rm psych stats & graphs

Research Methodsin Psychology

Stats and Graphs

Lesson 6:

Friday, 6 April 2012

Lesson 5EXAM QUESTION

Taken from VCAA 2011 Mid Year ExamFriday, 6 April 2012

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Lesson 6: StatisticsOBJECTIVES

* 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.


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.

3) Measures of Central Tendency(Measures in the Bell Curve)


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 DeviationBecause 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

A score of 88: 110-88 = 22 so a score of 88 is 22 below the mean therefore -22

A score of 119: 119-110 = 9 so a score of 119 is 19 over the mean therefore +9

The mean variance can be calculated by adding

all the variances together and dividing by

the total number of scores.

484+256+121+64+25+1+1+1+81+225+225+400 DIVIDED BY

12EQUALS

157

So the mean variance is 157.


Standard DeviationBecause 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 StatisticsInferential 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 relationshipCorrelational 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 correlationThe 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 = - 0.74r = + 1.00r = + 0.23r = - 0.15


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