Statistics is used more and more often to study the behavior of people, not only by the social sciences but also by companies. Everyone can learn how to use statistics, even without much knowledge of mathematics and even with fear of statistics. Most important are logic thinking and perseverance.To first step to using statistical methods is collecting data. Data are collected observations of characteristics of interest. For instance the opinion of 1000 people on whether marihuana should be allowed. Data can be obtained through questionnaires, experiments, observations or existing databases.But statistics aren't only numbers obtained from data. A broader definition of statistics entails all methods to obtain and analyze data. Before being able to analyze data, a design is made on how to obtain the data. Next there are two sorts of statistical analyses; descriptive statistics and inferential statistics. Descriptive statistics summarizes the information obtained from a collection of data, so the data is easier to interpret. Inferential statistics makes predictions with the help of data. Which kind of statistics is used, depends on the goal of the research (summarize or predict).To understand the differences better, a number of basic terms are important. The subjects are the entities that are observed in a research study, most often...

Descriptive statistics serves to create an overview or summary of data. There are two kinds of data, quantitative and categorical, each has different descriptive statistics.To create an overview of categorical data, it's easiest if the categories are in a list including the frequence for each category. To compare the categories, the relative frequencies are listed too. The relative frequency of a category shows how often a subject falls within this category compared to the sample. This can be calculated as a percentage or a proportion. The percentage is the total number of observations within a certain category, divided by the total number of observations * 100. Calculating a proportion works largely similar, but then the number isn't multiplied by 100. The sum of all proportions should be 1.00, the sum of all percentages should be 100.Frequencies can be shown using a frequency distribution, a list of all possible values of a variable and the number of observations for each value. A relative frequency distributions also shows the comparisons with the sample.Example (relative) frequency distribution:GenderFrequenceProportionPercentageMale1500.4343%Female2000.5757%Total350 (=n)1.00100%Aside from tables also other visual displays are used...

Sample data is used for estimating parameters that give information about the population, such as proportions and means. For quantitative variables the population mean is estimated (like how much money on average is spent on medicine in a certain year). For categorical variables the population proportions are estimated for the categories (like how many people do and don't have medical insurance in a certain year).Two kinds of parameter estimates exist;A point estimate is a number that is the best prediction.An interval estimate is an interval surrounding a point estimate, which you think contains the population parameter. There is a difference between the estimator (the way that estimates are made) and the estimate point (the estimated number itself). For instance, a sample is an estimator for the population parameter and 0,73 is an estimate point of the population proportion that believes in love at first sight.A good estimator has a sampling distribution that is centered around the parameter and that has a standard error as small as possible.An estimate isn't biased when the sampling distribution is centered around the parameter. This is especially the case when the sample mean is the population parameter. In that case ӯ (sample mean) equals µ (population mean). ӯ is then regarded a good estimator for µ.When an estimate is biased, the sample mean doesn't estimate the...

In social science often two groups are compared. For quantitative variables means are compared, for categorical variables proportions. When comparing two groups, a binary variable is created: a variable with two categories (also called dichotomous). For instance for sex as a variable the results are men and women. This is an example of bivariate statistics.Two groups can be dependent or independent. They are dependent when the respondents naturally match with each other. An example is longitudinal research, where the same group is measured in two moments in time. For an independent sample the groups don't match, for instance in cross-sectional research, where people are randomly selected from the population.Imagine comparing two independent groups: men and women and the time they spend sleeping. Men and women are two different groups, with two population means, two estimates and two standard errors. The standard error indicates how much the mean differs for each sample. Because we want to investigate the difference, also this difference has a standard error. The population difference is estimated by the sample difference. What you want to know, is µ₂ – µ₁, this is estimated by ȳ2 – ȳ1. This can be shown in a sampling distribution. The standard error of ȳ2 – ȳ1...

Regression analysis is the process of researching associations between quantitative response variables and explanatory variables. It has three aspects: 1) investigating whether an association exists, 2) determining the strength of the association and 3) making a regression equation to predict the value of the response variable using the explanatory variable.The response variable is denoted as y and the explanatory variable as x. A linear function means that there is a straight line throughout the points of data in a graph. A linear function is: y = α + β (x). In this alpha (α) is the y-intercept and beta (β) is the slope.The x-axis is the horizontal axis and the y-axis is the vertical axis. The origin is the point where x and y are both 0.The y-intercept is the value of y when x = 0. In that case β(x) equals 0, only y = α remains. The y-intercept is the location where the line starts on the y-axis.The slope (β) indicates the change in y for a change of 1 in x. So the slope is an indication of how steep the line is. Generally when β increases, the line becomes steeper.When β is positive, then y increases when x increases (a positive relationship). When β is negative, then y decreases when x increases (a negative relationship). When β = 0, the value of y is constant and doesn't change when x changes. This results in a horizontal line and means that the variables are...

A multiple regression model has more than one explanatory variable and sometimes also (a) controle variable(s): E(y) = α + β1x1 + β2x2. The explanatory variables are numbered: x1, x2, etc. When an explanatory variable is added, then the equation is extended with β2x2. The parameters are α, β1 and β2. The y-axis is vertical, x1 is horizontal and x2 is perpendicular to x1. In this three-dimensional graph the multiple regression equation describes a flat surface, called a plane.A partial regression equation describes only part of the possible observations, only those with a certain value.In multiple regression a coefficient indicates the effect of an explanatory variable on a response variable, while controlling for other variables. Bivariate regression completely ignores the other variables, multiple regression only brushes them aside for a bit. This is the basic difference between bivariate and multiple regression. The coefficient (like β1) of a predictor (like x1) tells what is the change in the mean of y when the predictor is raised by one point, controlling for the other variables (like x2). In that case, β1 is a partial regression coefficient. The parameter α...

Multiple regression is also feasible for a combination of quantitative and categorical predictors. In a lot of research it makes sense to control for a quantitative variable. A quantitative control variable is called a covariate and it is studied using analysis of covariance (ANCOVA).A graph helps to research the effect of quantitative predictor x on the response y, while controlling for the categorical predictor z. For two categories, z can be the dummy variable, else more dummy variables are required (like z1 and z2). The values of z can be 1 ('agree') or 0 ('don't agree'). If there is no interaction, the lines that fit the data best are parallel and the slopes are the same. It's even possible that the regression lines are exactly the same. But if they aren't parallel, there is interaction.The predictor can be quantitative and the control variable can be categorial, but this can also be the other way around. Software compares the means. A regression model with three categories is:: E(y) = α + βx + β1z1 + β2z2, in which β is the effect of x on y for all groups z. For every additional quantitative variable a βx is added. For every additional categorical variable a dummy variable is added (or several, depending on the number of categories). Cross-product terms are added in case of interaction....

A logistic regression model is a model with a binary response variable (like 'agree' or 'don't agree'). It's also possible for logistic regression models to have ordinal or nominal response variables. The mean is the proportion of responses that are 1. The linear probability model is P(y=1) = α + βx. This model often is too simple, a more extended version is:The logarithm can be calculated using software. The odds are:: P(y=1)/[1-P(y=1)]. The log of the odds, or logistic transformation (abbreviated as logit) is the logistic regression model: logit[P(y=1)] = α + βx.To find the outcome for a certain value of a predictor, the following formula is used:The e to a certain power is the antilog of that number.A straight line is drawn next to the curve of a logistic graph to analyze it. β is maximal where P(y=1) = ½. For logistic regression the maximal likelihood method is used instead of the least squares method. The model expressed in odds is:The estimate is:With this the odds ratio can be calculated.There are two possibilities to present the data. For ungrouped data a normal contingency table suffices. For grouped data a row contains data for every count in a cel, like just one row with the number of subjects that agreed, followed by...