# Relationship between z score and interpretation

### How do I interpret Z-Score Data In SPSS?

Z-scores are a useful way to combine scores from data that has different means, ranges, and If the middle is between two values, the difference is split. Definition of z-score, from the Stat Trek dictionary of statistical terms and concepts . This statistics The statistics dictionary will display the definition, plus links to related web pages. Select term: Here is how to interpret z-scores. A z-score. Z-scores are linearly transformed data values having a mean of zero and a here is that standardizing scores facilitates the interpretation of a single test score .

Whilst Sarah has still scored much higher than the mean score, she has not necessarily achieved one of the best marks in her class. How well did Sarah perform in her English Literature coursework compared to the other 50 students? Before answering this question, let us look at another problem. Join the 10,s of students, academics and professionals who rely on Laerd Statistics.

In the next academic year, he must choose which of his students have performed well enough to be entered into an advanced English Literature class. He decides to use the coursework scores as an indicator of the performance of his students. Therefore, we are left with two questions to answer.

First, how well did Sarah perform in her English Literature coursework compared to the other 50 students? Whilst it is possible to calculate the answer to both of these questions using the existing mean score and standard deviation, this is very complex. Therefore, statisticians have come up with probability distributions, which are ways of calculating the probability of a score occurring for a number of common distributions, such as the normal distribution.

### What is a Z score What is a p-value

In our case, we make the assumption that the students' scores are normally distributed. When the absolute value of the Z score is large in the tails of the normal distribution and the probabilities are small, you are seeing something unusual and generally very interesting. For the Hot Spot Analysis tool, for example, "unusual" means either a statistically significant hot spot or a statistically significant cold spot.

The Null Hypothesis Many of the statistics in the spatial statistics toolbox are inferential spatial pattern analysis techniques i. Inferential statistics are grounded in probability theory. Probability is a measure of chance, and underlying all statistical tests either directly or indirectly are probability calculations that assess the role of chance on the outcome of your analysis. Typically, with traditional non-spatial statistics, you work with a random sample and try to determine the probability that your sample data is a good representation is reflective of the population at large.

As an example, you might ask: When you compute a statistic the meanfor example for the entire population, you no longer have an estimate at all. You have a fact. Consequently, it makes no sense to talk about "likelihood" or "probabilities" any more.

## Statistics Dictionary

So what can you do in the case where you have all data values for a study area? You can only assess probabilities by postulating, via the null hypothesis, that your spatial data are, in fact, part of some larger population.

Where appropriate, the tools in the spatial statistics toolbox use the randomization null hypothesis as the basis for statistical significance testing.

The randomization null hypothesis postulates that the observed spatial pattern of your data represents one of many n!

If you could pick up your data values and throw them down onto the features in your study area, you would have one possible spatial arrangement. The randomization null hypothesis states that if you could do this exercise pick them up, throw them down infinite times, most of the time you would produce a pattern that would not be markedly different from the observed pattern your real data.

Once in a while you might accidentally throw all of the highest values into the same corner of your study area, but the probabilities of doing that are small. The randomization null hypothesis states that your data is one of many, many, many possible versions of complete spatial randomness. The data values are fixed; only their spatial arrangement could vary. A common alternative null hypothesis, not implemented for the spatial statistics toolbox, is the normalization null hypothesis.

The normalization null hypothesis postulates that the observed values are derived from an infinitely large, normally distributed population of values through some random sampling process.