due to random sampling errors. This can, for instance, help us to determine whether observed differences between the income of men and women (in a sample) are great enough to conclude that these differences are also present in the population from which the sample has been drawn. In other words, the method tells us whether the variable Gender has any impact on the variable Income, or more generally, whether a non-metric variable (which divides the cases into groups) is a factor in deciding the values that the cases have on a separate and metric variable. Analysis of variance looks at the total variance of the metric variable and tries to determine how much of this variance is due to, or can be explained by, the non-metric grouping variable. The method consists of the following building blocks; 1) total variance 2) within-group variance and 3) between-group variance. Total variance is the sum of the squared differences between the data values of each of the units and the mean value of all the units. This total variance can be broken down into within-group variance, which is the sum of the squared differences between the data values of each of the units and the mean of the group to which the unit belongs, and between-group variance, which is the sum of the squared differences between each of the group means and the mean of all the units.
- Asymmetrical distribution
- If you split the distribution in half at its mean (or median), then the distribution of the two sides of this central point would not be the same (i.e., not symmetrical) and the distribution would be considered skewed.
- b
- A parameter estimate of a regression equation that measures the increase or decrease in the dependent variable for a one-unit difference in the independent variable. In other words, b shows how sensitive the dependent variable is to changes in the independent variable.
- Beta
- Standardised b shows by how many standard deviations the dependent variable changes when the independent variable increases by 1 standard deviation. The beta coefficient should be used when comparing the relative explanatory power of several independent variables.
- Box-and-whisker plot
- The distribution can also be shown by means of a box-and-whisker plot. This form of presentation is based on a group of statistical measures which are known as median measures. All such measures are based on a sorted distribution, i.e. a distribution in which the cases have been sorted from the lowest to the highest value. The first quartile is the data value of the case where 25 % of the cases have lower values and 75 % of the cases have greater values. The third quartile is the data value of the case where 75 % of the cases have lower values and 25 % of the cases have greater values. The inter-quartile range is the distance from the first to the third quartile, i.e. the variation area of the half of the cases that lies at the centre of the distribution. The box-and-whisker plot consists of a rectangular box divided by one vertical line, with one horizontal line (whisker) extending from either end. The left and right ends of the box mark the first and third quartiles respectively. The dividing line at the centre represents the median. The length of the box is equal to the inter-quartile range and contains the middle half of the cases included in the sorted distribution. The end points of the two extending lines are determined by the data values of the most extreme cases, but do not extend more than one inter-quartile range from either end of the box (i.e. from the first and third quartiles). The maximum length of each of these lines, therefore, is equal to the length of the box itself. If there are no cases this far from either quartile, the lines will be shorter. If the maximum or minimum values of the entire distribution are beyond the end points of the line, a cross will indicate their position.
- Case
- By cases we mean the objects about which a data set contains information. If we are working with opinion polls or other forms of interview data, the cases will be the individual respondents. If data have been collected about the municipalities of a county or about the countries of the world, the cases will be the geographical areas, i.e. the municipalities or countries.
- Central tendency
- The central tendency is a number summarising the average value of a set of scores. The mode, the median and the mean are the commonly used central tendency statistics.
- Chi-square distribution
- A family of distributions, each of which has different degrees of freedom, on which the chi-square test statistic is based.
- Chi-square test
- A test of statistical significance based on a comparison of the observed cell frequencies of a joint contingency table with frequencies that would be expected under the null hypothesis of no relationship.
- Compute
- Compute is used for creating new variables on the basis of variables already present in the data matrix. It is possible to do calculations with existing variables, such as calculating the sums of the values on several variables, percentaging, multiplying variables by a constant, etc. The results of such arithmetic operations are saved as new variables, which can then be used just like the other variables in the data set.
- Confidence interval
- Research data are very often based on samples drawn from a larger population of cases. This applies to most types of questionnaire surveys, for instance. When we assume, on the basis of results from the analysis of such sample surveys, that the same results apply to the population from which the samples are drawn, we are making generalisations with some degree of uncertainty attached. The confidence interval is a method of estimating the uncertainty associated with computing mean values in sample data. We normally use a confidence interval with a significance level of 95 %. This means that there is a 5 % chance of being wrong if we assume that a mean value for a sample lies within the confidence interval.
- Correlation
- Correlation is a measure of the relation between two or more variables. Correlation coefficients can range from -1.00 (perfect negative) to +1.00 (perfect positive).
- Descriptive statistics
- Descriptive statistics is a branch of statistics that denotes any of the many techniques used to summarize a set of data. The techniques are commonly classified as: 1) Graphical description (graphs) 2) Tabular description (frequency, cross table) 3) Parametric description (central tendency, statistical variability).
- Standard deviation
- Standard deviation is a measure of dispersion based on the intervals between the individual data values and the arithmetic mean of these values. Roughly speaking, the standard deviation shows the mean interval between the variable's central tendency (mean) and the individual data values.
- Dichotomy
- Dichotomies are variables with only two values, e.g. the variable Gender with the two values Male and Female.
- Standard error
- The standard error is an expression of the uncertainty associated with the mean value when the latter is based on a sample drawn from a larger population (i.e. is estimated). Mathematically the standard error is computed by dividing the standard deviation by the square root of N.
- Factor analysis
- The objective with this technique is to explain the most of the variablility among a number of observable random variables in term of a smaller number of unobservable random variables called factors. The observable random variables are modeled as linear combinations of the factors, pluss "error" terms. The main application of factor analytic techniques are: 1. to reduce the number of variables and 2. to detect structure in the relationships between variables.
- Frequency
- Frequency is a method of describing how the cases are distributed over the different data values on a particular variable. The Frequency table gives an overview of the number of cases that have each of the values on a variable. Frequency tables are most suitable for variables with few data values.
- Index
- An index variable is a variable that in one way or another summarises information about several other variables. Index variables are most frequently used where the data set includes several measures of the same basic phenomenon, e.g. political participation, status, etc. We can combine these measures or indicators in one index to create a variable which gives an overall impression of the basic phenomenon.
- Kurtosis
- This statistic shows how the distribution of the variables deviates from the normal distribution. The normal distribution of a variable is a bell-shaped symmetric curve where approximately 2/3 of the cases are within 1 standard deviation on either side of the mean value and approximately 95 % of the cases fall within these 2 standard deviations. Kurtosis is a measure of the degree to which a variable meets this condition - whether it has a more concentrated (more peaked) or more even (flat) distribution. A positive kurtosis tells us that the distribution of the variable is more peaked than the normal distribution. A negative kurtosis tells us that the distribution is less peaked than the normal distribution. (Skewness tells us whether the variable meets the normal distribution curve's symmetry requirement.)
- Listwise
- Calculation is done for all the cases with valid values on all the variables included in the analysis.
- Data matrix
- When preparing data for statistical analysis, we structure the material in a data matrix. A data matrix has one row for each case and a fixed column for each variable. The cases are distributed over the values of each variable, so that the values are shown in the cells of the matrix.
- Mean
- The arithmetic mean shows the central tendency for metric variables. The mean is computed by adding the values of all the cases and dividing the sum by the number of cases.
- Median
- The median is a measure of the central tendency for ordinal or metric variables. The median is the value that divides a sorted distribution into two equal parts, i.e. the value of the case with 50 % of the cases above it and 50 % below. For example: If you have measured the variable Height for 25 persons and sorted the values in ascending order, the median will be the height of person no. 13 in the sorted sample, i.e. the person that divides the sample into two with an equal number of cases above and below him/her.
- Mode
- The mode is a measure of the central tendency. The mode of a sample is the value which occurs most frequently in the sample.
- Normal distribution
- Normal distribution is a theoretical distribution which many given empirical variable distributions resemble. If a variable has a normal distribution (i.e. resembles the theoretical normal distribution), the highest frequencies are concentrated round the variable's mean value. The distribution curve is symmetric round the mean and shaped like a bell. Approximately 2/3 of all cases will fall within 1 standard deviation to either side of the mean value. Approximately 95 % of the cases fall within 2 such deviations.
- Operationalisation
- Operationalisation is the process of converting concepts into specific observable behaviours or attitudes. For example, highest education completed could be an operationalisation of the concept academic skill.
- Pairwise
- The correlations between each pair of variables are determined on the basis of all cases with valid values on two variables. This takes place regardless of the values of these cases on other specified variables.
- Recode
- Recode reassigns the values of existing variables or collapses ranges of existing values into new values. For example, you could collapse income into income range categories.
- Regression
- Linear regression is a method of estimating the conditional expected value of one variable y given the values of some other variable x. Multiple regression is an extension of the simple bivariate regression. The objective is to explain variations in the dependent variable by means of the independent variables, in other words to find out how much of the variation in a dependent phenomenon is due to systematic co-variance with a set of causal factors.
- Reliability
- In psychometrics, reliability is the accuracy of the scores of a measure. The most common internal consistency measure is Cronbach's alpha. Reliability does not imply validity. A reliable measure is measuring something consistently. A valid measure is measuring what it is supposed to measure. A Rolex may be a very reliable instrument for measuring the time, but if it is wrong, it does not give a valid measure of what the time really is.
- Scattergram
- The scattergram is a graphic method of presentation, in which the different cases are plotted as points along two (three) axes defined by the two (three) variables included in the analysis.
- Significance
- A significant result is unlikely to have occurred by chance, given that the presumed null hypothesis is true. The significance figures tell us the probability of being wrong if we assume that the observed differences are also present in the population from which the sample has been drawn. Where the hypothesis is simply that the two variables are different (without stating which is the higher), we use two-tailed significance.
- Skewness
- Skewness is a measure that shows how the variable distribution deviates from the normal distribution. A variable with normal distribution has a bell-shaped symmetric distribution round the mean value of the variable. This means that the highest frequencies are in the vicinity of the mean value and that there is an equal number of cases on either side of the mean. Skewness measures deviation from this symmetry. Positive skewness tells us that the value of the majority of the cases is below the mean and hence there is a predominance of cases with positive extreme values. Negative skewness tells us that the majority of the cases are greater than the mean while there is a predominance of negative extreme values.
- Standard deviation
- The standard deviation is the most commonly used measure of statistical dispersion. It measures the spread of the values in a dataset. The standard deviation is defined as the square root of the variance.
- Standard error
- The standard error is an expression of the uncertainty associated with the mean value when the latter is based on a sample drawn from a larger population (i.e. is estimated). Mathematically the standard error is computed by dividing the standard deviation by the square root of N.
- Statistics
- Statistics is the science and practice of developing human knowledge through the use of empirical data. It is based soundly on statistical theory, which is a branch of applied mathematics.
- Tolerance
- This is a measure of the covariance of independent variables (normally called colinearity). The tolerance value shows how much of the variance of each independent variable is shared by other independent variables. The value can range from 0 (all variance is shared by other variables) to 1 (all variance is unique to the variable in question). If the tolerance value approaches 0, the results of the analysis may be unreliable. In such cases it is also difficult to determine which of the independent variables explain the variance of the dependant variable.
- T test
- The T test is used to determine whether the difference between the mean values for two groups of cases in a sample is sufficiently great for us to conclude that the difference is not due to sampling errors. This method can, for instance, help us to decide whether the observed differences in income between men and women (in a sample) are great enough for us to be able to conclude that they are also present in the population from which the sample has been drawn.
- Type I error
- In statistical hypothesis testing, a type I error involves rejecting a null hypothesis (there is no connection) that is true. In other words, finding a result to be significant when this in fact happened by chance.
- Type II error
- In statistical hypothesis testing, a type II error consists of failing to reject an invalid null hypothesis (i.e. falsely accepting an invalid hypothesis. As the likelihood of type II error decreases, the likelihood of type I error increases.
- Variable
- By variables we mean characteristics or facts about cases about which the data contain information, e.g. the individual questions on a questionnaire. For instance, if the cases are countries or other geographical areas, we may have population figures, etc. There are several types of variables, and the variable type determines which methods and forms of presentation should be used. Where the individual groups or values have no obvious order or ranking, the variable is called a nominal variable (gender). The next type is called an ordinal variable. In addition to the actual classification, there is a natural principle ranking the different values in a particular order. It can obviously be claimed that the response "Very interested in politics" is evidence of a stronger political interest than "Quite interested". The values of ordinal variables have a natural order, but the intervals between the values cannot be measured. The third type is called metric variables. These are variables that in some way measure parameters, quantities, percentages etc., using a scale based on the numerical system. The numerical values of these variables have a direct and intuitive meaning. They are not codes used as surrogates for the real responses as in the case of the nominal and ordinal variables. It follows that these variables also have the arithmetic properties of numbers. The values have a natural order, and the intervals between them can be measured. We can say that one person is three times the age of another without violating any logical or mathematical rules. It is also possible to compute the average age of a group of people.
- Variance
- The variance is a measure of the statistical dispersion, and it is defined as the mean square deviation of a continuous distribution.
- Variation
- The variation is a number indicating the dispersion in a distribution: How typical is the central tendency of the other sample observations? For continuous variables, the variance and the standard deviation are the most commonly used measures for dispersion.
- Weighting
- Weighting allows you to assign a different weight to the different cases in the analysis file. Weighting is usually used for correcting skewness in a sample that is meant to represent a particular population. It can also be used for "blowing up" sample data so that the analysis results are shown in figures that are in accordance with the size of the population.
