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A2 ~ Research methods STATISTICS AND DESCRIPTIVE STATS

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Today… Explore reasons as to why we might use statistics Identify measures of central tendency Identify measures of dispersion Recap the different types of data used in psychological research methods

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Task The 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!

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Question one What is the word for the number twelve? A) Триста B) Двенадцать C) Десять D) восемь

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Question two What is the word for the number six? A) Девятнадцать B) Пятнадцать C) Триста D) Шесть E) семь

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Question three What is the word for the number two? A) тринадцать B) сто C) два D) шестьсот E) девяносто

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Question four What is the word for the number four? A) восемнадцать B) шестьдесят C) четыре D) пятнадцать E) сто

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Question five What is the word for the number fifteen? A) пятнадцать B) пятьсот C) один D) одиннадцать

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Question six What is the word for the number ten? A) тридцать B) шесть тысяч C) десять D) восемнадцать E) сорок

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Answers 1=b. 2=d 3=c 4=c 5=a 6-c

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Scores How 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.

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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

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Measure of central tendency Gives a typical value for the data set Tells you where the middle of the data set is Measure of dispersion Indicates how the data are spread out Tells you what the rest of the data are doing DESCRIPTIVE STATISTICS

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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

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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

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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.

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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

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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.

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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

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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

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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

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LEVELS OF SIGNIFICANCE

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Probability: We 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

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Probability: Can 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

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Observed value: Every 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.

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Interpreting results: Usually 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

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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. /

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Test your understanding Answer the questions on probability using the handout

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Type 1 and type 2 errors: The 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

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Type 1 and type 2 errors Type 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

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Deciding on a statistical test You 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:

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DesignNominal Ordinal, interval, ratio Correlation/association Chi-square test of association Spearman's rank Independent measures Chi-squared test of independent samples Mann-Whitney Repeated Measures Sign Test Wilcoxons matched pairs What test to use?

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Test your understanding! Using 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

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Test your understanding! Using 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

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