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Chapter 2

PSYC 2040 Chapter Notes - Chapter 2: Repeated Measures Design, Central Limit Theorem, Standard Deviation


Department
Psychology
Course Code
PSYC 2040
Professor
Naseem Al- Aidroos
Chapter
2

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Chapter 2 – The t-test
General Rationale
- Two main questions the test explores:
- How reasonable it is to assume that a sample originated from a population with a given
mean
- How reasonable it is that the two samples came from populations with identical means
- Standard normal distribution such that 95% of the area lies between – 1.96 and + 1.96
would be significant at the .05 (probability of a type 1 error at this level is .05)
- Standard normal distribution such that 99% of the area lies between – 2.58 and + 2.58
would be significant at the .01 level (probability of a type 1 error at this level is .01
Inferences Involving a Single Sample Mean
- Used to determine how likely it is that a sample with a given mean (statistic) could
originate from a population with a given mean (parameter)
- Can only do this if it is normally distributed, if the sample is large enough you can
assume it is because of the central limit theorem
- If the standard deviation is unknown it can be calculated from the sample data, this
standard deviation is then referred to as the biased estimate
Inferences Involving Two Sample Means
- Used to determine if the difference between two sample means was large enough to
suggest that the two samples were drawn from populations with different means
- Use the critical ratio equation to determine if they are truly different, and if so at what
level (.05, .01, .001)
- * note critical ratio is no longer used
The Density Function for t
- The density function is an equation that describes that shape of the distribution and can
be used to determine the area under the curve between any two points
- The equation has two variables df and t
- The nature of the function changes as a function of df, as df increases the t distribution
get more like the standard normal distribution
Determining is Variances are Heterogeneous or Homogenous
- F-Ratio used to determine whether or not the variances in the underlying populations are
the same or different
- SPSS uses levenes to test this
Probability Values and One and Two Tailed Tests
- One-Tailed test: only concerned about differences in one direction (either positive or
negative), significance gets divided by two
- Two-Tailed: concerned with either a positive or negative outcome
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