lecture 10 - p values

imperfect estimates

-samples can offer imperfect estimates of the characteristics of the population for two reasons:

1. sampling error

2. unsystematic variation

decision error

-if sample statistics do not match population parameters, researchers will make a decision error when making inferences about the population based on the results of a study

-specifically, the decision to either reject the null hypothesis or fail to reject the null hypothesis could be wrong

type 1 error

-occurs when a researcher finds an effect in a sample, when no effect exists in the population

-a researcher rejects the null hypothesis when the null hypothesis is actually true in the population

reasons for a type 1 error

-sampling error → effect is not present in the overall population, but the individuals in the population who do show the effect are overrepresented in the sample

-bias in participants responses to show the effect, which is produced by some aspects of the study e.g., demand characteristics

-effect occurred randomly/by chance and does not exist in the population

type 2 error

-a researcher finds no effect in a sample, when an effect does exist in the population

-a researcher fails to reject the null hypothesis, when the null hypothesis is actually not true in the population

reasons for type 2 error

-sampling error → effect is present in the overall population, but the individuals in the population who do not show the effect are over-represented in the sample

-unsystematic variation in participants’ responses is produced by some aspect of the study e.g., low internal validity

p value

-probability of finding an effect in a sample if there is no effect in the population

-probability of incorrectly finding an effect in a study

-probability of making a type 1 error

data analysis

-every test of the null hypothesis will have a p value to indicate the chance of having made a type 1 error

-p value range is 0 (certainly will not occur) to 1 (certainly will occur)

• p value can never be exactly 0 or 1 because we can never be 100 certain about our inferences

small p value

-low probability of having made a type 1 error

-low chance that we found an effect in our sample if there is no effect in the population

-this reject the null hypothesis when the p value is small

aim of null hypothesis testing

-to falsify the idea there is no effect in the population

-want the chance that there is no effect in the population to be as small as possible

-because then it is more likely that there is an effect in the population

null hypothesis testing

-compare the sample characteristics to the predicted population characteristics stated in the null hypothesis, with the aim to falsify/reject the null hypothesis

-impossible to explain/prove systematic variation

-but we can falsify/disprove unsystematic variation

process of null hypothesis testing

-assess the probability that you found the effect in your sample while there actually is no effect in the population

-p value the probability of finding an effect in the sample if there is no effect in the population

significant effect or not significant

-researchers have agreed if the probability is less than .05 (5%) then the significance is small enough to reject the null hypothesis in favour of the experimental hypothesis

-thus, we believe there is a significant effect in the population