A2 ~ Research methods STATISTICS AND DESCRIPTIVE STATS

A2 ~ Research methods

STATISTICS AND DESCRIPTIVE STATS

Today…•E

xplore reasons as to why we might use statistics•I

dentify measures of central tendency•I

dentify measures of dispersion•R

ecap the different types of data used in psychological research methods

Task•T

he next 6 slides will ask you to choose the Russian word for a given number. It is multiple choice, if you don’t know the answer have an educated guess!

Question one•W

hat is the word for the number twelve?•A

) Триста•B

) Двенадцать•C

) Десять•D

) восемь

Question two•W

hat is the word for the number six?•A

) Девятнадцать•B

) Пятнадцать•C

) Триста•D

) Шесть•E

) семь

Question three•W

hat is the word for the number two?•A

) тринадцать•B

) сто•C

) два•D

) шестьсот•E

) девяносто

Question four•W

hat is the word for the number four?•A

) восемнадцать•B

) шестьдесят•C

) четыре•D

) пятнадцать•E

) сто

Question five•W

hat is the word for the number fifteen?•A

) пятнадцать•B

) пятьсот•C

) один•D

) одиннадцать

Question six•W

hat is the word for the number ten?•A

) тридцать•B

) шесть тысяч•C

) десять•D

) восемнадцать•E

) сорок

Answers•1

=b. •2

=d•3

=c•4

=c•5

=a•6

-c

Scores•H

ow did you do? What was your score out of six?

•If you got one or more right, but don’t speak Russian why do you think this is???

•The answer is chance. It was chance that you picked the right word and not your knowledge of Russian.

What has this got to do with statistics????

•The reason we use statistical tests in Psychology is because a statistical test calculates the percentage the results could be down to chance and allows us to see if we have found something above chance

•Did the IV really effect the DV or were the findings a fluke?!

•The more significant a finding is the more effect the IV had on the DV

•The normal percentage we allow for in psychology is initially 5%, meaning 5% of the time the findings are down to chance

Measure of central tendencyGives a typical value for the data set

Tells you where the middle of the data set is

Measure of dispersionIndicates how the data are spread out

Tells you what the rest of the data are doing

DESCRIPTIVE STATISTICS

Descriptive Statistics

•The aim of descriptive statistics is to give an accurate summary of the data

•The wrong choice of statistic gives a distorted picture of the data

•This can lead to the wrong conclusions being drawn from the data

•Each measure of CT and D has its advantages and disadvantages

Measures of Central Tendency

•The mean• Adv: it uses all the values in the set, so is most sensitive to

variations in the data• Dis: it can be artificially raised or lowered by an extreme

value, or by skewed data

•Use it when the data are normally distributed, unskewed and there are no outliers

Measures of Central Tendency

•The median• Adv: it is based on the order of the data, not their actual

values, so not distorted by extreme values• Dis: however, this makes it less sensitive to variations in

the data

•Use it when you can’t use the mean because of skew, outliers etc.

Measures of Central Tendency

•The mode• Adv: it’s the only measure suitable for summarising

category/frequency data• Dis: for many data sets there is no modal value, or their

may be several

•Use when dealing with frequency data, and/or where there is a clear modal value in the set

Standard Deviation

•Standard deviation (SD) is a statistical measure of the amount the results vary from the mean.

•There are 2 formulas that can be used to work out the standard deviation:

•Formula 1

•Formula 2:

S= √∑d²

n

S= √∑d² n-1

Formula 1 is used to calculate the SD where the whole population has been used.

Formula 2 is used to calculate the SD where part the population has been used. This is the formula used most often.

TYPES OF DATA(LEVELS OF MEASUREMENT)

•Nominal Data (counting)• There are 4 men and 5 women in the room• 64% of people believe in capital punishment, 36% disagree

•Categories are mutually exclusive – there is no overlap

TYPES OF DATA

•Ordinal Data (Ordering)• Results of many sporting events are given in the form of

ordinal data (sometimes called ranked data) e.g. horse races – you don’t know the actual finish times of the horses, just the order they finished

TYPES OF DATA

•Interval and Ratio Data (Measuring)• Interval data is defined as data measured on an instrument

that has equal intervals e.g. temperature

• Ratio data is like interval data but the scale has a meaningful value of zero e.g. length and time

LEVELS OF SIGNIFICANCE

Probability:•W

e need to use inferential statistics to tell us if the result that we have found is due to chance or not.

•To establish if our results are reliable we have to look at the probability of a result being due to chance or not.

•The minimum accepted level of probability commonly used in psychology is 5%, this is represented as 0.05.

•If the level of significance achieved from a test is equal to or less 0.05 than the results are said to be significant.

•This would mean that we are 95% sure that the IV caused the change in the DV

Probability:•C

an be expressed as:• A proportion: a 1 in 5 chance.• As a percentage: 20%• More commonly expressed as a decimal in psychology: 0.2.

•In psychology: 10%=0.10, 5%=0.05, 1%=0.01 and 0.1%=0.001

•To go from % to decimal % by 100, move decimal place 2 spaces to the right.

•Remember the more stringent (lower) the level of significance the more significant the results are

Observed value:•E

very time you perform a statistical test you get an OBSERVED VALUE.

•This observed value tells you the extent to which your results are valid, you then have to compare this observed value to a table of CRITICAL VALUES to see of your results are significant or not.

•To be significant the observed value should be greater than the critical value

•Note that there will be a different table of values for different statistical tests.

Interpreting results:•U

sually in psychology if a critical value is BELOW 0.5 we would accept the experimental hypothesis and reject the null

•If below P<0.05 the results are significant- would accept the experimental hypothesis (in general)

•This means that the probability of the result being due to chance is 5% or below

Interpreting results:•P

is used to represent “the probability that is due to chance”•>

n=means greater than•<

n=means less than•>

/ means greater then or equal to.•/

<means less than or equal to.•

SO………………•P

<0.05 means that the probability that the result is due to chance is less than 5%.

Test your understanding•A

nswer the questions on probability using the handout

Type 1 and type 2 errors:•T

he 5% level of significance has been accepted as it represents a reasonable balance between the chances of making a type 1 or type 2 error

•These can occur because:• Badly designed• Level of probability accepted is too lenient (too high) or too

stringent

Type 1 and type 2 errors•T

ype 1 error:• Occurs when we conclude that

there IS a significant difference when there is NOT

• This can happen if the accepted level of probability is set TOO LENIENT

•Type 2 error:• Occurs when we reject the

experimental hypothesis and accept the null when there IS a difference

• This can happen if the probability level is TOO STRINGENT

Deciding on a statistical test•Y

ou must decide the following:• Are you trying to find out if your samples are related

(correlate) or different?• What design you have used- related, non related, matched

pairs• What level of measurement you have used.

• You can use the following table to help decide:

DesignDesign NominalNominal Ordinal, Ordinal, interval, ratiointerval, ratio

Correlation/Correlation/

associationassociationChi-square Chi-square test of test of associationassociation

Spearman's Spearman's rankrank

Independent Independent measuresmeasures

Chi-squared Chi-squared test of test of independent independent samplessamples

Mann-Mann-WhitneyWhitney

Repeated Repeated MeasuresMeasures

Sign TestSign Test Wilcoxons Wilcoxons matched pairsmatched pairs

What test to use?

Test your understanding!•U

sing your newly found knowledge identify the test that would be suitable for the following: • An experiment with nominal data and an independent groups

design• Ordinal data on both measures in a study to see if two measures

are associated• An experiment with and independent groups design in which the

DV is measured on a ratio scale• A study using a correlational technique in which one measure is

ordinal and the other is ratio. • A study testing an association using a nominal level of

measurement• An experiment in which all participants were tested with alcohol

and without alcohol on a memory test• An experiment in which reaction time was tested using an

independent subject design

Test your understanding!•U

sing your newly found knowledge identify the test that would be suitable for the following: • An experiment with nominal data and an independent groups

design-chi-squared test • Ordinal data on both measures in a study to see if two measures

are associated-Spearman’s rank correlation• An experiment with and independent groups design in which the

DV is measured on a ratio scale –Mann-Whitney• A study using a correlation technique in which one measure is

ordinal and the other is ratio. –Spearman’s rank• A study testing an association using a nominal level of

measurement-Chi-Square test of association• An experiment in which all participants were tested with alcohol

and without alcohol on a memory test- Wilcoxon’s• An experiment in which reaction time was tested using an

independent subject design- Mann-Whitney