Levels of measurement
● Categorical: categories with no logical order
○ Ex: gender, voting, behavior
● Ordinal: categories with order but distance isn’t meaningful
○ Ex: highest level of qualification
● Interval: numbers with no absolute zero
○ Ex: IQ score
● Ratio: numbers with meaningful zero point
○ Ex: reaction time, number of siblings
Types of Data:
● Continuous: can take any value of range
○ Ex: heigh, speed
● Discrete: can only take certain values
○ Ex: number of people
Types of Study:
● Case study: detailed study of a specific person
○ Can’t use statistics and cannot generalize
● Quasi-experimental: allows independent and dependent variable to vary naturally
● Experimental: manipulation of independent variable, then allows dependent variable to vary
naturally
Within vs Between experiments
● Within: each person takes part in each condition
● Between: each person only takes part in one condition
Sampling distribution
● Sampling distribution of the mean: distribution of all possible sample means
○ Has a normal distribution
● Two rules
○ Mean of sample means = population mean
○ Standard deviation of sample means = standard deviation of the population/sqrt(sample
size)
● The larger the sample size, the narrower the distribution of sample means
Standard error: standard deviation of the sampling distribution of the mean → can estimate from a
sample → how accurate is our sample mean relative to the population mean
●
● Standard error decreases as sample size increases
● Interpreting standard error
, ○ We can be 68% confident that the population mean lies within 1 standard error of the
sample mean
Confidence intervals: gives an interval of plausible values for a parameter
● Interpreting a confidence interval (95%)
○ We are 95% confident that the interval [x,x] captures (tested hypothesis).
○ Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the
population mean.
○ 95% chance that a normally-distributed quantity will fall within 1.96 standard deviations
of the mean
● Formula relies on accurately calculated population standard deviation (which is unknown) →
uses sample standard deviation as an estimate
○ When sample size is small → underestimate the variability of the data, so you use the
T-distribution
Hypothesis Testing
● Null Hypothesis (H0): alternative hypothesis is not true and observed value is consistent with
chance → “no difference”
● Alternative hypothesis (Ha): observed value is the result of a real effect, not just chance
P-values
● P-value: probability, assuming that H0 is true, that the statistic will take a value at least as
extreme as the observed results specified by H0
○ If p-value is very small, it is unlikely that the observed value would be so extreme if the
null hypothesis were true
● Alpha: controls type I error → we are willing to accept a Type I error about 5% of the time
● If p-value is smaller than alpha → results of the study are statistically significant
○ P-value < 0.05, then we reject the null hypothesis
○ P-value > 0.05, then we fail to reject null hypothesis
● P-value is not:
○ Evidence that the alternative hypothesis is TRUE
○ Evidence that the null hypothesis is TRUE
○ A measure of the size of an effect, or the importance of the result
● Categorical: categories with no logical order
○ Ex: gender, voting, behavior
● Ordinal: categories with order but distance isn’t meaningful
○ Ex: highest level of qualification
● Interval: numbers with no absolute zero
○ Ex: IQ score
● Ratio: numbers with meaningful zero point
○ Ex: reaction time, number of siblings
Types of Data:
● Continuous: can take any value of range
○ Ex: heigh, speed
● Discrete: can only take certain values
○ Ex: number of people
Types of Study:
● Case study: detailed study of a specific person
○ Can’t use statistics and cannot generalize
● Quasi-experimental: allows independent and dependent variable to vary naturally
● Experimental: manipulation of independent variable, then allows dependent variable to vary
naturally
Within vs Between experiments
● Within: each person takes part in each condition
● Between: each person only takes part in one condition
Sampling distribution
● Sampling distribution of the mean: distribution of all possible sample means
○ Has a normal distribution
● Two rules
○ Mean of sample means = population mean
○ Standard deviation of sample means = standard deviation of the population/sqrt(sample
size)
● The larger the sample size, the narrower the distribution of sample means
Standard error: standard deviation of the sampling distribution of the mean → can estimate from a
sample → how accurate is our sample mean relative to the population mean
●
● Standard error decreases as sample size increases
● Interpreting standard error
, ○ We can be 68% confident that the population mean lies within 1 standard error of the
sample mean
Confidence intervals: gives an interval of plausible values for a parameter
● Interpreting a confidence interval (95%)
○ We are 95% confident that the interval [x,x] captures (tested hypothesis).
○ Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the
population mean.
○ 95% chance that a normally-distributed quantity will fall within 1.96 standard deviations
of the mean
● Formula relies on accurately calculated population standard deviation (which is unknown) →
uses sample standard deviation as an estimate
○ When sample size is small → underestimate the variability of the data, so you use the
T-distribution
Hypothesis Testing
● Null Hypothesis (H0): alternative hypothesis is not true and observed value is consistent with
chance → “no difference”
● Alternative hypothesis (Ha): observed value is the result of a real effect, not just chance
P-values
● P-value: probability, assuming that H0 is true, that the statistic will take a value at least as
extreme as the observed results specified by H0
○ If p-value is very small, it is unlikely that the observed value would be so extreme if the
null hypothesis were true
● Alpha: controls type I error → we are willing to accept a Type I error about 5% of the time
● If p-value is smaller than alpha → results of the study are statistically significant
○ P-value < 0.05, then we reject the null hypothesis
○ P-value > 0.05, then we fail to reject null hypothesis
● P-value is not:
○ Evidence that the alternative hypothesis is TRUE
○ Evidence that the null hypothesis is TRUE
○ A measure of the size of an effect, or the importance of the result
