22. Inferential Statistics Flashcards
What is statistical significance
- You can never be 100% certain that results arent all down to chance. So instead of ‘proving’ a hypothesis, you have to be content w finding out whether it’s likely to be true. This is called statistical significance.
- If your results are statistically significant, it means that you can read smth into them - theyre unlikely to be just down to chance.
- If your results are NOT statistically significant, it means they could have happened by chance rather than being the effect of changes in your IV, so you cant rlly read anything into them.
What are statistical tests used for
To find out if your results mean anything.
Method of statistical tests
- Write out your null hypothesis - this is the prediction you want to test. You assume that your null hypothesis is *true** for now, & that any hint of a significant difference between your groups is actually just by chance.
- Choose a significance level - this is a ‘level of proof’ that you’re looking for before you read anything into your results. The smaller the s.l, the stronger the evidence you’re looking for that your results aren’t just down to chance. A s.l is a probability, & so is a no. between 0 & 1 (probabilities near 1 means very likely, near 0 mean very unlikely). Significance levels are always very small - bc of this, events w probabilities smaller than the SL are very unlikely to happen.
- Turn all your experimental results into a single test statistic. You can then find out what the probability is that this test statistic, & therefore your results, were the result of a fluke (making your null hypothesis true after all).
- If the probability of your results being a fluke is less than the s.l, then you reject your null hypothesis (assume that the difference you’ve noticed between the groups was down to change in IV not chance), & assume your alternative hypothesis is true instead.
- If you reject your null hypothesis, you can say that your results are statistically significant.
- If you DONT reject the null, it means your results could have occurred by chance, rather than bc your null was wrong. If this happens, you’d proved nothing - not rejecting the null doesnt mean it must be true.
- Using a s.l of 0.05 (5%) is okay for most tests. If the probability of your results being down to chance is less than or equal to this (p≤0.05), then its prett good ev that your null wasn’t true after all. So the researchers can be at least 95% confident in their conclusion.
If a s.l of 0.01 (1%) is used, then you’re looking at really strong ev that the null wasn’t true. The researchers can be at least 99% confident.
2 types of potential error
Its possible to make errors when you’re deciding whether or not to reject the null hypothesis.
- Type I error
- Type II error
What is Type I error
- When you reject the null hypothesis when it was actually true.
- The s.l gives you the probability of this happening. Eg. a p=0.05 level means the probability that the null hypothesis is actually true is 5%.
- This is why s.l’s are small.
What is Type II error
- When you dont reject the null hypothesis when it was actually false.
- This can happen if your s.l is too small (eg. if you want very strong ev of the need to reject a null hypothesis & so use a 0.01 s.l).
- So you dont reject your null hypothesis, even if your alternative hypothesis was significant at p=0.05, then theres a 95% chance you’ll have made a Type II error.
How can Type I & Type II errors occur
- Choosing significance levels is a compromise - if the level you choose is TOO BIG, you risk making a Type I error.
- If the significance level you choose is TOO SMALL, you could make a Type II error.
When would a very small significance level (eg. 0.01) be used
A very small s.l is used when you need to be very confident in your results, like when testing new theories.
What are critical values
- Remember that you can never be 100% sure that a hypothesis is correct - it’s always possible that results are just due to chance.
- You use inferential tests to calculate what’s called an observed value. The observed value is then compared against a critical value, which is provided for each test in a critical value table. This indicates whether or not the results are significant.
- In some tests, if the observed value is more than or equal to the c.r, the results are considered to be significant. In others, the observed value must be equal to or less than the c.r to show significance.
What are inferential statistical tests used for
To help decide whether or not to reject the null hypothesis.
When is a one-tailed test used
- When the researcher has predicted an association & all has also stated which way the results will go (ie. a directional hypothesis, sa ‘the lower the mood, the higher the calorie consumption’.
When is a two-tailed test used
- When the researcher has produced an association, but hasn’t stated which way the results will go (ie. a non-directional hypothesis).
(The hypothesis in the eg (124) is non-directional, so its a two-tailed test)
How to use critical values table
1. Firstly, decide if its a one-tailed or two-tailed test.
2. The observed value is then looked up in a critical value table.
3. Read off the table.
4. Make a conclusion abt significance.
see pg124-125 for worked eg.
What determines which inferential test should be used
- Experimental design
- Research aims
- Level of measurement / type of data
What determines which inferential test should be used: Experimental design
- Research may have either related measures (if a repeated measures or matched participants design was used), or unrelated measures (if an independent measures design was used).
What determines which inferential test should be used: Research aims
Some inferential statistics test whether there is a significant difference between groups of scores:
- For eg, ‘did the P’s in group A have significantly higher average scores than those in group B?’
- This is what happens in an experiment. The IV is manipulated to see if it produces changes in the DV that are significantly different from the control condition.
Some inferential statistics test to see if there is a significant association between 2 (or more) variables:
- For eg, whether they occur tg more than would be expected by chance.
- This is what we look for in correlation studies - to see if 2 variables are positively or negatively associated, more than would be expected by chance factors alone. If they are, a significant correlation has been shown.
What determines which inferential test should be used: Level of measurement / type of data
Studies can collect different types of data, which affects how it can be analysed.
- Nominal data
- Ordinal data
- Interval data
What are the 3 levels of measurement
- Nominal data
- Ordinal data
- Interval data
What is Nominal data
- Thiis is the most basic level of measurement - a frequency count for completely distinct categories.
- For eg, in a study where a confederate pretends to need help, you could assign each passer-by to either an ‘altruistic’ category (if they helped) or a ‘non-altruistic’ category (if they’d did nothing).
What is Ordinal data
- All of the measurements relate to the same variable, & measurements can be placed in ascending or descending rank order.
- Eg. on a rating scale for aggression where 1=not aggressive & 10=extremely aggressive.
- But you cant say a person w a score of 10 is twice as aggressive as a person w score 5, just which one was more or less aggressive.
What is Interval data
- Measurements are taken on a scale where each unit is the same size.
- Eg. length in cm. Interval data places P’s along an objective, scientific scale. You then know exactly how far apart the scores are.
- Eg. in a race, P ‘F’ was quickest, in 15.8secs & P ‘B’ was 2nd, in 16.5secs.
- Technically, an absolute zero point is needed to make judgements abt whether one score is twice that of another. When we have this, (eg. 0secs, 0cm), then we call it a ratio scale.
