Lecture 11

# Lecture 11 - POL2156B FOUNDATIONS OF RESEARCH STATISTICAL...

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POL2156B FOUNDATIONS OF RESEARCH STATISTICAL SIGNIFICANCE & COURSE RECAP

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LECTURE PLAN Hypothesis testing Course recap The Final Examination
DETERMINING THE ACCURACY OF YOUR RESULTS: A RECAP Researchers hardly ever want to merely describe their samples alone. They almost always want to reach conclusions about the larger population from which the sample has been drawn. Inferential statistics are crucial to reaching conclusions (making inferences ) about the larger population.

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DETERMINING THE ACCURACY OF YOUR RESULTS Whether you’re trying describe the distribution of one or many variables within a population, or trying to determine the relationship between two variables within a population, it’s critical to assess the degree of certainty with which you can say that the results you found in your sample correspond to what’s actually going on in the population you’re trying to study (even though what’s actually going on is typically unknown!). The group of statistics called tests of statistical significance allow you to determine how accurate your results are.
PROBABILITY THEORY 1. Each sample is a random sample drawn from the population.

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PROBABILITY THEORY 2. If you draw random samples repeatedly from a population, measure a single estimator (statistic) each time, you’ll find something interesting: those sample estimators, taken altogether, will be normally distributed .
WHAT’S A NORMAL DISTRIBUTION? To understand what a normal distribution is, imagine if we organized a bunch of samples according to some statistic (say, the percentage of people in the sample who said they would vote Conservative). If we order those sample percentages from lowest value (on the left) to highest value (on the right) and put them on a horizontal axis, with the frequency (the number of samples) in each category on the vertical axis, it’ll look something like this:

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THE STANDARD NORMAL DISTRIBUTION Frequency of Samples 1 Standard Deviation (68 % of samples) 2 Standard Deviations (95 % of samples) Estimator Values The true value of the statistic in the population
PROBABILITY THEORY (CONTINUED) Assumptions about the distribution of the sample proportion (or another sample statistic) continued: 3. The mean of the distribution of sample proportions from repeated samples equals the true proportion in the population. 4. The standard error (the spread of values around the mean) of the mean of sample proportions is always the same: one standard error represents 34.13% of samples in either direction from the mean of the sample proportions (roughly 68% overall), and two standard errors represent 47.73% of samples in either direction from the mean (roughly 95% overall).

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PROBABILITY THEORY (CONTINUED) The standard error is another term for the standard deviation of the mean of sample proportions. Repeated sample proportions form a normal
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## Lecture 11 - POL2156B FOUNDATIONS OF RESEARCH STATISTICAL...

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