Descriptive Statistics PDF

- Statistics are used to make sense of numbers in research - Statistics can help make inferences and generalize results to populations - Population measures are parameters, sample measures are statistics - Each statistical test yields a p value - If p \< 0.05, you reject the nu...

- Statistics are used to make sense of numbers in research - Statistics can help make inferences and generalize results to populations - Population measures are parameters, sample measures are statistics - Each statistical test yields a p value - If p \< 0.05, you reject the null - If p \> 0.05, you do not reject/accept the null - Roll of one dice a bunch of times results in uniform distribution, ⅙ probability of rolling any number every time - Sum of rolling two dice a bunch of times results in normal distribution with a bell-shaped curve shape - Frequency distributions are a way to summarize data - Population mean is μ, sample mean is x̄ - Population st dev is σ, sample st dev is s - Measures of central tendency are mean, median, mode - Mean: add all scores and divide by number of scores, also called average - Median: middle number in a rank-ordered data set or average of the two middle values, divides the data into equal halves, often more reliable than mean for salary and household income because doesn't include extremes - Mode: value that occurs most frequently, easiest to determine by looking at freq distribution - Measures of variability are range, percentiles, variance, standard deviation, coefficient of variation - Range: subtract highest value minus lowest value - Percentile: score's position within a distribution, converts actual score to comparative, provides reference point - Variance: variation within a full set of scores - Standard deviation: measure of the amount of variation/dispersion/spread of a set of values - Coefficient of variation: ratio of standard deviation to the mean, needd when comparing different units - Many biological, psychological, and social phenomena are normally distributed, but non-normal data can still be valid. - Z scores are standardized scores - You can get percentile from z score in normal distribution - Standard error of the mean: standard deviation of a theoretical sampling distribution of the mean - Estimate is based on st. dev and sample size - As sample size increased, SEM decreases because getting closer to pop - SEM forms basis for confidence intervals - Confidence interval is a range of scores within specific boundaries - Degree of confidence is often represented by percentages (90%, 95%, 99%) - You can use the z score associated with the percentage - 90% = 1.645 - 95% = 1.96 - 99% = 2.58 - CI are more accurate than mean +/- standard deviation - Statistical inferences allow estimation of population characteristics from sample data - Assumptions are based on  - Probability: likelihood any one event will occur given all possible outcomes - Sampling error: tendency for sampling values to differ from population values - Hypothesis testing: estimation of population parameters is only one part of statistical inference. We want to see is one treatment more effective than another - Null hypothesis: stating the group means are not different or the same and that they come from the same population (=) - Goal is to test Ho - Never actually PROVE Ho - Purpose is to give data a chance to disprove - Alternative hypothesis: stating that the observed differences between parameters are not due to chance and they are different, can be directional or non-directional (not = to, greater or less than) - Type I Error: false positive, the researcher rejects the null when it is true, denoted by alpha, level of significance is 0.05 - Type II Error: false negative, the researcher does not reject the null when it is false, denoted by B, usually 20% acceptable, statistical power (1-B), sensitivity, the more sensitive a test is, the more likely it will detect important clinical differences, power is a function of alpha, variance, sample size, and effect size, design of a test procedure - Parametric statistics: used to estimate population parameters, assumes samples are randomly drawn from normal pops, homogenous variances, and scores are subject ot arithmetic manipulation - Non-parametric statistics: when parametric assumptions cannot be used, works better with smaller samples, can use measures like median, do not assume a distribution most importantly -