When there are only one or two degrees of freedom, the chi-square distribution is shaped like a backwards ‘J’. When there are three or more degrees of freedom, the distribution is shaped like a right-skewed hump. As the degrees of freedom increase, the hump becomes less right-skewed and the peak of the hump moves to the right. The distribution becomes more and more similar to a normal distribution.
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 analyse 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 analyse 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:
Statistical analysis is the main method for analyzing quantitative research data. It uses probabilities and models to test predictions about a population from sample data.
The null hypothesis is often abbreviated as H0. When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).
The alternative hypothesis is often abbreviated as Ha or H1. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).
As the degrees of freedom increase, Student’s t distribution becomes less leptokurtic, meaning that the probability of extreme values decreases. The distribution becomes more and more similar to a standard normal distribution.
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