PSYCH211-25A (week 7)

Inferential Statistics

Probability distributions

  • Discrete

  • Continuous

  • Probability distribution - a way to link a possible value of a variable with the probability of occurrence

  • Characteristics:

    • caqn be any shape

    • represented by curve

    • area under the curve represents the probability

    • total area under the curve is always 1

    • area under the curve between x values represents the probability of getting those x values

  • Example: Chi-Square

  • The higher the function (density) the more likely a value

  • area under the curve gives us probability

  • most concerned with normally distributed variables

    i.e - IQ scores

  • to aid both understanding and calculations, it is often good to standardise the variable in question

Standard normal distribution:

  • Standard normal distribution - a normal distribution with a mean of 0 and standard deviation of 1

  • ANY normal distribution of scores can be transformed into the standard normal distribution

  • when we do this, we call the new variable z-scores

  • z-scores - the number of standard deviations a value is away from the mean

Z-Scores:

  • give us a marker to calculate area under the curve

  • dont have to use the whole standard deviations

  • all we need is a shape to calculate the area

Inferential statisitcs:

  • inferential statistics - a set of statistical procedures to test hypotheses about a population

  • Sampling error - differences between a population parameter and sample statistic that is the result of the sampling procedures

  • sampling error is unknown in real life because we do not know the population parameter

Sampling distributions:

  • Sampling distribution - a distribution of a sample statistic (usually the mean) that would occur if we took an infinite number of samples from a population

  • governed by the central limit theorem

  • The SD of the sampling distribution of a mean is also known as the standard of error

  • Standard error - the average sampling error we can expect in our sample

Confidence interval:

  • confidence interval - an interval estimate of a population parameter from a sample statistic

  • relies on standard error

  • confidence level: 99%,95%,90%

  • interval - spread consisting of a lower limit and an upper limit

  • Upper bound: Mean +

  • Lower Bound: Mean -

NSHT:

  • NSHT - the process by which researchers determine if their data supports or fails to support their hypothesis

  • based on probability theory

  • Null hypothesis

    • a treatment has no effect

    • our variables are not related

    • our results come from the same population

  • Four steps in Hypothesis testing:

    1) State your hypothesis

    2) set the criterion for burden of proof (alpha level)

    3) Collect data and calculate stats

    4) make a decision about the null hypothesis according to the criterion in step 2

  • Two types of inferential errors

    • Type 1 error

    • Type 2 error