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Variance of a single variable represents the average amount that the data vary from the mean. The cross-product deviation multiplies the deviation for one variable by the corresponding deviation for the second variable. The average value of the cross-product deviation is the covariance. This is an averaged sum of combined deviation. It uses the following formula:

A positive covariance indicates that if one variable deviates from the mean, the other variable deviates in the same direction. A negative covariance indicates that if one variable deviates from the mean, the other variable deviates in the opposite direction.

Covariance is not standardized and depends on the scale of measurement. The standardized covariance is the correlation coefficient and is calculated using the following formula:

A correlation coefficient of values

Non-parametric tests can be used when the assumptions of the regular statistical tests have been violated. Non-parametric tests use fewer assumptions and are robust. A non-parametric test has less power than parametric tests if the sampling distribution is normally distributed.

Ranking the data refers to giving the lowest score the rank of 1, the next highest score a rank of 2 and so on. This eliminates the effect of outliers. It does neglect the difference in magnitude between the scores. If there are two scores that are the same, there are tied ranks. These scores are ranked by the value of the average potential rank for those scores (e.g. rank 3 and 4 will become rank 3.5).

There are several alternatives to the four most used non-parametric tests:

1. Kolmogorov-Smirnov Z
   It tests whether two groups have been drawn from the same population.

There are three main misconceptions of statistical significance:

1. A significant result means that the effect is important
   Statistical significance is not the same as practical significance.
2. A non-significant result means that the null hypothesis is true
   Rejecting the alternative hypothesis does not mean we accept the null hypothesis.
3. A significant result means that the null hypothesis is false
   If we reject the null hypothesis in favour of the alternative hypothesis, this does not mean that the null hypothesis is false, as rejection is all based on probability and there still is a probability of it not being false.

The use of NHST encourages ‘all-or-nothing’ thinking. A result is either significant or not. If a confidence interval contains zero, it could be that the population effect might be zero.

An empirical probability is the proportion of events that

The research process generally starts with an observation. After the observation, relevant theories are consulted and hypotheses are generated, from which predictions are made. After that, data is collected to test the predictions and finally the data is analysed. The data analysis either supports or does not support the hypothesis. A theory is an explanation or set of principles that is well substantiated by repeated testing and explains a broad phenomenon. A theory should be able to explain all of the data. A hypothesis is a proposed explanation for a fairly narrow phenomenon or set of observations. Hypotheses are theory-driven. Predictions are often used to move from the conceptual domain to the observable domain to be able to collect evidence. Falsification is the act of disproving a hypothesis or theory. A scientific theory should be falsifiable and explain as much of the data as possible.

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