1. Statistics

2. 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

3. 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

4. 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

5. 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

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

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

8. 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

9. Descriptive Statistics (describe & summarize)
Normal Distribution
Remember this:
Mean, median, and mode are the same or VERY similar

10. 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

11. 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

12. 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

13. 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

14. 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

15. Let’s play with candy!

16. 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

17. 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

18. 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

19. 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