Scatterplots provide descriptive information on the direction, form, and strength of the relationship between the two variables by representing individuals as points on a two-dimensional graph. These points may aggregate to describe a linear relationship, curvilinear relationship, or no relationship. Scatterplots may also indicate whether there is positive or negative association between variables, and suggest the strength of their relationship.
A positive association means that high values in one variable are associated with high values in the other variable, whereas a negative association shows that high values in one variable are associated with low values in the other variable e. The Pearson product moment correlation coefficient can be calculated to quantify a linear relationship between two quantitative variables.
These coefficients take values between -1 and 1, where values closer to 0 indicate weak relationships, and values closer to 1 or -1 indicate stronger relationships.
Positive values show a positive association, whereas negative values show a negative association of the two variables. The narrated presentation provides more details on the interpretation of scatterplots and correlation coefficients. The software tutorials demonstrate how to generate scatterplots and to compute the Pearson product moment coefficient in SPSS.
Simple linear regression allows researchers to predict or explain the variance of a response variable using a predictor variable. For instance, simple linear regression may be used in educational research to predict college GPA based on SAT scores. The narrated presentation bellow provides an introduction to the topic of simple linear regression.
It discusses basic concepts related to simple linear regression, the assumptions on which this procedure is based, and how to interpret and use the regression equation. The software tutorial demonstrates how to conduct a simple linear regression in SPSS. The chi-square test is used to determine whether there is a statistically significant association between two or more categorical variables.
For instance, educational researchers may want to determine whether the proportions of students preferring online instruction and face to face instruction differ significantly across undergraduate and graduate students.
This procedure allows researchers to compare categorical variables across more than two groups and uses the chi-square statistic to determine statistical significance.
The following narrated presentation describes the properties of the chi-square distribution and explains how to conduct and interpret the results of chi-square tests. The software tutorial demonstrates how to conduct this procedure in SPSS. ANOVA is comparing the variation of means across several samples to the variations of scores within each sample.
It allows researchers to compare more than two groups, and uses the F statistic to determine statistical significance. Improve Article. Like Article. Previous Scales of Measurement. Next Mathematics Hypergeometric Distribution model. Recommended Articles. Article Contributed By :. The AIC function is 2K — 2 log-likelihood. Lower AIC values indicate a better-fit model, and a model with a delta-AIC the difference between the two AIC values being compared of more than -2 is considered significantly better than the model it is being compared to.
The Akaike information criterion is a mathematical test used to evaluate how well a model fits the data it is meant to describe. It penalizes models which use more independent variables parameters as a way to avoid over-fitting. AIC is most often used to compare the relative goodness-of-fit among different models under consideration and to then choose the model that best fits the data.
If any group differs significantly from the overall group mean, then the ANOVA will report a statistically significant result. Significant differences among group means are calculated using the F statistic, which is the ratio of the mean sum of squares the variance explained by the independent variable to the mean square error the variance left over.
If the F statistic is higher than the critical value the value of F that corresponds with your alpha value, usually 0. If you are only testing for a difference between two groups, use a t-test instead. The formula for the test statistic depends on the statistical test being used. Generally, the test statistic is calculated as the pattern in your data i. Linear regression most often uses mean-square error MSE to calculate the error of the model.
MSE is calculated by:. Linear regression fits a line to the data by finding the regression coefficient that results in the smallest MSE. Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line.
Both variables should be quantitative. For example, the relationship between temperature and the expansion of mercury in a thermometer can be modeled using a straight line: as temperature increases, the mercury expands. This linear relationship is so certain that we can use mercury thermometers to measure temperature. A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line or a plane in the case of two or more independent variables.
A regression model can be used when the dependent variable is quantitative, except in the case of logistic regression, where the dependent variable is binary. A t-test should not be used to measure differences among more than two groups, because the error structure for a t-test will underestimate the actual error when many groups are being compared.
A one-sample t-test is used to compare a single population to a standard value for example, to determine whether the average lifespan of a specific town is different from the country average. A paired t-test is used to compare a single population before and after some experimental intervention or at two different points in time for example, measuring student performance on a test before and after being taught the material. A t-test measures the difference in group means divided by the pooled standard error of the two group means.
In this way, it calculates a number the t-value illustrating the magnitude of the difference between the two group means being compared, and estimates the likelihood that this difference exists purely by chance p-value. Your choice of t-test depends on whether you are studying one group or two groups, and whether you care about the direction of the difference in group means.
If you are studying one group, use a paired t-test to compare the group mean over time or after an intervention, or use a one-sample t-test to compare the group mean to a standard value. If you are studying two groups, use a two-sample t-test. If you want to know only whether a difference exists, use a two-tailed test. If you want to know if one group mean is greater or less than the other, use a left-tailed or right-tailed one-tailed test. A t-test is a statistical test that compares the means of two samples.
It is used in hypothesis testing , with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero. Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test.
Significance is usually denoted by a p -value , or probability value. Statistical significance is arbitrary — it depends on the threshold, or alpha value, chosen by the researcher.
When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant. A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.
The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis.
Different test statistics are used in different statistical tests. The measures of central tendency you can use depends on the level of measurement of your data. Ordinal data has two characteristics:. Nominal and ordinal are two of the four levels of measurement. Nominal level data can only be classified, while ordinal level data can be classified and ordered. If your confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If your confidence interval for a correlation or regression includes zero, that means that if you run your experiment again there is a good chance of finding no correlation in your data. In both of these cases, you will also find a high p -value when you run your statistical test, meaning that your results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.
If you want to calculate a confidence interval around the mean of data that is not normally distributed , you have two choices:. The standard normal distribution , also called the z -distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.
Any normal distribution can be converted into the standard normal distribution by turning the individual values into z -scores. In a z -distribution, z -scores tell you how many standard deviations away from the mean each value lies. The z -score and t -score aka z -value and t -value show how many standard deviations away from the mean of the distribution you are, assuming your data follow a z -distribution or a t -distribution. These scores are used in statistical tests to show how far from the mean of the predicted distribution your statistical estimate is.
If your test produces a z -score of 2. The predicted mean and distribution of your estimate are generated by the null hypothesis of the statistical test you are using. The more standard deviations away from the predicted mean your estimate is, the less likely it is that the estimate could have occurred under the null hypothesis. To calculate the confidence interval , you need to know:. Then you can plug these components into the confidence interval formula that corresponds to your data.
The formula depends on the type of estimate e. The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way. The confidence interval is the actual upper and lower bounds of the estimate you expect to find at a given level of confidence.
These are the upper and lower bounds of the confidence interval. Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable. These categories cannot be ordered in a meaningful way.
For example, for the nominal variable of preferred mode of transportation, you may have the categories of car, bus, train, tram or bicycle. The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average. Statistical tests commonly assume that:. If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.
Measures of central tendency help you find the middle, or the average, of a data set. Some variables have fixed levels. For example, gender and ethnicity are always nominal level data because they cannot be ranked. However, for other variables, you can choose the level of measurement. For example, income is a variable that can be recorded on an ordinal or a ratio scale:.
If you have a choice, the ratio level is always preferable because you can analyze data in more ways. The higher the level of measurement, the more precise your data is. The level at which you measure a variable determines how you can analyze your data. Depending on the level of measurement , you can perform different descriptive statistics to get an overall summary of your data and inferential statistics to see if your results support or refute your hypothesis.
Levels of measurement tell you how precisely variables are recorded. There are 4 levels of measurement, which can be ranked from low to high:. The p -value only tells you how likely the data you have observed is to have occurred under the null hypothesis. The alpha value, or the threshold for statistical significance , is arbitrary — which value you use depends on your field of study.
In most cases, researchers use an alpha of 0. P -values are usually automatically calculated by the program you use to perform your statistical test. Having an idea of the type of questions you might be asked during a business analyst interview will not only give you confidence but it will also help you to formulate your thoughts and to be better prepared to answer the interview questions you might get during the interview for a business analyst position.
Of course, just memorizing a list of business analyst interview questions will not make you a great business analyst but it might just help you get that next job.
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