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Stats Terms
| Term | Definition |
|---|---|
| Descriptive Statistics | Used to summarize, simplify, and present data |
| Central tendency | Measure used to determine a single score that best defines the center of a distribution |
| mean, median, and mode | Three major groups of central tendency |
| Arithmetic mean | The sum of the scores divided by the number of scores |
| Different types of means | Harmonic, Trimmed, Geometric, midmean |
| Midmean | Arithmetic mean of 50% of scores |
| Median | The middle score that divides a distribution in half so that 50% of the scores fall above or below the median |
| Different types of medians | Midrange, Midhinge, Trimean |
| Mode | Score or category with the greatest frequency |
| Different types of modes | Minor mode, Crude, Refined |
| Positive skew | The data tends to be more frequent on the lower ends of the x-axis, and less frequent on the higher ends of the x-axis |
| Negative skew | There is more frequency in the scores in the higher end, and less scores on the lower end of the scale |
| Variability (dispersion) | The degree to which scores in distribution are spread out or clustered together |
| Range | Distance between the largest scores and the smallest score in a distribution |
| Interquartile Range (IQR) | First breaks down the distribution into quartiles and then subtracts the value from the third quartile versus the first quartile |
| First Quartile | Defines the lowest 25% of a distribution |
| Second Quartile | Defines the center of a distribution |
| Third Quartile | Defines the upper 25% of a distribution |
| Sum of squares | The numerator in the variance |
| Variance | Sum of squares divided by the number of cases |
| Standard Deviation | Square root of the variance |
| Difference between populations and samples: | having n-1 for the sample and N for the population |
| Bessel's Correction | When you end with a systematically smaller denominator for the sample formulas, so the smaller denominators will produce a larger overall variance and SD term, thus making it more accurate estimate of the population parameters |
| Normal Distribution | Described with 2 parameters (shaper parameters)- mean and SD |
| Normal Distributions properties | Symmetrical, Unimodal, Asymptotic |
| Skew | Describes the symmetry of the distribution |
| Kurtosis | Describes the peak of the distribution as well as the tails |
| Leptokurtic (positive kurtosis) | Distribution with heavier tails and a higher peak |
| Platykurtic (negative kurtosis) | Distribution with a flattened center and a lighter tails |
| Z-scores | Communicates information about the score, mean, and standard deviation in a single value and are the primary way to standardize (put on the same scale/units) |
| Formula for calculating z-score | Z= raw score-mean/standard deviation |
| Probability | The degree of plausibility of a proposition given the information available |
| Bayes Theorem | A way to calculate the probability that our hypothesis is correct given the evidence |
| Likelihood | How likely is it to get some data given a particular hypothesis? |
| Prior | How probable was our hypothesis BEFORE the data? |
| Posterior | How probable is our hypothesis given the observed evidence? |
| Marginal | How probable is the new evidence under ALL possible considerations? |
| Likelihood ratio | Ratio of likelihoods at fixed parameter values |
| Bayes factor | Ratio of MARGINAL likelihood (averaged over priors) |
| Random sampling error | When a random sample is selected, one never knows exactly what the sample will look like |
| Denominator of the hypothesis test | Where is the standard error going to be found? |
| Large | If you have a really SMALL SAMPLE, what will the standard error be? |
| Small | If you have a LARGE SAMPLE with a small SD what will the standard error be? |
| Central limit theorem | Predicts the shape of a sampling distribution based on the sample size |
| Conceptual benchmarks | Null Hypothesis (H0), Alternative Hypothesis (HA or H1) |
| Null Hypothesis | There is no effect in the population or that things are equal- the irritating child that says the opposite of whatever you say |
| Alpha | Probability of rejecting the null hypothesis when it is true Function: A numerical benchmark that we can compare our p-value |
| P-value | The probability of the observed result, plus more extreme results, if the null hypothesis were true |
| p-value, alpha, null | Use the ___ to compare to ___ to make a statement about the ___ |
| T distributions | Generate values to find the same types of probabilities. -Represents a family of curves with a different shape at each degree of freedom |
| Type 1 error | Rejecting the null hypothesis when it is actually true (false positive) |
| Type 2 error | Failing to reject the null hypothesis when it is actually false |
| Effect sizes | A concept that measures the strength of the relationship between two variables on a numeric scale. |
| Confidence Interval | A range of values that are expected to capture the parameter of interest |
| David Hume | Person that said eyewitness testimony could never prove a miracle happened because they violate natural laws |
| Reverend Thomas Bayes | Created a probability equation that later became known as Bayes rules/ Bayes theorem |
| Richard Price | Realized the importance of Bayes work and after reworking some things had it published |
| Pierre-Simon, marquis de Laplace | Independently created the same probability theorem but much more worked out and detailed |
| Prior odds x Likelihood Ratio | Bayes theorem in the odds form (posterior odds) |
| The formula is the standard deviation of the sample divided by the square root of the sample size | Calculation of the standard error of the means |
| William Sealy Gosset (aka student) Students t-test | Specifies the sampling distribution of the test statistic t |
| Correlation | A number that represents the strength of the linear association between two variables |
| Covariance | As X is changing, how does Y change? -> raw differences in X relative to Y |
| Positive Correlation | Values on the two variables tend to make in the same direction -As scores on one variable go up, scores on the other variable go up as well |
| Standard error | A sense of variability in the sample mean |
| Negative Correlation | Values on the two variables move in opposite directions -As scores on one variable go up, scores on the other variable go down |
| The stronger the association | The further away from zero... |
| the degree of linear association | What does the value of r tell us? |
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