Descriptive statistics

Why is statistics important in research?

Statistics describes data

• Application of mathematical methods to reach conclusions about the world made from observations (experiments) 

• Allows to make accurate inferences from incomplete observations

What is descriptive statistics?

describe data only 

• No manipulation, no comparing data 

• Presenting the numbers 

• Mean, median, mode (how does the data fall in the middle) 

• Need to get descriptive stats. First to do inferential

What is inferential statistics?

Apply specific test to make an inference in regards to the experiment 

• Is it due to chance? Or is it based on experimental manipulation 

• Is sample representative of population? 

• P value = level of significance  

• Reject/fail to reject null hypothesis  

• Used to make conclusion 

What are the measures of central tendency?

1. Mode = most frequent data point (most frequent in distribution) 

• Not always near the center of data 

• Useful to report most common outcome 

• Highest peak on skewed distribution 

2. Median = physically middle number 

• The value above which there are as many scores as below it 

• Divides a rank-ordered distribution into 2 equal halves 

• Between mode and mean in skewed distribution (resistant to outliers) 

3. Mean = sum set of scores divided by the number of scores 

• Represented by X-bar 

• Average 

• Closest to skewed area (most impacted) 

• Gets pulled (NOT resistant to outliers) 

What is an outlier? what does it do to central tendency

An observation that falls well above/below the overall bulk of the data 

• Skews data towards its direction 

• Mean is the most impacted by outliers 

• Therefore, should use median (resistant to outliers) 

• Median is RESISTANT to outliers 

What are the measures of variability

Range & standard deviation

Define range

Difference between the largest and smallest value 

• Subtract the highest from the lowest 

• Every data point is within a __ range from each other 

Define standard deviation

The typical value of how far the data fall from the mean, by summarizing the deviation from the mean 

• Uses all the data to describe the spread 

• SD = X – X-bar (mean) 

• Deviation from every data point, from the mean 

• Often shown as error bars in research 

How do you find SD

1^st get the deviation for each data point (*find mean first if not provided) 

2^nd square every point (deviation squared) 

3^rd sum up all of the deviations squared to get sum of squares  

4^th determine N-1 (N = number of observations) 

5^th divide sum of squares by N-1 

6^th take the square root of sum of squares/N-1 

How do you use coefficient of variation to compare variability between groups?

Coefficient of variation = measure of variability that is the ratio of the SD to the mean

A low CV means that there is little variation from the mean (smaller range) 

• Low CV = little variability 

A high CV means that there is a lot of variation from the mean (bigger range) 

• High CV = more variable 

Describe the characteristics of normal distribution. (shape, empirical rule, area under the curve, z-scores)

1. Shape = bell curve (where the majority of the data is around the center/mean 

• Mean, median, and mode are the same (because symmetrical) 

• Found in nature (manifested in biology, psychologically, and socially) 

2. The empirical rule (std deviation units) =  standard deviations away from the mean you can expect to see % of the data. Meaning that % of the data will fall in SD of the mean 

• Majority of data falls in 3 SD of the mean 

• What % of the data falls in __ of the SD 

3. Area under the curve =  

• 68.2% of the data will fall in 1 standard deviation of the mean 

• 95.5% of the data will fall in 2 standard deviations of the mean 

• 99.7% of the data will fall in 3 standard deviations of the mean 

4. Z-scores = Expressing scores (values) in terms of standard deviation units 

• The exact standard deviation from the mean 

• Below the mean = negative z-score 

• Above the mean = positive z-score 

• (X – X-bar)/SD 

How do you calculate coefficient of variation

CV = (s/mean)*100