Transcript Distributions

Unit 2 (F):
Statistics in
Psychological Research:
Measures of Central Tendency
Mr. Debes
A.P. Psychology
Statistics in Psychology

Statistics:
The collection, classification,
analysis, and interpretation of
numerical psychological data
 Descriptive Statistics:

 Describes
collected data
 Frequency Distribution:
Bar Graph
 Histogram

Statistics in Psychology

Types of Psychological Data:

Nominal:
 Categorical
 Non-numerical
 Bar graph


E.g. Favorite ice cream flavor
Ordinal:
 Ordered
 Non-numerical
 Bar graph

E.g. 1st place, 2nd place, 3rd place
Statistics in Psychology

Types of Psychological Data:

Interval:
 Equal
interval between points; no true zero point
 Numerical; can compute mean
 Histogram


E.g. Degrees in Fahrenheit
Ratio:
 Equal
interval between points; true
zero point
 Numerical; can compute mean
 Histogram

E.g. Height/weight
Statistics in Psychology
Statistics in Psychology


Inferential Statistics
Allow us to determine if results can be
generalized to a larger population.
Well reasoned inferences about the population in question
 Representative sample is very important
 Random sample-everyone in the target population has
an equal chance of being selected for the sample
 Sample size-the larger the sample size, the better, but
there are trade-offs in time & money when it comes to
sample size

Statistics in Psychology

Statistical Significance

How likely it is than an obtained result occurred by chance
A level of significance is selected prior to conducting statistical
analysis. Traditionally, either the 0.05 level (sometimes called
the 5% level) or the 0.01 level (1% level) is used. If the
probability is less than or equal to the significance level, then
the outcome is said to be statistically significant. The 0.01 level
is more conservative than the 0.05 level.

Measures of Central Tendency

Mean:
The arithmetic average of a distribution
 Obtained by adding all scores together, and dividing by the
number of scores


Median:
The middle score of a distribution
 Half of the scores are above it and half are below it


Mode:

The most frequently occurring score(s) in a distribution
Distributions

Distribution: the way scores are distributed
(spread out) around the mean score
Normal Distribution (normal curve/bell curve):
 Symmetrical, Bell-shaped distribution
 Mean, Median, Mode all are the same

Distributions

Skewed Distribution:
Positively skewed; “Skewed to the Right”-scores pull the
mean toward the higher end of the scores
 Negatively skewed; “Skewed to the Left”-scores pull the
mean toward the lower end of the scores

Distributions
Positively Skewed Distribution
Measures of Variation

Range:


The difference between the highest and lowest scores in a
distribution
Standard Deviation:

A computed measure of how much scores vary around the
mean
Measures of Variation

Calculating standard deviation:
For your set of data, calculate the mean.
 Subtract the mean from each item of data (half of your
outcomes will be negative). This is the DEVIATION of
each value from the mean.
 Square each deviation.
 Add all of the squares from step 3, and divide by the
number of items in the data set. This is the VARIANCE.
 Take the square root of the variance. This is the
STANDARD DEVIATION.

Measures of Variation
Data Set 1:
44, 45, 47, 48, 49, 51, 52, 53, 55, 56
1) Calculate mean:
500/10=50
2) Subtract mean from each data point:
-6, -5, -3, -2, -1, 1, 2, 3, 5, 6
(these are the individual deviations)
3) Square each individual deviation:
36, 25, 9, 4, 1, 1, 4, 9, 25, 36
4) Add all squares, then divide by items
in the data set:
150/10=15 (VARIANCE)
5) Find the square root of the variance:
3.87 (STANDARD DEVIATION)
Data Set 2:
2, 3 , 5, 7, 9, 17, 48, 49, 137, 223
1) Calculate mean:
500/10=50
2) Subtract mean from each data point:
-48, -47, -45, -43, -41, -33, -2, -1, 87, 173
(these are the individual deviations)
3) Square each individual deviation:
2304, 2209, 2025, 1849, 1681, 1089, 4,
1, 7569, 29929
4) Add all squares, then divide by items
in the data set:
48660/10=4866(VARIANCE)
5) Find the square root of the variance:
69.76 (STANDARD DEVIATION)
Measures of Variation

Usefulness of Standard deviation:
Standard deviation gives a better gauge of whether a set of
scores are packed closely together, or more widely
dispersed.
 The higher the standard deviation, the less similar the
scores are.
 In nature, large numbers of data often form a bell-shaped
distribution, called a “normal curve.”
 In a normal curve, most cases fall near the mean, and fewer
cases fall near the extremes

Normal Distribution
Z-scores

A z-score is the number of standard deviations a
score is from the mean





If a Z-Score:
Has a value of 0, it is equal to the group mean.
Is equal to +1, it is 1 Standard Deviation above the mean.
Is equal to -2, it is 2 Standard Deviations below the mean.
Z-Scores can help us understand:



How typical a particular score is within bunch of scores.
If data are normally distributed, approximately 95% of the data
should have Z-score between -2 and +2.
Z-scores that do not fall within this range may be less typical of the
data in a bunch of scores.
Measures of Variation
Homework





Explain the difference between the following types of
data: Nominal, Ordinal, Interval, Ratio
What is a normal distribution?
What is the difference between a positively and
negatively-skewed distribution?
Explain the difference between the measures of
variation: Range & Standard Deviation
What is a Z-score? How is it computed?