Statistics

Statistics Statistics: The use of math to describe, summarize, and interpret numerical data from research. 2 Types of Statistics: 1. Descriptive: used to describe and summarize research data 2. Inferential: used to interpret data and infer conclusions from research data

Descriptive Statistics (describe & summarize) Measures of Central Tendency Median: the middle score of a distribution Mean: the average score of a distribution Mode: the score that appears most frequent in a distribution Bimodal- more than 1 mode

Descriptive Statistics (describe & summarize) Measures of Variation/Dispersion Range: the difference between the highest and lowest scores in a distribution Standard Deviation: how much a score varies from the mean Variance: how far a set of scores are spread out SD²

Descriptive Statistics (describe & summarize) Graphing Data Frequency Distribution: An orderly arrangement of scores indicating the frequency of each score or group of scores. Used to summarize research data Used to make a graph Y-axis: frequency X-axis: data measure

Descriptive Statistics (describe & summarize) Histogram: a bar graph that presents data from a frequency distribution

Descriptive Statistics (describe & summarize) Frequency Polygon: a line graph that presents data from a frequency distribution Conversion of histogram into frequency polygon

Descriptive Statistics (describe & summarize) Types of Distributions 1. Normal: a symmetrical, bell-shaped distribution 2. Positive: an asymmetrical, skewed distribution 3. Negative: an asymmetrical, skewed distribution

Descriptive Statistics (describe & summarize) Normal Distribution Remember this: 68-95-99 Mean, median, and mode are the same or VERY similar

Descriptive Statistics (describe & summarize) Standard Score Z-Score: the number of standard deviations away from the mean for a particular score -z = scores below the mean +z = scores above the mean Z=X-M/SD

Descriptive Statistics (describe & summarize) Percentile Score Percentile: the distance of a score from zero Measure of relative position for comparable scores Indicates what percent of people scored below and above a given score Each 25% is known as a quartile

Descriptive Statistics (describe & summarize) Skewed Distributions Caused by outliers Outliers: extreme scores Affect measures of central tendency Since the median splits your data exactly in half, it will always fall between the mean and the mode, regardless of whether your distribution is positively or negatively skewed The mean will always be closest to the outlier

Descriptive Statistics (describe & summarize) Negative Skewed Distribution The order of the measures of central tendency are mean, median, mode Caused by an outlier with a LOW score Most scores are high Scores pile up at the high end of the scale

Descriptive Statistics (describe & summarize) Positive Skewed Distribution The order of the measures of central tendency are mode, median, mean Caused by an outlier with a HIGH score Most scores are low Scores pile up at the low end of the scale

Let’s play with candy!

INFERENTIAL Statistics (interpret & infer) Null Hypothesis (Ho): predicts no relationship between variables Alternative Hypothesis (Ha): predicts a cause and effect relationship between variables Chance: random Statistically Significant: experiment results are NOT likely due to chance P-value: calculated probability used for hypothesis testing

INFERENTIAL Statistics (interpret & infer) P-Value Probability that the results are due to chance <5/100 = <.05 = <5% When running inferential tests, if the results reveal a p-value less than .05 (p<.05), we say the results are “statistically significant” Another way to say it is “less than 5/100 (or 5%) chances that the observed results are random” Results are NOT due to chance

INFERENTIAL Statistics (interpret & infer) Hypothesis Testing When the p-value is <.05 you reject the null hypothesis because you have statistically significant results When you reject the null hypothesis you accept the alternative hypothesis There is a cause and effect relationship between the IV and DV shown by the differences between the experimental and the control groups

INFERENTIAL Statistics (interpret & infer) Making Inferences When the difference between the results of the control group and experimental groups are relatively large, we say the difference has “statistical significance” This means that the difference between the two groups did NOT happen by chance So there is a causal relationship between the IV and the DV that account for the differences in the groups