    Chapter 5: Analysing the Data Part II : Inferential Statistics # Confidence intervals

Interval estimation is used when we wish to be fairly certain that the true population value is contained within that interval. When we attach a probability statement to an estimated interval, we obtain a confidence interval.

Confidence is defined as 1 - (1 minus the significance level). Thus, when we construct a 95% confidence interval, we are saying that we are 95% certain that the true population mean is covered by the interval - consequently, of course, we have a 5% chance of being wrong. Any statistic that can be evaluated in a test of significance ("hypothesis testing") can be used in constructing a confidence interval. Always, when constructing a confidence interval, two limits, "Upper" and "Lower", are computed. For each limit, the information needed is the computed statistic (e.g., ), the two-tailed critical values (e.g., t /2), and the standard error for the statistic (e.g., S.E.M.).

The upper and lower boundaries for the confidence interval for the t-statistic given above are:

Lower Limit = - t /2 Upper Limit = + t /2 In Psychology we are not often concerned with estimating the actual value of a population parameter, hence confidence intervals are not very common. Actual values are more common in agriculture say where you want to establish, with a certain degree of confidence, whether 6 bags to the hectare are needed, or 10.7 grams of protein per day, or, in public surveys and opinion polls. where findings are often reported as say: "46% ± 2% are in favour of the government". In research psychology we are mostly concerned with whether two groups are significantly different, or whether there is a significant relationship between two variables and not so much the actual value of the difference or relationship. Hence in this unit we exclusively follow the hypothesis testing aspect of inferential statistics.

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