Statistics I Success Package (All Lecture
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2025/026) University of Toronto
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Definition
- The unit normal table (or z table) tells us the proportions of the
normal distribution for a full range of z-scores
- The z-score divides into two parts
- Body: larger part
- Tall: smaller part
- Example: what proportion of scores are greater than z = 0.35?
- We technically only need one column due to the properties of the
normal distribution
- Example: what is the proportion of scores below z = 1.50?
- Tip: always helpful to draw a curve
- p(z <1.5) = 0.9332
,- p(z>1.5) = 0.0668
- Example: what z-scores separate the middle 95% of the distribution
from the remaining 5%?
- Tip: always helpful to draw a curve
- Find the score that corresponds to 0.025 in the tails!
- z = +/-1.96
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The Unit Normal Table What is Probability?
What Have We Done So Far? Interquartile Range
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Definition
- The standard error of the mean provides a measure of the
expected error between a sample mean (M) and population mean
(Mu)
- Can be referred to as SEM, SE
- The standard error is determined by (1) the size of the sample and
(2) the standard deviation of the population
- As sample size increases, the error between the sample mean and
population mean decreases
- The Law of Large Number states that if we collect many, many
observations, the average population mean increases
- Standard error decreases with bigger sample sizes
- When n = 1 (e.g., the smallest sample), stigma = stigma
- The population standard deviation acts as the "starting point" for
,standard error
- The standard error provides and estimate for the precision of your
estimate of the population mean
- Often reported when describing your samples and in graphs
- Note that error bars do not always represent standard error
- Important to confirm what they are depicting!
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The Axioms of Probability Learning Check
Effect Size Standard Error
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Definition
- NHST is somewhat analogous to the criminal system
- We need to determine guilt "beyond a reasonable doubt"
- Example: should prison sentences be based on crimes that have
not been committed?
- What happens when standards are made more stringent? More
lenient?
- What would be the analogous concept of "standards" in hypothesis
testing?
- What would be analogous to a false positive? False negative?
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, Usage of the Normal Distribution Types of Frequency Distributions?
Trial of the Null Hypothesis Measure of Central Tendency?
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Definition
- We need to actually report our results and talk about how it relates
back to our hypotheses
- We will introduce formal APA style when we talk about t-tests next
lecture
- Note that we usually only read about this step when research is
reported
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Types of Frequency Distributions? Step 5: Report and Summarize
Usage of the Normal Distribution Standard Deviation
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Definition