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Introduction to Inferential Statistics

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**1. **Introduction toInferential Statistics

**2. **Inferential statistics Go beyond simple evaluations, such as comparing proportions or calculating a correlation (r)
Inferential statistics allow us to legitimately “generalize” our findings – apply the results from a sample to a population
We must sample from a population, using probability (e.g., random) sampling
If our sample is a population, we cannot use these methods.

**3. **Review: Sample and Population Population: the entire group
Sample: a subset
Sample statistic
Percentage
Proportion
Mean
Standard deviation
Population parameter: Corresponding measures that we usually do not know

**4. **General Procedure We use a statistic (for example, the r or correlation statistic) to calculate a relationship between variables
The computer determines whether the results are sufficiently large to overcome the “null hypothesis”
Null hypothesis: Assumption that any apparent relationship between variables is caused by chance, not by the effect of the independent variable on the dependent variable.
“Caused by chance”: For no observable (“empirical”) or scientifically demonstrated reason. For example, lunar cycles and homicides

**5. **Details The statistic we use to measure association between variables (say, the r statistic) will never be zero – there will always be a numerical result, perhaps small, perhaps large.
This result will always be the sum of two components:
“Error” effect caused by the sampling process itself: that portion of an association between variables... that is due to chance alone
“Systematic” or real effect: that portion of an association that is caused by the influence of the independent variable on the dependent variable