quiz 1 Flashcards
Measures to condense data
descriptive stats
Measures to condense data include frequency distributions, frequency counts, graphic presentations and percentages
measures of central tendency
descriptive stats
Measures of Central Tendency describe the average or common value for a group of data. This includes measurements of mode, median and mean, which reduce the frequency distributions to single numbers.
measures of variability
descriptive stats
Measures of Variability or Spread show what the spread is like within a distribution of values. Common measures of variability include the range, interquartile percentile, standard deviation and variance.
confidence interval
range of values likely to occur with a degree of confidence (expressed as a percentage)
A 95% confidence interval is a range of values (upper and lower) that you can be 95% certain contains the true mean of the population.
P values
Thepvalue, or probability value, tells you how likely it is that your data could have occurred under the null hypothesis. Thepvalue gets smaller as the test statistic calculated from your data gets further away from therangeof test statistics predicted by the null hypothesis.
Pvalues are used inhypothesis testingto help decide whether to reject the null hypothesis. The smaller thepvalue, the more likely you are to reject the null hypothesis.
Thepvalue is a proportion: if yourpvalue is 0.05, that means that 5% of the time you would see a test statistic at least as extreme as the one you found if the null hypothesis was true.
P values and statisical signifcant
Pvalues are most often used by researchers to say whether a certain pattern they have measured is statistically significant.
Statistical significanceis another way of saying that thepvalue of a statistical test is small enough to reject the null hypothesis of the test.
The most common threshold isp <0.05; that is, when you would expect to find a test statistic as extreme as the one calculated by your test only 5% of the time. Meaning the test has produced a significant result.
In general, if an observed result is statistically significant at a P-value of 0.05, then the null hypothesis should not fall within the 95% CI.
A 95% confidence interval = p value of 0.05
null hypothesis
predicts no effect
alternative hypothesis
predicts an effect
type I error
A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is actually true in the population;
type II error
a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population.
Nominal
levels of measurement
you can categorize your data by labelling them in mutually exclusive groups, but there is no order between the categories.
* City of birth
* Gender
* Ethnicity
* Car brands
* Marital status
Ordinal
levels of measurement
You can categorize and rank your data in an order, but you cannot say anything about the intervals between the rankings.
Although you can rank the top 5 Olympic medallists, this scale does not tell you how close or far apart they are in number of wins.
- Top 5 Olympic medallists
- Language ability (e.g., beginner, intermediate, fluent)
- Likert-type questions (e.g., very dissatisfied to very satisfied)
Interval
levels of measurement
You can categorize, rank, and infer equal intervals between neighboring data points, but there is no true zero point.
The difference between any two adjacent temperatures is the same: one degree. But zero degrees is defined differently depending on the scale – it doesn’t mean an absolute absence of temperature.
The same is true for test scores and personality inventories. A zero on a test is arbitrary; it does not mean that the test-taker has an absolute lack of the trait being measured.
- Test scores (e.g., IQ or exams)
- Personality inventories
- Temperature in Fahrenheit or Celsius
Ratio
levels of measurement
You can categorize, rank, and infer equal intervals between neighboring data points, and there is a true zero point.
A true zero means there is an absence of the variable of interest. In ratio scales, zero does mean an absolute lack of the variable.
For example, in the Kelvin temperature scale, there are no negative degrees of temperature – zero means an absolute lack of thermal energy.
- Height
- Age
- Weight
- Temperature in Kelvin
interquartile range
measures of dispersion
Interquartile range is defined as the difference between the 25th and 75th percentile (also called the first and third quartile). Hence the interquartile range describes the middle 50% of observations
standard deviation
measures of dispersion
Standard deviation (SD) is the most commonly used measure of dispersion. It is a measure of spread of data about the mean. SD is the square root of sum of squared deviation from the mean divided by the number of observations.
The reason why SD is a very useful measure of dispersion is that, if the observations are from a normal distribution, then[3] 68% of observations lie between mean ± 1 SD 95% of observations lie between mean ± 2 SD and 99.7% of observations lie between mean ± 3 SD
