Rm psych stats & graphs

Lesson 6:

Research Methods
in Psychology
Stats and Graphs

Friday, 6 April 2012

Lesson 5
EXAM QUESTION

Taken from VCAA 2011 Mid Year Exam

Lesson 6: Statistics
OBJECTIVES

* Define descriptive statistics
* Define inferential statistics
* Describe the types of statistics in Psychology:
- calculate measures of central tendency including mean,
median and mode
-interpret p-values and draw conclusions based on, reliability
including internal consistency; validity including construct and
external
-evaluate research in terms of generalizing the findings to
the population


Why research?
The sole purpose for research is to be able to
generalise results to the population.

We research areas for two types of results: cause &
effect, and correlations.

Cause and effect studies aim to ﬁnd what causes
something e.g. smoking causes lung cancer

Correlational studies aim to ﬁnd relationships between
two factors, e.g. as the population of smokers
increases so to does the diagnosis of lung cancer.

It is much easier to determine correlational results
than causative.

Generalising Results
To be able to generalise results, the following criteria
must be met:

The results show statistical signiﬁcance (p<0.05)

All sampling procedures were appropriate

All experimental procedures were appropriate

All measures were valid

All possible confounding variables were controlled.


Types of Statistics

In psychology there are two types of
statistics

1) Descriptive Statistics, show results

2) Inferential Statistics, explains results in
relation to hypotheses.


Descriptive Statistics

Includes the following:

1) Organising raw data into clear tables

2) Representing the data in graphs

3) Measures of Central Tendency

4) Measures of Variability


1)Organising Raw Data
Frequency tables are the most common form of organising raw
data.

For example, Julie rolled a die 80 times and recorded the number
shown on each throw: 1, 3, 6, 5, 2, 1, 6, 1, 5, 2, 1, 2, 5, 4, 3, 6, 5,
2, 3, 4, 1, 4, 3, 2, 5, 1, 6, 2, 3, 1, 5, 5, 2, 3, 5, 4, 1, 3, 5, 3, 6, 3, 1,
6, 6, 3, 3, 4, 3, 3, 6, 3, 1, 3, 4, 6, 2, 4, 6, 3, 4, 5, 4, 6, 2, 3, 4, 5, 5,
4, 2, 1, 5, 4, 5, 6, 1, 6, 2, 5. - This is raw data.

To organise the data, a frequency
table can be used. Here the
amount of times the number was
rolled (frequency) is listed beside
the dice number. In frequency
tables we also include the
percentage of that frequency.


Calculating the
percentage

Number of times score occurs DIVIDED BY
Total number of scores in data set
MULTIPLIED BY 100

E.G. The percentage of rolling a 6 would be:

13/80 = 0.1625 x 100 = 16.25%


2) Representing the data

Histogram

Frequency
Polygon

Pie Chart


The normal distribution
“Bell Curve”
When one variable is continuous (meaning that it can have any
value within a certain range) such as age in months or IQ, we
can express the data as a line graph.

For example, a teacher sets a group classwork activity and wants
to ﬁnd out the group size that is most efﬁcient.


When data is presented in a line graph, psychologists
hope that it forms a normal curve.

This enables statistical procedures to be applied
without further manipulation of the data.


3) Measures of Central Tendency
(Measures in the Bell Curve)
Tells us how the data are clustered near the central
point of the dataset.

There are three measures of central tendency
1) Mean - average of all the scores (calculated by
adding up all the scores and dividing that total by the
number of scores)
2) Median - the score that occurs exactly halfway
between the lowest and the highest score.
3) Mode - the most commonly occurring score in the
dataset.


4) Measures of Variability

Opposite to measures of central tendency, measures of
variability tell us about how scores are spread out.

Three measures are used in measuring variability.

1) Range: Difference between the highest score and
lowest score, E.G. 130 - 88 = 42

2) Variance: Provides a measure of how much, on
average, each score differs from the mean.

3) Standard Deviation: Representation of the variance.


Calculating Variance and Standard Deviation
Because some scores are higher and others are lower than the mean, if we were
to simply average the differences , the negatives and positives would even out
leading to an incorrect calculation.

To overcome this, we square the differences, so that all ﬁgures are positive.
(Remember two negatives equal a positive!)

Mean: 110 The mean variance can
be calculated by adding
A score of 88: all the variances
110-88 = 22 so a together and dividing by
score of 88 is 22 the total number of
below the mean scores.
therefore -22
484+256+121+64+25+1+1+1+81+22
5+225+400
A score of 119: DIVIDED BY
119-110 = 9 so a 12
EQUALS
score of 119 is 19 157
over the mean
therefore +9 So the mean variance is 157.


Standard Deviation
Because the variance is a squared number, it makes it
difﬁcult to compare results.

This is why we use standard deviation (SD).

The standard deviation puts the variance into a form
that is useful in data analyse.

To calculate the SD you take the square root of the
mean variance. E.G. Square root of 157 = 12.5

Only get the SD for the mean variance! All the other
variances still along the normal curve as SD from the
mean.

Skewness


Inferential Statistics
Inferential Statistics are used once the descriptive
statistics have identiﬁed there is a difference
(variation) from the mean.

What next is to determine if this difference or
variance is signiﬁcant, or is it just due to chance.

Inferential tests give a probability that the difference
is caused by chance.

This is expressed as a p value.

Generally the lower the p value the better, however
p<0.05 (that is 5 times in 100 or 5% of the time it is
due to chance) is widely accepted.

p = 0.03 means there are 3 chances in 100 (3%)
that this difference would be achieved by chance
alone.

If the level of significance is p<0.05 then these
results can be said to be statistically significant as it
is less then (<) 0.05

If the p value = 0.3 then the results are not
significant as 0.3 is greater then 0.05.


Complete ‘INVESTIGATE 1.6’ p 24 of textbook


Measures of relationship
Correlational studies intend to establish the strength
and direction of any relationship between two
variables.

Correlation: A statistical measure of how much two
variables are related.

Positive Correlation: Where the two variables change in
the same direction. As one increases so to does the
other.

Negative Correlation: Where the two variables change
in the opposite direction. As one increases the other
decreases.

Strength in correlation
The strength of a correlation can be calculated using
the correlation coefficient (r).

The (+) or (-) sign before the coefficient indicates if it
is a positive or negative correlation.

The number is the coefficient, the higher the number
the stronger the relationship.


Scatter Plots


Determine the strength (strong or weak) and
direction (positive or negative) of the following
correlations:
r=- 0.74
r=+ 1.00
r=+ 0.23
r=- 0.15


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