Inferential Statistics And Testing For Differences at University Of Manchester | Flashcards & Summaries

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What are inferential statistics?
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- Used to make inferences from our data to more general conditions 
- they allow us to make probabilistic statements about the truth of hypotheses
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What is hypothesis testing? 
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- a technique for using data to validate or invalidate a claim about a population
- you set your research questions first then hypothesis for this 
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What are the 5 key steps to hypothesis testing?

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1. State statistical hypotheses
2. Set significance level
3. Calculate test statistic
4. Evaluate the statistic
5. Interpret your results 
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What two statements does state statistical hypotheses have?
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They have two opposing statements about a population characteristic:
- null hypothesis 
- alternative (research) hypothesis 
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What is Null Hypothesis? 
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- research question is written as a statement that can be rejected 
- looking for the relationship between the data
- usually expressed in the form “there is no significant difference“ or “there is no relationship between“

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What is the Alternative (research) Hypothesis? 
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- if the null hypotheses is rejected by the statistical test used then it is logical to favour the alternative hypothesis 
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An example of a statistical hypotheses:

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RQ- ‘to what extent is the precipitation in areas over 500m in altitude different to the precipitation in areas below 500m in altitude?’
Null: there is o significant difference in precipitation between areas above and below 500m altitude
Alternative: there is a significant difference in precipitation between areas above and below 500m altitude 
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3. How to calculate test statistic?
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- each inferential statistical test involves the calculation of a single value called the test statistic 
- examples include: t, R, F and Z values 
- gives an indication of the strength of the pattern observed in the data
- enables the significance of the result to be calculated
- (more likely to be significant)
- once you have statistic you might have to do another test to see if the test is significant or not 
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4. How to evaluate the statistic: automatically using SPSS
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- it will calculate significance value for you 
- to be significant, the resultant sig value should be smaller than the sig value you have set.
- i.e. If you have set the sig level at 0.05, and the software gave you a sig value of 0.3, this would be significant at the chosen level 
- we are usually looking for sig values <0.05 (lower)
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5. How to interpret results 
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- if the result is significant, we would “Reject null in favour of alternative”
   - rejecting the null suggests that the alternative hypothesis may be true

- if the result is not significant: “do not reject null“
   - “do not reject the null” does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence against null in favour of alternative 

- the final conclusion is always given in terms of the null hypothesis
   - we always conclude “reject alternative” or even “accept alternative“
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what test do you carry out if the variances of the two datastes are equal?
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Levene’s test for Homogeneity of Variances 
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What does the data show in SPSS?
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- you will get the test statistic (F) and a sig value 
- if you get low sig. value > low probability the differences have occurred by chance > the groups have unequal variances
- if the sig value is large > high probability the differences have occurred by chance > the groups have equal variances
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Q:
What are inferential statistics?
A:
- Used to make inferences from our data to more general conditions 
- they allow us to make probabilistic statements about the truth of hypotheses
Q:
What is hypothesis testing? 
A:
- a technique for using data to validate or invalidate a claim about a population
- you set your research questions first then hypothesis for this 
Q:
What are the 5 key steps to hypothesis testing?

A:
1. State statistical hypotheses
2. Set significance level
3. Calculate test statistic
4. Evaluate the statistic
5. Interpret your results 
Q:
What two statements does state statistical hypotheses have?
A:
They have two opposing statements about a population characteristic:
- null hypothesis 
- alternative (research) hypothesis 
Q:
What is Null Hypothesis? 
A:
- research question is written as a statement that can be rejected 
- looking for the relationship between the data
- usually expressed in the form “there is no significant difference“ or “there is no relationship between“

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Q:
What is the Alternative (research) Hypothesis? 
A:
- if the null hypotheses is rejected by the statistical test used then it is logical to favour the alternative hypothesis 
Q:
An example of a statistical hypotheses:

A:
RQ- ‘to what extent is the precipitation in areas over 500m in altitude different to the precipitation in areas below 500m in altitude?’
Null: there is o significant difference in precipitation between areas above and below 500m altitude
Alternative: there is a significant difference in precipitation between areas above and below 500m altitude 
Q:
3. How to calculate test statistic?
A:
- each inferential statistical test involves the calculation of a single value called the test statistic 
- examples include: t, R, F and Z values 
- gives an indication of the strength of the pattern observed in the data
- enables the significance of the result to be calculated
- (more likely to be significant)
- once you have statistic you might have to do another test to see if the test is significant or not 
Q:
4. How to evaluate the statistic: automatically using SPSS
A:
- it will calculate significance value for you 
- to be significant, the resultant sig value should be smaller than the sig value you have set.
- i.e. If you have set the sig level at 0.05, and the software gave you a sig value of 0.3, this would be significant at the chosen level 
- we are usually looking for sig values <0.05 (lower)
Q:
5. How to interpret results 
A:
- if the result is significant, we would “Reject null in favour of alternative”
   - rejecting the null suggests that the alternative hypothesis may be true

- if the result is not significant: “do not reject null“
   - “do not reject the null” does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence against null in favour of alternative 

- the final conclusion is always given in terms of the null hypothesis
   - we always conclude “reject alternative” or even “accept alternative“
Q:
what test do you carry out if the variances of the two datastes are equal?
A:
Levene’s test for Homogeneity of Variances 
Q:
What does the data show in SPSS?
A:
- you will get the test statistic (F) and a sig value 
- if you get low sig. value > low probability the differences have occurred by chance > the groups have unequal variances
- if the sig value is large > high probability the differences have occurred by chance > the groups have equal variances
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