Research Methods in Psychology PSY 311 Week 3: Means, standard deviations & distributions Dr Sabahat Çiğdem Bağcı

Hypotheses Statements about the objective world around us Men earn more than women Women are more intelligent than men As study hours increases, exam grades will get better... Null hypothesis(H0) vs Alternative hypothesis(H1) (H0): Men do NOT earn more than women (men and women earn equally) (H1): Men earn more than women (men and women earn differentially)

Statistical significance Psychological research – subject to probabilities You cannot ‘prove’ something, you need to have some probabilities a p-value of 0.05 or below indicates that a finding is significant (i.e. it is the threshold)

p value p value < .05 – the likelihood that you found a relationship or difference (as you initially observed) by random chance is smaller than .05%. So you can be (at least) 95% sure that what you found is not because of random chance.

Type I – Type II errors

Session Overview Central tendency measures Means, SD, and distributions

Central tendency measures For continious data Mean Median Mode Range For categorical data Frequencies

Means A measure of ‘central tendency’; the average = the arithmetic mean A way of describing a sample of continuous data Add values of each participant and divide by the sample size

Data Window: Data View

Median Median is the value that cut your sample in half If you have a sample of 9 participants, you rank your values and the value of the 5th person – the median 1,1,2,3,4,5,5,6,7 => Median = 4 If you have a sample of 10 participants, you rank values and the average value of 5th and 6th persons 1,1,2,3,4,5,5,6,7,8 => Median = 4.5

Mode Simply the most frequent value in your data set 1,1,2,3,4,5,5,6,7

Range Range = the highest value – the lowest value 1,1,2,3,4,5,5,6,7

Exercise Find mean, mode, median and range for these values 13, 18, 13, 14, 13, 16, 14, 21, 13

Standard Deviation (SD) A measure of dispersion or spread of data from the mean When values clustered around mean, SD is low When values spread away from mean, SD is high There is no such thing as a ‘good’ standard deviation

Standard deviation example Dataset 1: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5 Dataset 2: 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5 Which dataset has the lower SD?

Normal Distribution

A Normal Distribution

Characteristics of a Normal Distribution The distribution is bell-shaped The curve is symmetrical around a single mid-point at which the mode, median and mean are equal to each other

Normal Distribution & Std Deviation

Research Methods in Psychology PSY 311 Week 3: Means, standard deviations & distributions Dr Sabahat Çiğdem Bağcı

Normal Distribution & Std Deviation

Sample Size & Normal Distributions The higher the sample size, the more the distribution gets closer to normal distribution

From Samples to Population Why increasing sample size affects the distribution? Population distribution Sample 2 Sample 1 Sample 3 Sample 4 Population mean

Sampling Distributions If you sampled a number of people from a population you could obtain sample statistics e.g. the sample mean (e.g. Mean IQ) If you collected this mean for a number of different samples from the same population and plotted the means, you have a “sampling distribution of the means” The more samples you obtained, the closer the mean of these sample means would be to the population mean If you collected so many samples that you covered all people in the population, the mean of these samples would be the same as the population

Standard Error of the mean A measure of dispersion (SD) of the sampling distribution of the a statistic (e.g. the mean) The greater the standard error, the less precision of a sample statistic (i.e. how accurately any one sample represents the population) Sample mean Standard deviation Sampling distribution of the means Standard error

Non-normal Distributions -Skewness Negative Skew Positive Skew Most people gave higher ratings, e.g. Self-esteem Most people gave lower ratings, e.g. Aggression

Non-normal Distributions - Kurtosis Leptokurtic Platykurtic Most people gave similar ratings around the mean, low SD Most people gave many different ratings than the mean, high SD

Skewness Skewness > 0 - Right skewed distribution - most values are concentrated on left of the mean, with extreme values to the right. Skewness < 0 - Left skewed distribution - most values are concentrated on the right of the mean, with extreme values to the left. Skewness = 0 - mean = median, the distribution is symmetrical around the mean.

Kurtosis Kurtosis > 3 - Leptokurtic distribution, sharper than a normal distribution, with values concentrated around the mean. Kurtosis < 3 - Platykurtic distribution, flatter than a normal distribution with a wider peak. The values are wider spread around the mean. Kurtosis = 3 - Mesokurtic distribution - normal distribution for example.

SPSS Analysis Everything works through the ‘Analyze’ menu

Descriptive Statistics For counts and percentages Analyse – Descriptive Statistics – Frequencies For means, modes, medians and standard deviations Analyse – Descriptive Statistics - Descriptives

Frequencies

Frequencies Output

Descriptives

Descriptives Output

Producing Graphs/Charts

Checking for normality