OT 580 Research: Understanding Descriptive Statistics and Data Analysis Techniques

descriptive statistics are used to....

describe and summarize a distribution of data

what is the advantage of descriptive statistics?

describe a whole lot of numbers in a sample with a few numbers

when indices are calculated from a sample they are called....

statistics

when the numbers are derived from the population they are called....

parameters

frequency distribution

an arrangement of data that indicates how often a particular score or observation occurs

ex.

score frequency

20 1

30 1

33 2

35 1

40 2

43 1

group frequency distribution

score frequency

20-29 1

30-39 3

40-49 6

50-59 7

how to make frequency distribution more readable?

graphing techniques (bar graphs, pie graphs...)

normal curve

symmetrical bell-shaped graph

draw out a normal curve

w/ standard deviations/z scores

percentiles

IQ/DQ scores

T-scores

percentile ranks (advantage & disadvantage) EXAMPLE

represents the number of participants who achieved a lower score

advantage

easy to explain to people

disadvantage

percentiles lie, over-estimate differences toward the middle and underestimate differences toward the extreme

EXAMPLE

5'11 ---> 6'4 (5 percentiles between)

6'4 ---> 6'10 (1 percentile between)

standard scores (advantage & example)

when a score is converted to a standard score, the transformed score indicates the examinee's position in terms of standard deviations from the mean

advantage

represent a scale of measurement that is the same scale of the raw scores

EXAMPLES

Z-scores: Mean= 0, SD= 1

T scores: multiple z-score by 10 and add 50

IQ scores: mean of 100, SD=15

what is the most common used standard score and define it

z-score; expresses how far a score is from the mean in SD units

draw a negative and positive skewed distribution

positively= right-skewed (more Cs & Ds)

negatively= left-skewed (more As & Bs)

list the measures of central tendency (advantages/disadvantages)

mode

category or score that occurs most frequently

advantage- easy to identify

disadvantage- vary from sample to sample, doesn't use all the numbers in distribution, not useful for other techniques

median

score that divides a distribution in half when the data has been ordered high to low

advantage- not affected by outliers (useful when distribution contains outliers)

disadvantage- hard to use in quantitative statistics

mean

advantages- least susceptible to sampling fluctuation (good estimate) and can be used in many statistical procedures

disadvantages- effected by outliers

what is multimodal?

when a distribution has two or more modes

what are measures of variability?

range, variance, standard deviation

what is disadvantage of central tendencies?

often presents incomplete picture of distribution of data (ex. two distributions might have identical means and medians)

EXAMPLE:

1, 2, 50, 99, 100

47, 49, 50, 51, 52

describe range and its disadvantages

subtracting lowest score from highest score

can be misleading because of outliers

describe variance

reflects the variation of the distribution within a full set of scores (calculated by obtaining the sum of squares and dividing it by N-1)

describe standard deviation

expressed in the same unit of measurement as the original scores (square root of variance)

SD can be interpreted through the use of

normal distribution

SD=2 vs SD=25

lower SD means less variability

what is inferential statistics?

wide variety of group stats that attempt to say how likely it is that research findings are due to chance

meaning of alpha OR P value

less than 0.05= less than 1/20 chance that findings are due to chance

less than 0.01= less than 1/100 chance that findings are due to chance